Merge branch 'circ_polarizations'

14 files changed, 1979 insertions, 0 deletions

diff --git a/xmds2/realistic_Rb_and_fields/Makefile b/xmds2/realistic_Rb_and_fields/Makefile
new file mode 100644
index 0000000..bc7cf13
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/Makefile
@@ -0,0 +1,84 @@
+###  -*- make -*-
+### This file is part of the Debian xmds package
+### Copyright (C) 2006 Rafael Laboissiere
+### This file is released under the GNU General Public License
+### NO WARRANTIES!
+
+INSTALL = install --mode=664 -D 
+
+### This makefile can be used to build and run the XMDS examples
+
+XMDS_FILES = $(shell ls *.xmds)
+RUN_FILES = $(patsubst %.xmds,%.run,$(XMDS_FILES))
+CC_FILES = $(patsubst %.xmds,%.cc,$(XMDS_FILES))
+XSIL_FILES = $(patsubst %.xmds,%.xsil,$(XMDS_FILES))
+M_FILES = $(patsubst %.xmds,%.m,$(XMDS_FILES))
+
+test_dir = tests
+test_result_dir = $(test_dir)/testsuite_results
+XMDS_INCLUDES_misc  = RbChosenRho.txt RbInits.cdata RbEquations.cdata \
+		      RbAtomConstants.cdata RbPropEquations.cdata
+XMDS_INCLUDES_xmds_in_target_dir = $(XMDS_INCLUDES_misc:%=$(test_dir)/%)
+XMDS_INCLUDES_cdata_in_target_dir = $(XMDS_INCLUDES_misc:%=$(test_result_dir)/%)
+
+MATHEMATICA_DIR = ../../mathemathica_fwm
+
+XMDS = xmds2
+XSIL2GRAPHICS = xsil2graphics
+
+all: $(RUN_FILES) 
+
+%.run: %.xmds
+	$(XMDS) $<
+	mv $(patsubst %.xmds,%,$<) $@
+
+%.xsil: %.run
+	./$<  --E1o=0 --E3o=0
+
+%.m: %.xsil
+	$(XSIL2GRAPHICS) $<
+
+plot: $(M_FILES)
+	octave pp.m
+
+clean:
+	rm -f $(CC_FILES) $(RUN_FILES) $(M_FILES) $(XSIL_FILES) *.wisdom.fftw3 *.dat octave-core *.wisdom *.pdf 
+	rm -f $(png_targets)
+	rm -f $(eps_targets)
+
+eps_targets  = $(wildcard *.eps)
+pdf_targets  = $(eps_targets:%.eps=%.pdf)	
+png_targets  = $(pdf_targets:%.pdf=%.png)
+
+png: pdf $(png_targets) 
+
+$(png_targets): %.png : %.pdf
+	convert -density 300 $< $@
+
+pdf: $(pdf_targets) 
+
+$(XMDS_INCLUDES_cdata_in_target_dir): $(test_result_dir)/% : %
+	$(INSTALL) $< $@
+
+$(XMDS_INCLUDES_xmds_in_target_dir): $(test_dir)/% : %
+	$(INSTALL) $< $@
+
+test: $(XMDS_INCLUDES_cdata_in_target_dir) $(XMDS_INCLUDES_xmds_in_target_dir)
+	$(INSTALL) $(XMDS_FILES) tests/testsuite/
+	cd tests; ./run_tests.py
+
+test_from_scratch:
+	rm -r tests/testsuite_results
+
+$(XMDS_INCLUDES_misc): %: $(MATHEMATICA_DIR)/%
+	cp $< $@
+
+copy_mathematica_generated_files: $(XMDS_INCLUDES_misc)
+
+$(pdf_targets): %.pdf : %.eps
+	cat $< | ps2eps -B > __tt.eps
+	epspdf __tt.eps $@
+	rm -f __tt.eps
+	#ps2eps -B $< | epspdf $< $@
+.PRECIOUS: %.run %.xsil %.m
+.PHONY: all clean
diff --git a/xmds2/realistic_Rb_and_fields/Makefile.fig b/xmds2/realistic_Rb_and_fields/Makefile.fig
new file mode 100644
index 0000000..71fba31
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/Makefile.fig
@@ -0,0 +1,39 @@
+###  -*- make -*-
+### This makefile can be used to build and run the XMDS examples
+
+GNUPLOT_FILES = $(wildcard *.gp)
+
+SCRIPTS_DIR = .
+
+
+eps_targets  = $(wildcard *.eps)
+eps_bb_targets  =  $(eps_targets:%.eps=%.bb)
+pdf_targets  = $(eps_targets:%.eps=%.pdf)	
+png_targets  = $(pdf_targets:%.pdf=%.png)
+
+fig: png
+
+pdf: $(pdf_targets) 
+
+# fix bounding box
+$(eps_bb_targets): %.bb : %.eps
+	@cat $< | ps2eps -q -B > $@
+
+$(pdf_targets): %.pdf : %.bb
+	epspdf $< $@
+
+png: $(png_targets) 
+
+$(png_targets): %.png : %.pdf
+	convert -density 300 $< $@
+
+clean:
+	rm -f *.pdf
+	rm -f *.eps
+	rm -f *.bb
+
+real_clean: clean
+	rm -f *.png
+
+.PRECIOUS: %.run %.xsil %.m
+.PHONY: all clean
diff --git a/xmds2/realistic_Rb_and_fields/Makefile.par b/xmds2/realistic_Rb_and_fields/Makefile.par
new file mode 100644
index 0000000..5fddce1
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/Makefile.par
@@ -0,0 +1,41 @@
+###  -*- make -*-
+### This file is part of the Debian xmds package
+### Copyright (C) 2006 Rafael Laboissiere
+### This file is relased under the GNU General Public License
+### NO WARRANTIES!
+
+### This makefile can be used to build and run the XMDS examples
+
+
+XMDS_FILES = $(wildcard *.xmds)
+BASE_NAME = $(patsubst %.xmds,%,$(XMDS_FILES))
+RUN_FILES = $(patsubst %.xmds,%.run,$(XMDS_FILES))
+XSIL_FILES = $(patsubst %.xmds,%.xsil,$(XMDS_FILES))
+PARAMS_FILES = $(wildcard *.params)
+PP_DIR = $(PARAMS_FILES:%.params=%)
+CALC_XSIL_FILES = $(PARAMS_FILES:%.params=%/$(BASE_NAME).xsil)
+
+default: $(CALC_XSIL_FILES) 
+
+$(CALC_XSIL_FILES): %/$(BASE_NAME).xsil : %  %.params  
+	echo processing $$(dirname $(@)) dir
+	$(MAKE) -C $$(dirname $(@)) \
+		-f ../Makefile.pp \
+		SCRIPTS_DIR=../ \
+		PARAMS_FILE=../$<.params \
+		XSIL_FILES=$(XSIL_FILES) \
+		RUN_FILES=$(RUN_FILES)
+
+$(PP_DIR): % : %.params
+	echo need to make dir
+	[ -d $@ ] ||  mkdir -p  $@
+
+clean:
+	for d in $(PP_DIR); \
+	do $(MAKE) -C $$d SCRIPTS_DIR=../ -f ../Makefile.pp $@; done
+
+real_clean:
+	for d in $(PP_DIR); \
+	do $(MAKE) -C $$d SCRIPTS_DIR=../ -f ../Makefile.pp $@; done
+
+.PHONY: all clean
diff --git a/xmds2/realistic_Rb_and_fields/Makefile.pp b/xmds2/realistic_Rb_and_fields/Makefile.pp
new file mode 100644
index 0000000..e24107e
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/Makefile.pp
@@ -0,0 +1,47 @@
+###  -*- make -*-
+### This makefile can be used to build and run the XMDS examples
+
+
+GNUPLOT_FILES = $(wildcard *.gp)
+XSIL_FILES = $(wildcard *.xsil)
+RUN_FILES = $(patsubst %.xsil,%.run,$(XSIL_FILES))
+M_FILES = $(patsubst %.xsil,%.m,$(XSIL_FILES))
+
+SCRIPTS_DIR = ..
+
+XSIL2GRAPHICS = xsil2graphics
+
+include $(PARAMS_FILE)
+
+all: $(XSIL_FILES)  $(M_FILES) plot fig
+
+$(XSIL_FILES): ../$(RUN_FILES) $(PARAMS_FILE)
+	$< $(PARAMS) | grep "Time elapsed for simulation is:" > exact_analysis_execution_time.txt
+
+%.m: %.xsil
+	$(XSIL2GRAPHICS) $<
+
+fig: pp_I2.stamp
+	$(MAKE) -f $(SCRIPTS_DIR)/Makefile.fig $@
+
+
+pretty_plots: pp_I2.stamp $(GNUPLOT_FILES)
+	gnuplot $(SCRIPTS_DIR)/plot_fields_propagation_I2.gp
+	gnuplot $(SCRIPTS_DIR)/plot_fields_propagation_I4.gp
+
+plot: pp_I2.stamp
+
+pp_I2.stamp: $(XSIL_FILES) $(M_FILES)
+	octave -q $(SCRIPTS_DIR)/pp_I2.m
+
+clean:
+	rm -f pp_I2.stamp
+	$(MAKE) -f $(SCRIPTS_DIR)/Makefile.fig $@
+
+real_clean: clean
+	rm -f $(M_FILES) $(XSIL_FILES) *.dat octave-core 
+	$(MAKE) -f $(SCRIPTS_DIR)/Makefile.fig $@
+	rm -f exact_analysis_execution_time.txt
+
+.PRECIOUS: %.run %.xsil %.m
+.PHONY: all clean
diff --git a/xmds2/realistic_Rb_and_fields/RbAtomConstants.cdata b/xmds2/realistic_Rb_and_fields/RbAtomConstants.cdata
new file mode 100644
index 0000000..49b96a1
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/RbAtomConstants.cdata
@@ -0,0 +1,17 @@
+<![CDATA[
+//---------------- RbAtomConstants.cdata starts ------------------
+const double ha0 = 2.1471788680034824e10;
+const double ha1 = 2.558764384495815e9;
+const double g1 = 3.612847284945266e7;
+const double ha2 = 5.323020344462938e8;
+const double hb2 = 7.85178251911697e7;
+const double g2 = 3.8117309832741246e7;
+const double lambda1 = 7.949788511562656e-7;
+const double lambda2 = 7.802412096860509e-7;
+const double eta1 = 5.450949336831401e-6;
+const double eta2 = 5.5397657647874e-6;
+const double rt6 = 2.449489742783178;
+const double rt3 = 1.7320508075688772;
+const double rt2 = 1.4142135623730951;
+//---------------- RbAtomConstants.cdata ends   ------------------
+]]>
diff --git a/xmds2/realistic_Rb_and_fields/RbEquations.cdata b/xmds2/realistic_Rb_and_fields/RbEquations.cdata
new file mode 100644
index 0000000..39bd357
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/RbEquations.cdata
@@ -0,0 +1,140 @@
+<![CDATA[
+//---------------- RbEquations.cdata starts ------------------
+dr0101_dt = gt/8. - gt*r0101 + (g1*r0909)/2. + (g2*r1212)/3. + (g2*r1313)/6. - i*((conj(Em1a)*conj(r0109))/4. - (conj(Em4a)*conj(r0113))/(4.*rt6) - (Em1a*r0109)/4. + (Em4a*r0113)/(4.*rt6) + r0201*(WLx/2. - (i*WLy)/2.) - conj(r0201)*(WLx/2. + (i*WLy)/2.));
+dr0109_dt = (-(gt*r0109) - (gt + g1)*r0109)/2. - i*(-(conj(Ep1a)*conj(r0301))/(4.*rt6) + (conj(Ep2a)*conj(r0701))/(4.*rt6) - (conj(Em4a)*conj(r0913))/(4.*rt6) - (conj(Em1a)*r0101)/4. + (conj(Em1a)*r0909)/4. + r0209*(WLx/2. - (i*WLy)/2.) - r0110*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0109*(-delta1 - v*Kvec1 - WLz/6.) + r0109*WLz);
+dr0110_dt = (-(gt*r0110) - (gt + g1)*r0110)/2. - i*(-(conj(Em1a)*conj(r0201))/(4.*rt2) - (conj(Ep1a)*conj(r0401))/(4.*rt2) - (conj(Em2a)*conj(r0601))/(4.*rt6) + (conj(Ep2a)*conj(r0801))/(4.*rt6) + (conj(Em1a)*conj(r1009))/4. - (conj(Em4a)*conj(r1013))/(4.*rt6) + (delta1 + v*Kvec1)*r0110 + r0210*(WLx/2. - (i*WLy)/2.) - r0111*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0110*WLz);
+dr0111_dt = (-(gt*r0111) - (gt + g1)*r0111)/2. - i*(-(conj(Em1a)*conj(r0301))/(4.*rt6) - (conj(Ep1a)*conj(r0501))/4. - (conj(Em2a)*conj(r0701))/(4.*rt6) + (conj(Em1a)*conj(r1109))/4. - (conj(Em4a)*conj(r1113))/(4.*rt6) + r0211*(WLx/2. - (i*WLy)/2.) - r0110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0111*(-delta1 - v*Kvec1 + WLz/6.) + r0111*WLz);
+dr0112_dt = (-(gt*r0112) - (gt + g2)*r0112)/2. - i*(-(conj(Ep4a)*conj(r0201))/(4.*rt6) - (conj(Ep3a)*conj(r0601))/(4.*rt2) + (conj(Em1a)*r0912)/4. - (conj(Em4a)*r1312)/(4.*rt6) + r0212*(WLx/2. - (i*WLy)/2.) - r0113*((2*WLx)/3. + (2*i*WLy)/3.) + r0112*WLz - r0112*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0113_dt = (-(gt*r0113) - (gt + g2)*r0113)/2. - i*(-(conj(Ep4a)*conj(r0301))/8. - (conj(Ep3a)*conj(r0701))/8. + (conj(Em4a)*r0101)/(4.*rt6) + (conj(Em1a)*r0913)/4. - (conj(Em4a)*r1313)/(4.*rt6) - r0112*((2*WLx)/3. - (2*i*WLy)/3.) + r0213*(WLx/2. - (i*WLy)/2.) - r0114*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r0113*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) + r0113*WLz);
+dr0114_dt = (-(gt*r0114) - (gt + g2)*r0114)/2. - i*((conj(Em4a)*conj(r0201))/8. - (conj(Ep4a)*conj(r0401))/8. - (conj(Em3a)*conj(r0601))/(8.*rt3) - (conj(Ep3a)*conj(r0801))/(8.*rt3) - (conj(Em4a)*conj(r1413))/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0114 + (conj(Em1a)*r0914)/4. + r0214*(WLx/2. - (i*WLy)/2.) - r0113*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0115*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0114*WLz);
+dr0115_dt = (-(gt*r0115) - (gt + g2)*r0115)/2. - i*((conj(Em4a)*conj(r0301))/8. - (conj(Ep4a)*conj(r0501))/(4.*rt6) - (conj(Em3a)*conj(r0701))/8. - (conj(Em4a)*conj(r1513))/(4.*rt6) + (conj(Em1a)*r0915)/4. + r0215*(WLx/2. - (i*WLy)/2.) - r0116*((2*WLx)/3. + (2*i*WLy)/3.) - r0114*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0115*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0115*WLz);
+dr0116_dt = (-(gt*r0116) - (gt + g2)*r0116)/2. - i*((conj(Em4a)*conj(r0401))/(4.*rt6) - (conj(Em3a)*conj(r0801))/(4.*rt2) - (conj(Em4a)*conj(r1613))/(4.*rt6) + (conj(Em1a)*r0916)/4. - r0115*((2*WLx)/3. - (2*i*WLy)/3.) + r0216*(WLx/2. - (i*WLy)/2.) - r0116*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0116*WLz);
+dr0201_dt = -(gt*r0201) + (g1*r1009)/(2.*rt2) + (g2*r1312)/6. + (g2*r1413)/(2.*rt6) - i*((conj(Em1a)*conj(r0110))/(4.*rt2) + (conj(Ep4a)*conj(r0112))/(4.*rt6) - (conj(Em4a)*conj(r0114))/8. - (Em1a*r0209)/4. + (Em4a*r0213)/(4.*rt6) + r0101*(WLx/2. + (i*WLy)/2.) - r0202*(WLx/2. + (i*WLy)/2.) + r0301*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - (r0201*WLz)/2.);
+dr0202_dt = gt/8. - gt*r0202 + (g1*r0909)/4. + (g1*r1010)/4. + (g2*r1212)/6. + (g2*r1313)/12. + (g2*r1414)/4. - i*((conj(Em1a)*conj(r0210))/(4.*rt2) + (conj(Ep4a)*conj(r0212))/(4.*rt6) - (conj(Em4a)*conj(r0214))/8. - (Em1a*r0210)/(4.*rt2) - (Ep4a*r0212)/(4.*rt6) + (Em4a*r0214)/8. - r0201*(WLx/2. - (i*WLy)/2.) + conj(r0201)*(WLx/2. + (i*WLy)/2.) + r0302*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - conj(r0302)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0209_dt = (-(gt*r0209) - (gt + g1)*r0209)/2. - i*(-(conj(Ep1a)*conj(r0302))/(4.*rt6) + (conj(Ep2a)*conj(r0702))/(4.*rt6) + (conj(Ep4a)*conj(r0912))/(4.*rt6) - (conj(Em4a)*conj(r0914))/8. - (conj(Em1a)*r0201)/4. + (conj(Em1a)*r1009)/(4.*rt2) + r0109*(WLx/2. + (i*WLy)/2.) + r0309*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0210*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0209*(-delta1 - v*Kvec1 - WLz/6.) + (r0209*WLz)/2.);
+dr0210_dt = (-(gt*r0210) - (gt + g1)*r0210)/2. - i*(-(conj(Ep1a)*conj(r0402))/(4.*rt2) - (conj(Em2a)*conj(r0602))/(4.*rt6) + (conj(Ep2a)*conj(r0802))/(4.*rt6) + (conj(Ep4a)*conj(r1012))/(4.*rt6) - (conj(Em4a)*conj(r1014))/8. - (conj(Em1a)*r0202)/(4.*rt2) + (delta1 + v*Kvec1)*r0210 + (conj(Em1a)*r1010)/(4.*rt2) + r0110*(WLx/2. + (i*WLy)/2.) + r0310*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0211*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0209*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + (r0210*WLz)/2.);
+dr0211_dt = (-(gt*r0211) - (gt + g1)*r0211)/2. - i*(-(conj(Em1a)*conj(r0302))/(4.*rt6) - (conj(Ep1a)*conj(r0502))/4. - (conj(Em2a)*conj(r0702))/(4.*rt6) + (conj(Em1a)*conj(r1110))/(4.*rt2) + (conj(Ep4a)*conj(r1112))/(4.*rt6) - (conj(Em4a)*conj(r1114))/8. + r0111*(WLx/2. + (i*WLy)/2.) + r0311*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0210*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0211*(-delta1 - v*Kvec1 + WLz/6.) + (r0211*WLz)/2.);
+dr0212_dt = (-(gt*r0212) - (gt + g2)*r0212)/2. - i*(-(conj(Ep3a)*conj(r0602))/(4.*rt2) - (conj(Ep4a)*r0202)/(4.*rt6) + (conj(Em1a)*r1012)/(4.*rt2) + (conj(Ep4a)*r1212)/(4.*rt6) - (conj(Em4a)*r1412)/8. + r0112*(WLx/2. + (i*WLy)/2.) - r0213*((2*WLx)/3. + (2*i*WLy)/3.) + r0312*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + (r0212*WLz)/2. - r0212*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0213_dt = (-(gt*r0213) - (gt + g2)*r0213)/2. - i*(-(conj(Ep4a)*conj(r0302))/8. - (conj(Ep3a)*conj(r0702))/8. + (conj(Ep4a)*conj(r1312))/(4.*rt6) + (conj(Em4a)*r0201)/(4.*rt6) + (conj(Em1a)*r1013)/(4.*rt2) - (conj(Em4a)*r1413)/8. - r0212*((2*WLx)/3. - (2*i*WLy)/3.) + r0113*(WLx/2. + (i*WLy)/2.) - r0214*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0313*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0213*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) + (r0213*WLz)/2.);
+dr0214_dt = (-(gt*r0214) - (gt + g2)*r0214)/2. - i*(-(conj(Ep4a)*conj(r0402))/8. - (conj(Em3a)*conj(r0602))/(8.*rt3) - (conj(Ep3a)*conj(r0802))/(8.*rt3) + (conj(Ep4a)*conj(r1412))/(4.*rt6) + (conj(Em4a)*r0202)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0214 + (conj(Em1a)*r1014)/(4.*rt2) - (conj(Em4a)*r1414)/8. + r0114*(WLx/2. + (i*WLy)/2.) - r0213*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0215*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0314*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + (r0214*WLz)/2.);
+dr0215_dt = (-(gt*r0215) - (gt + g2)*r0215)/2. - i*((conj(Em4a)*conj(r0302))/8. - (conj(Ep4a)*conj(r0502))/(4.*rt6) - (conj(Em3a)*conj(r0702))/8. + (conj(Ep4a)*conj(r1512))/(4.*rt6) - (conj(Em4a)*conj(r1514))/8. + (conj(Em1a)*r1015)/(4.*rt2) + r0115*(WLx/2. + (i*WLy)/2.) - r0216*((2*WLx)/3. + (2*i*WLy)/3.) - r0214*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0315*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0215*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + (r0215*WLz)/2.);
+dr0216_dt = (-(gt*r0216) - (gt + g2)*r0216)/2. - i*((conj(Em4a)*conj(r0402))/(4.*rt6) - (conj(Em3a)*conj(r0802))/(4.*rt2) + (conj(Ep4a)*conj(r1612))/(4.*rt6) - (conj(Em4a)*conj(r1614))/8. + (conj(Em1a)*r1016)/(4.*rt2) - r0215*((2*WLx)/3. - (2*i*WLy)/3.) + r0116*(WLx/2. + (i*WLy)/2.) + r0316*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0216*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + (r0216*WLz)/2.);
+dr0301_dt = -(gt*r0301) + (g1*r1109)/(2.*rt6) + (g2*r1513)/(2.*rt6) - i*((conj(Ep1a)*conj(r0109))/(4.*rt6) + (conj(Em1a)*conj(r0111))/(4.*rt6) + (conj(Ep4a)*conj(r0113))/8. - (conj(Em4a)*conj(r0115))/8. - (Em1a*r0309)/4. + (Em4a*r0313)/(4.*rt6) - r0302*(WLx/2. + (i*WLy)/2.) + r0401*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0201*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0301*WLz);
+dr0302_dt = -(gt*r0302) + (g1*r1009)/(2.*rt3) + (g1*r1110)/(4.*rt3) + (g2*r1312)/(2.*rt6) + (g2*r1514)/4. - i*((conj(Ep1a)*conj(r0209))/(4.*rt6) + (conj(Em1a)*conj(r0211))/(4.*rt6) + (conj(Ep4a)*conj(r0213))/8. - (conj(Em4a)*conj(r0215))/8. - (Em1a*r0310)/(4.*rt2) - (Ep4a*r0312)/(4.*rt6) + (Em4a*r0314)/8. - r0301*(WLx/2. - (i*WLy)/2.) + r0402*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0202*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0303*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0302*WLz)/2.);
+dr0303_dt = gt/8. - gt*r0303 + (g1*r0909)/12. + (g1*r1010)/3. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1515)/4. - i*((conj(Ep1a)*conj(r0309))/(4.*rt6) + (conj(Em1a)*conj(r0311))/(4.*rt6) + (conj(Ep4a)*conj(r0313))/8. - (conj(Em4a)*conj(r0315))/8. - (Ep1a*r0309)/(4.*rt6) - (Em1a*r0311)/(4.*rt6) - (Ep4a*r0313)/8. + (Em4a*r0315)/8. - r0302*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0403*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + conj(r0302)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - conj(r0403)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0309_dt = (-(gt*r0309) - (gt + g1)*r0309)/2. - i*((conj(Ep2a)*conj(r0703))/(4.*rt6) + (conj(Ep4a)*conj(r0913))/8. - (conj(Em4a)*conj(r0915))/8. - (conj(Em1a)*r0301)/4. - (conj(Ep1a)*r0303)/(4.*rt6) + (conj(Ep1a)*r0909)/(4.*rt6) + (conj(Em1a)*r1109)/(4.*rt6) + r0409*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0209*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0310*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0309*(-delta1 - v*Kvec1 - WLz/6.));
+dr0310_dt = (-(gt*r0310) - (gt + g1)*r0310)/2. - i*(-(conj(Ep1a)*conj(r0403))/(4.*rt2) - (conj(Em2a)*conj(r0603))/(4.*rt6) + (conj(Ep2a)*conj(r0803))/(4.*rt6) + (conj(Ep1a)*conj(r1009))/(4.*rt6) + (conj(Ep4a)*conj(r1013))/8. - (conj(Em4a)*conj(r1015))/8. - (conj(Em1a)*r0302)/(4.*rt2) + (delta1 + v*Kvec1)*r0310 + (conj(Em1a)*r1110)/(4.*rt6) + r0410*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0210*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0311*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0309*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr0311_dt = (-(gt*r0311) - (gt + g1)*r0311)/2. - i*(-(conj(Ep1a)*conj(r0503))/4. - (conj(Em2a)*conj(r0703))/(4.*rt6) + (conj(Ep1a)*conj(r1109))/(4.*rt6) + (conj(Ep4a)*conj(r1113))/8. - (conj(Em4a)*conj(r1115))/8. - (conj(Em1a)*r0303)/(4.*rt6) + (conj(Em1a)*r1111)/(4.*rt6) + r0411*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0211*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0310*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0311*(-delta1 - v*Kvec1 + WLz/6.));
+dr0312_dt = (-(gt*r0312) - (gt + g2)*r0312)/2. - i*(-(conj(Ep3a)*conj(r0603))/(4.*rt2) - (conj(Ep4a)*r0302)/(4.*rt6) + (conj(Ep1a)*r0912)/(4.*rt6) + (conj(Em1a)*r1112)/(4.*rt6) + (conj(Ep4a)*r1312)/8. - (conj(Em4a)*r1512)/8. - r0313*((2*WLx)/3. + (2*i*WLy)/3.) + r0412*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0212*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0313_dt = (-(gt*r0313) - (gt + g2)*r0313)/2. - i*(-(conj(Ep3a)*conj(r0703))/8. + (conj(Em4a)*r0301)/(4.*rt6) - (conj(Ep4a)*r0303)/8. + (conj(Ep1a)*r0913)/(4.*rt6) + (conj(Em1a)*r1113)/(4.*rt6) + (conj(Ep4a)*r1313)/8. - (conj(Em4a)*r1513)/8. - r0312*((2*WLx)/3. - (2*i*WLy)/3.) - r0314*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0413*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0213*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0313*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0314_dt = (-(gt*r0314) - (gt + g2)*r0314)/2. - i*(-(conj(Ep4a)*conj(r0403))/8. - (conj(Em3a)*conj(r0603))/(8.*rt3) - (conj(Ep3a)*conj(r0803))/(8.*rt3) + (conj(Ep4a)*conj(r1413))/8. + (conj(Em4a)*r0302)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0314 + (conj(Ep1a)*r0914)/(4.*rt6) + (conj(Em1a)*r1114)/(4.*rt6) - (conj(Em4a)*r1514)/8. - r0313*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0315*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0414*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0214*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0315_dt = (-(gt*r0315) - (gt + g2)*r0315)/2. - i*(-(conj(Ep4a)*conj(r0503))/(4.*rt6) - (conj(Em3a)*conj(r0703))/8. + (conj(Ep4a)*conj(r1513))/8. + (conj(Em4a)*r0303)/8. + (conj(Ep1a)*r0915)/(4.*rt6) + (conj(Em1a)*r1115)/(4.*rt6) - (conj(Em4a)*r1515)/8. - r0316*((2*WLx)/3. + (2*i*WLy)/3.) - r0314*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0415*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0215*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0315*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr0316_dt = (-(gt*r0316) - (gt + g2)*r0316)/2. - i*((conj(Em4a)*conj(r0403))/(4.*rt6) - (conj(Em3a)*conj(r0803))/(4.*rt2) + (conj(Ep4a)*conj(r1613))/8. - (conj(Em4a)*conj(r1615))/8. + (conj(Ep1a)*r0916)/(4.*rt6) + (conj(Em1a)*r1116)/(4.*rt6) - r0315*((2*WLx)/3. - (2*i*WLy)/3.) + r0416*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0216*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0316*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr0401_dt = -(gt*r0401) - (g2*r1512)/6. + (g2*r1613)/6. - i*((conj(Ep1a)*conj(r0110))/(4.*rt2) + (conj(Ep4a)*conj(r0114))/8. - (conj(Em4a)*conj(r0116))/(4.*rt6) - (Em1a*r0409)/4. + (Em4a*r0413)/(4.*rt6) + r0501*(WLx/2. - (i*WLy)/2.) - r0402*(WLx/2. + (i*WLy)/2.) + r0301*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (3*r0401*WLz)/2.);
+dr0402_dt = -(gt*r0402) + (g1*r1109)/4. + (g2*r1412)/(2.*rt6) - (g2*r1513)/12. + (g2*r1614)/(2.*rt6) - i*((conj(Ep1a)*conj(r0210))/(4.*rt2) + (conj(Ep4a)*conj(r0214))/8. - (conj(Em4a)*conj(r0216))/(4.*rt6) - (Em1a*r0410)/(4.*rt2) - (Ep4a*r0412)/(4.*rt6) + (Em4a*r0414)/8. - r0401*(WLx/2. - (i*WLy)/2.) + r0502*(WLx/2. - (i*WLy)/2.) + r0302*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0403*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0402*WLz);
+dr0403_dt = -(gt*r0403) + (g1*r1009)/(4.*rt3) + (g1*r1110)/(2.*rt3) + (g2*r1413)/4. + (g2*r1615)/(2.*rt6) - i*((conj(Ep1a)*conj(r0310))/(4.*rt2) + (conj(Ep4a)*conj(r0314))/8. - (conj(Em4a)*conj(r0316))/(4.*rt6) - (Ep1a*r0409)/(4.*rt6) - (Em1a*r0411)/(4.*rt6) - (Ep4a*r0413)/8. + (Em4a*r0415)/8. + r0503*(WLx/2. - (i*WLy)/2.) - r0402*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0303*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0404*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0403*WLz)/2.);
+dr0404_dt = gt/8. - gt*r0404 + (g1*r1010)/4. + (g1*r1111)/4. + (g2*r1414)/4. + (g2*r1515)/12. + (g2*r1616)/6. - i*((conj(Ep1a)*conj(r0410))/(4.*rt2) + (conj(Ep4a)*conj(r0414))/8. - (conj(Em4a)*conj(r0416))/(4.*rt6) - (Ep1a*r0410)/(4.*rt2) - (Ep4a*r0414)/8. + (Em4a*r0416)/(4.*rt6) + r0504*(WLx/2. - (i*WLy)/2.) - conj(r0504)*(WLx/2. + (i*WLy)/2.) - r0403*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + conj(r0403)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0409_dt = (-(gt*r0409) - (gt + g1)*r0409)/2. - i*((conj(Ep2a)*conj(r0704))/(4.*rt6) + (conj(Ep4a)*conj(r0914))/8. - (conj(Em4a)*conj(r0916))/(4.*rt6) - (conj(Em1a)*r0401)/4. - (conj(Ep1a)*r0403)/(4.*rt6) + (conj(Ep1a)*r1009)/(4.*rt2) + r0509*(WLx/2. - (i*WLy)/2.) + r0309*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0410*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0409*(-delta1 - v*Kvec1 - WLz/6.) - (r0409*WLz)/2.);
+dr0410_dt = (-(gt*r0410) - (gt + g1)*r0410)/2. - i*(-(conj(Em2a)*conj(r0604))/(4.*rt6) + (conj(Ep2a)*conj(r0804))/(4.*rt6) + (conj(Ep4a)*conj(r1014))/8. - (conj(Em4a)*conj(r1016))/(4.*rt6) - (conj(Em1a)*r0402)/(4.*rt2) - (conj(Ep1a)*r0404)/(4.*rt2) + (delta1 + v*Kvec1)*r0410 + (conj(Ep1a)*r1010)/(4.*rt2) + r0510*(WLx/2. - (i*WLy)/2.) + r0310*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0411*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0409*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - (r0410*WLz)/2.);
+dr0411_dt = (-(gt*r0411) - (gt + g1)*r0411)/2. - i*(-(conj(Ep1a)*conj(r0504))/4. - (conj(Em2a)*conj(r0704))/(4.*rt6) + (conj(Ep1a)*conj(r1110))/(4.*rt2) + (conj(Ep4a)*conj(r1114))/8. - (conj(Em4a)*conj(r1116))/(4.*rt6) - (conj(Em1a)*r0403)/(4.*rt6) + r0511*(WLx/2. - (i*WLy)/2.) + r0311*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0410*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0411*(-delta1 - v*Kvec1 + WLz/6.) - (r0411*WLz)/2.);
+dr0412_dt = (-(gt*r0412) - (gt + g2)*r0412)/2. - i*(-(conj(Ep3a)*conj(r0604))/(4.*rt2) - (conj(Ep4a)*r0402)/(4.*rt6) + (conj(Ep1a)*r1012)/(4.*rt2) + (conj(Ep4a)*r1412)/8. - (conj(Em4a)*r1612)/(4.*rt6) + r0512*(WLx/2. - (i*WLy)/2.) - r0413*((2*WLx)/3. + (2*i*WLy)/3.) + r0312*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0412*WLz)/2. - r0412*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0413_dt = (-(gt*r0413) - (gt + g2)*r0413)/2. - i*(-(conj(Ep3a)*conj(r0704))/8. + (conj(Em4a)*r0401)/(4.*rt6) - (conj(Ep4a)*r0403)/8. + (conj(Ep1a)*r1013)/(4.*rt2) + (conj(Ep4a)*r1413)/8. - (conj(Em4a)*r1613)/(4.*rt6) - r0412*((2*WLx)/3. - (2*i*WLy)/3.) + r0513*(WLx/2. - (i*WLy)/2.) - r0414*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0313*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0413*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - (r0413*WLz)/2.);
+dr0414_dt = (-(gt*r0414) - (gt + g2)*r0414)/2. - i*(-(conj(Em3a)*conj(r0604))/(8.*rt3) - (conj(Ep3a)*conj(r0804))/(8.*rt3) + (conj(Em4a)*r0402)/8. - (conj(Ep4a)*r0404)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0414 + (conj(Ep1a)*r1014)/(4.*rt2) + (conj(Ep4a)*r1414)/8. - (conj(Em4a)*r1614)/(4.*rt6) + r0514*(WLx/2. - (i*WLy)/2.) - r0413*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0415*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0314*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0414*WLz)/2.);
+dr0415_dt = (-(gt*r0415) - (gt + g2)*r0415)/2. - i*(-(conj(Ep4a)*conj(r0504))/(4.*rt6) - (conj(Em3a)*conj(r0704))/8. + (conj(Ep4a)*conj(r1514))/8. + (conj(Em4a)*r0403)/8. + (conj(Ep1a)*r1015)/(4.*rt2) - (conj(Em4a)*r1615)/(4.*rt6) + r0515*(WLx/2. - (i*WLy)/2.) - r0416*((2*WLx)/3. + (2*i*WLy)/3.) - r0414*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0315*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0415*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - (r0415*WLz)/2.);
+dr0416_dt = (-(gt*r0416) - (gt + g2)*r0416)/2. - i*(-(conj(Em3a)*conj(r0804))/(4.*rt2) + (conj(Ep4a)*conj(r1614))/8. + (conj(Em4a)*r0404)/(4.*rt6) + (conj(Ep1a)*r1016)/(4.*rt2) - (conj(Em4a)*r1616)/(4.*rt6) - r0415*((2*WLx)/3. - (2*i*WLy)/3.) + r0516*(WLx/2. - (i*WLy)/2.) + r0316*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0416*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - (r0416*WLz)/2.);
+dr0501_dt = -(gt*r0501) - (g2*r1612)/3. - i*((conj(Ep1a)*conj(r0111))/4. + (conj(Ep4a)*conj(r0115))/(4.*rt6) - (Em1a*r0509)/4. + (Em4a*r0513)/(4.*rt6) + r0401*(WLx/2. + (i*WLy)/2.) - r0502*(WLx/2. + (i*WLy)/2.) - 2*r0501*WLz);
+dr0502_dt = -(gt*r0502) + (g2*r1512)/6. - (g2*r1613)/6. - i*((conj(Ep1a)*conj(r0211))/4. + (conj(Ep4a)*conj(r0215))/(4.*rt6) - (Em1a*r0510)/(4.*rt2) - (Ep4a*r0512)/(4.*rt6) + (Em4a*r0514)/8. - r0501*(WLx/2. - (i*WLy)/2.) + r0402*(WLx/2. + (i*WLy)/2.) - r0503*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (3*r0502*WLz)/2.);
+dr0503_dt = -(gt*r0503) + (g1*r1109)/(2.*rt6) + (g2*r1513)/(2.*rt6) - i*((conj(Ep1a)*conj(r0311))/4. + (conj(Ep4a)*conj(r0315))/(4.*rt6) - (Ep1a*r0509)/(4.*rt6) - (Em1a*r0511)/(4.*rt6) - (Ep4a*r0513)/8. + (Em4a*r0515)/8. + r0403*(WLx/2. + (i*WLy)/2.) - r0502*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0504*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0503*WLz);
+dr0504_dt = -(gt*r0504) + (g1*r1110)/(2.*rt2) + (g2*r1514)/(2.*rt6) + (g2*r1615)/6. - i*((conj(Ep1a)*conj(r0411))/4. + (conj(Ep4a)*conj(r0415))/(4.*rt6) - (Ep1a*r0510)/(4.*rt2) - (Ep4a*r0514)/8. + (Em4a*r0516)/(4.*rt6) + r0404*(WLx/2. + (i*WLy)/2.) - r0505*(WLx/2. + (i*WLy)/2.) - r0503*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - (r0504*WLz)/2.);
+dr0505_dt = gt/8. - gt*r0505 + (g1*r1111)/2. + (g2*r1515)/6. + (g2*r1616)/3. - i*((conj(Ep1a)*conj(r0511))/4. + (conj(Ep4a)*conj(r0515))/(4.*rt6) - (Ep1a*r0511)/4. - (Ep4a*r0515)/(4.*rt6) - r0504*(WLx/2. - (i*WLy)/2.) + conj(r0504)*(WLx/2. + (i*WLy)/2.));
+dr0509_dt = (-(gt*r0509) - (gt + g1)*r0509)/2. - i*((conj(Ep2a)*conj(r0705))/(4.*rt6) + (conj(Ep4a)*conj(r0915))/(4.*rt6) - (conj(Em1a)*r0501)/4. - (conj(Ep1a)*r0503)/(4.*rt6) + (conj(Ep1a)*r1109)/4. + r0409*(WLx/2. + (i*WLy)/2.) - r0510*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0509*(-delta1 - v*Kvec1 - WLz/6.) - r0509*WLz);
+dr0510_dt = (-(gt*r0510) - (gt + g1)*r0510)/2. - i*(-(conj(Em2a)*conj(r0605))/(4.*rt6) + (conj(Ep2a)*conj(r0805))/(4.*rt6) + (conj(Ep4a)*conj(r1015))/(4.*rt6) - (conj(Em1a)*r0502)/(4.*rt2) - (conj(Ep1a)*r0504)/(4.*rt2) + (delta1 + v*Kvec1)*r0510 + (conj(Ep1a)*r1110)/4. + r0410*(WLx/2. + (i*WLy)/2.) - r0511*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0509*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0510*WLz);
+dr0511_dt = (-(gt*r0511) - (gt + g1)*r0511)/2. - i*(-(conj(Em2a)*conj(r0705))/(4.*rt6) + (conj(Ep4a)*conj(r1115))/(4.*rt6) - (conj(Em1a)*r0503)/(4.*rt6) - (conj(Ep1a)*r0505)/4. + (conj(Ep1a)*r1111)/4. + r0411*(WLx/2. + (i*WLy)/2.) - r0510*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0511*(-delta1 - v*Kvec1 + WLz/6.) - r0511*WLz);
+dr0512_dt = (-(gt*r0512) - (gt + g2)*r0512)/2. - i*(-(conj(Ep3a)*conj(r0605))/(4.*rt2) - (conj(Ep4a)*r0502)/(4.*rt6) + (conj(Ep1a)*r1112)/4. + (conj(Ep4a)*r1512)/(4.*rt6) + r0412*(WLx/2. + (i*WLy)/2.) - r0513*((2*WLx)/3. + (2*i*WLy)/3.) - r0512*WLz - r0512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0513_dt = (-(gt*r0513) - (gt + g2)*r0513)/2. - i*(-(conj(Ep3a)*conj(r0705))/8. + (conj(Em4a)*r0501)/(4.*rt6) - (conj(Ep4a)*r0503)/8. + (conj(Ep1a)*r1113)/4. + (conj(Ep4a)*r1513)/(4.*rt6) - r0512*((2*WLx)/3. - (2*i*WLy)/3.) + r0413*(WLx/2. + (i*WLy)/2.) - r0514*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r0513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - r0513*WLz);
+dr0514_dt = (-(gt*r0514) - (gt + g2)*r0514)/2. - i*(-(conj(Em3a)*conj(r0605))/(8.*rt3) - (conj(Ep3a)*conj(r0805))/(8.*rt3) + (conj(Em4a)*r0502)/8. - (conj(Ep4a)*r0504)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0514 + (conj(Ep1a)*r1114)/4. + (conj(Ep4a)*r1514)/(4.*rt6) + r0414*(WLx/2. + (i*WLy)/2.) - r0513*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0515*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r0514*WLz);
+dr0515_dt = (-(gt*r0515) - (gt + g2)*r0515)/2. - i*(-(conj(Em3a)*conj(r0705))/8. + (conj(Em4a)*r0503)/8. - (conj(Ep4a)*r0505)/(4.*rt6) + (conj(Ep1a)*r1115)/4. + (conj(Ep4a)*r1515)/(4.*rt6) + r0415*(WLx/2. + (i*WLy)/2.) - r0516*((2*WLx)/3. + (2*i*WLy)/3.) - r0514*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0515*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r0515*WLz);
+dr0516_dt = (-(gt*r0516) - (gt + g2)*r0516)/2. - i*(-(conj(Em3a)*conj(r0805))/(4.*rt2) + (conj(Ep4a)*conj(r1615))/(4.*rt6) + (conj(Em4a)*r0504)/(4.*rt6) + (conj(Ep1a)*r1116)/4. - r0515*((2*WLx)/3. - (2*i*WLy)/3.) + r0416*(WLx/2. + (i*WLy)/2.) - r0516*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r0516*WLz);
+dr0601_dt = -(gt*r0601) - i*((conj(Em2a)*conj(r0110))/(4.*rt6) + (conj(Ep3a)*conj(r0112))/(4.*rt2) + (conj(Em3a)*conj(r0114))/(8.*rt3) - (Em1a*r0609)/4. + (Em4a*r0613)/(4.*rt6) - r0602*(WLx/2. + (i*WLy)/2.) + r0701*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0601*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0601*WLz);
+dr0602_dt = -(gt*r0602) - i*((conj(Em2a)*conj(r0210))/(4.*rt6) + (conj(Ep3a)*conj(r0212))/(4.*rt2) + (conj(Em3a)*conj(r0214))/(8.*rt3) - (Em1a*r0610)/(4.*rt2) - (Ep4a*r0612)/(4.*rt6) + (Em4a*r0614)/8. - r0601*(WLx/2. - (i*WLy)/2.) - r0603*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0702*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0602*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - (r0602*WLz)/2.);
+dr0603_dt = -(gt*r0603) - i*((conj(Em2a)*conj(r0310))/(4.*rt6) + (conj(Ep3a)*conj(r0312))/(4.*rt2) + (conj(Em3a)*conj(r0314))/(8.*rt3) - (Ep1a*r0609)/(4.*rt6) - (Em1a*r0611)/(4.*rt6) - (Ep4a*r0613)/8. + (Em4a*r0615)/8. - r0602*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0604*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0703*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0603*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0604_dt = -(gt*r0604) - i*((conj(Em2a)*conj(r0410))/(4.*rt6) + (conj(Ep3a)*conj(r0412))/(4.*rt2) + (conj(Em3a)*conj(r0414))/(8.*rt3) - (Ep1a*r0610)/(4.*rt2) - (Ep4a*r0614)/8. + (Em4a*r0616)/(4.*rt6) - r0605*(WLx/2. + (i*WLy)/2.) - r0603*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0704*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0604*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + (r0604*WLz)/2.);
+dr0605_dt = -(gt*r0605) - i*((conj(Em2a)*conj(r0510))/(4.*rt6) + (conj(Ep3a)*conj(r0512))/(4.*rt2) + (conj(Em3a)*conj(r0514))/(8.*rt3) - (Ep1a*r0611)/4. - (Ep4a*r0615)/(4.*rt6) - r0604*(WLx/2. - (i*WLy)/2.) + r0705*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0605*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + r0605*WLz);
+dr0606_dt = gt/8. - gt*r0606 + (g1*r0909)/12. + (g1*r1010)/12. + (g2*r1212)/2. + (g2*r1313)/4. + (g2*r1414)/12. - i*((conj(Em2a)*conj(r0610))/(4.*rt6) + (conj(Ep3a)*conj(r0612))/(4.*rt2) + (conj(Em3a)*conj(r0614))/(8.*rt3) - (Em2a*r0610)/(4.*rt6) - (Ep3a*r0612)/(4.*rt2) - (Em3a*r0614)/(8.*rt3) - conj(r0706)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0706*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0609_dt = (-(gt*r0609) - (gt + g1)*r0609)/2. - i*((conj(Ep2a)*conj(r0706))/(4.*rt6) + (conj(Ep3a)*conj(r0912))/(4.*rt2) + (conj(Em3a)*conj(r0914))/(8.*rt3) - (conj(Em1a)*r0601)/4. - (conj(Ep1a)*r0603)/(4.*rt6) + (conj(Em2a)*r1009)/(4.*rt6) - r0610*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r0709*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0609*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0609*(-delta1 - v*Kvec1 - WLz/6.));
+dr0610_dt = (-(gt*r0610) - (gt + g1)*r0610)/2. - i*((conj(Ep2a)*conj(r0806))/(4.*rt6) + (conj(Ep3a)*conj(r1012))/(4.*rt2) + (conj(Em3a)*conj(r1014))/(8.*rt3) - (conj(Em1a)*r0602)/(4.*rt2) - (conj(Ep1a)*r0604)/(4.*rt2) - (conj(Em2a)*r0606)/(4.*rt6) + (delta1 + v*Kvec1)*r0610 + (conj(Em2a)*r1010)/(4.*rt6) - r0611*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0609*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0710*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0610*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0611_dt = (-(gt*r0611) - (gt + g1)*r0611)/2. - i*(-(conj(Em2a)*conj(r0706))/(4.*rt6) + (conj(Em2a)*conj(r1110))/(4.*rt6) + (conj(Ep3a)*conj(r1112))/(4.*rt2) + (conj(Em3a)*conj(r1114))/(8.*rt3) - (conj(Em1a)*r0603)/(4.*rt6) - (conj(Ep1a)*r0605)/4. - r0610*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0711*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0611*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0611*(-delta1 - v*Kvec1 + WLz/6.));
+dr0612_dt = (-(gt*r0612) - (gt + g2)*r0612)/2. - i*(-(conj(Ep4a)*r0602)/(4.*rt6) - (conj(Ep3a)*r0606)/(4.*rt2) + (conj(Em2a)*r1012)/(4.*rt6) + (conj(Ep3a)*r1212)/(4.*rt2) + (conj(Em3a)*r1412)/(8.*rt3) - r0613*((2*WLx)/3. + (2*i*WLy)/3.) + r0712*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0612*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0613_dt = (-(gt*r0613) - (gt + g2)*r0613)/2. - i*(-(conj(Ep3a)*conj(r0706))/8. + (conj(Ep3a)*conj(r1312))/(4.*rt2) + (conj(Em4a)*r0601)/(4.*rt6) - (conj(Ep4a)*r0603)/8. + (conj(Em2a)*r1013)/(4.*rt6) + (conj(Em3a)*r1413)/(8.*rt3) - r0612*((2*WLx)/3. - (2*i*WLy)/3.) - r0614*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0713*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0613*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0614_dt = (-(gt*r0614) - (gt + g2)*r0614)/2. - i*(-(conj(Ep3a)*conj(r0806))/(8.*rt3) + (conj(Ep3a)*conj(r1412))/(4.*rt2) + (conj(Em4a)*r0602)/8. - (conj(Ep4a)*r0604)/8. - (conj(Em3a)*r0606)/(8.*rt3) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0614 + (conj(Em2a)*r1014)/(4.*rt6) + (conj(Em3a)*r1414)/(8.*rt3) - r0613*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0615*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0714*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0614*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0615_dt = (-(gt*r0615) - (gt + g2)*r0615)/2. - i*(-(conj(Em3a)*conj(r0706))/8. + (conj(Ep3a)*conj(r1512))/(4.*rt2) + (conj(Em3a)*conj(r1514))/(8.*rt3) + (conj(Em4a)*r0603)/8. - (conj(Ep4a)*r0605)/(4.*rt6) + (conj(Em2a)*r1015)/(4.*rt6) - r0616*((2*WLx)/3. + (2*i*WLy)/3.) - r0614*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0715*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0615*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0616_dt = (-(gt*r0616) - (gt + g2)*r0616)/2. - i*(-(conj(Em3a)*conj(r0806))/(4.*rt2) + (conj(Ep3a)*conj(r1612))/(4.*rt2) + (conj(Em3a)*conj(r1614))/(8.*rt3) + (conj(Em4a)*r0604)/(4.*rt6) + (conj(Em2a)*r1016)/(4.*rt6) - r0615*((2*WLx)/3. - (2*i*WLy)/3.) + r0716*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0616*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0616*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0701_dt = -(gt*r0701) - i*(-(conj(Ep2a)*conj(r0109))/(4.*rt6) + (conj(Em2a)*conj(r0111))/(4.*rt6) + (conj(Ep3a)*conj(r0113))/8. + (conj(Em3a)*conj(r0115))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0701 - (Em1a*r0709)/4. + (Em4a*r0713)/(4.*rt6) - r0702*(WLx/2. + (i*WLy)/2.) + r0601*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0801*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0701*WLz);
+dr0702_dt = -(gt*r0702) - i*(-(conj(Ep2a)*conj(r0209))/(4.*rt6) + (conj(Em2a)*conj(r0211))/(4.*rt6) + (conj(Ep3a)*conj(r0213))/8. + (conj(Em3a)*conj(r0215))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0702 - (Em1a*r0710)/(4.*rt2) - (Ep4a*r0712)/(4.*rt6) + (Em4a*r0714)/8. - r0701*(WLx/2. - (i*WLy)/2.) - r0703*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0602*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0802*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - (r0702*WLz)/2.);
+dr0703_dt = -(gt*r0703) - i*(-(conj(Ep2a)*conj(r0309))/(4.*rt6) + (conj(Em2a)*conj(r0311))/(4.*rt6) + (conj(Ep3a)*conj(r0313))/8. + (conj(Em3a)*conj(r0315))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0703 - (Ep1a*r0709)/(4.*rt6) - (Em1a*r0711)/(4.*rt6) - (Ep4a*r0713)/8. + (Em4a*r0715)/8. - r0702*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0704*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0603*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0803*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0704_dt = -(gt*r0704) - i*(-(conj(Ep2a)*conj(r0409))/(4.*rt6) + (conj(Em2a)*conj(r0411))/(4.*rt6) + (conj(Ep3a)*conj(r0413))/8. + (conj(Em3a)*conj(r0415))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0704 - (Ep1a*r0710)/(4.*rt2) - (Ep4a*r0714)/8. + (Em4a*r0716)/(4.*rt6) - r0705*(WLx/2. + (i*WLy)/2.) - r0703*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0604*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0804*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + (r0704*WLz)/2.);
+dr0705_dt = -(gt*r0705) - i*(-(conj(Ep2a)*conj(r0509))/(4.*rt6) + (conj(Em2a)*conj(r0511))/(4.*rt6) + (conj(Ep3a)*conj(r0513))/8. + (conj(Em3a)*conj(r0515))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0705 - (Ep1a*r0711)/4. - (Ep4a*r0715)/(4.*rt6) - r0704*(WLx/2. - (i*WLy)/2.) + r0605*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0805*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0705*WLz);
+dr0706_dt = -(gt*r0706) + (g1*r1110)/12. + (g2*r1312)/(2.*rt2) + (g2*r1413)/(2.*rt3) + (g2*r1514)/(4.*rt3) - i*(-(conj(Ep2a)*conj(r0609))/(4.*rt6) + (conj(Em2a)*conj(r0611))/(4.*rt6) + (conj(Ep3a)*conj(r0613))/8. + (conj(Em3a)*conj(r0615))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0706 - (Em2a*r0710)/(4.*rt6) - (Ep3a*r0712)/(4.*rt2) - (Em3a*r0714)/(8.*rt3) + r0606*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0707*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0806*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0706*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0707_dt = gt/8. - gt*r0707 + (g1*r0909)/12. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1414)/3. + (g2*r1515)/4. - i*(-(conj(Ep2a)*conj(r0709))/(4.*rt6) + (conj(Em2a)*conj(r0711))/(4.*rt6) + (conj(Ep3a)*conj(r0713))/8. + (conj(Em3a)*conj(r0715))/8. + (Ep2a*r0709)/(4.*rt6) - (Em2a*r0711)/(4.*rt6) - (Ep3a*r0713)/8. - (Em3a*r0715)/8. + conj(r0706)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - conj(r0807)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0706*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0807*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0709_dt = (-(gt*r0709) - (gt + g1)*r0709)/2. - i*((conj(Ep3a)*conj(r0913))/8. + (conj(Em3a)*conj(r0915))/8. - (conj(Em1a)*r0701)/4. - (conj(Ep1a)*r0703)/(4.*rt6) + (conj(Ep2a)*r0707)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0709 - (conj(Ep2a)*r0909)/(4.*rt6) + (conj(Em2a)*r1109)/(4.*rt6) + r0609*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0710*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r0809*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0709*(-delta1 - v*Kvec1 - WLz/6.));
+dr0710_dt = (-(gt*r0710) - (gt + g1)*r0710)/2. - i*((conj(Ep2a)*conj(r0807))/(4.*rt6) - (conj(Ep2a)*conj(r1009))/(4.*rt6) + (conj(Ep3a)*conj(r1013))/8. + (conj(Em3a)*conj(r1015))/8. - (conj(Em1a)*r0702)/(4.*rt2) - (conj(Ep1a)*r0704)/(4.*rt2) - (conj(Em2a)*r0706)/(4.*rt6) + (delta1 + v*Kvec1)*r0710 + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0710 + (conj(Em2a)*r1110)/(4.*rt6) + r0610*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0711*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0709*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0810*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0711_dt = (-(gt*r0711) - (gt + g1)*r0711)/2. - i*(-(conj(Ep2a)*conj(r1109))/(4.*rt6) + (conj(Ep3a)*conj(r1113))/8. + (conj(Em3a)*conj(r1115))/8. - (conj(Em1a)*r0703)/(4.*rt6) - (conj(Ep1a)*r0705)/4. - (conj(Em2a)*r0707)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0711 + (conj(Em2a)*r1111)/(4.*rt6) + r0611*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0710*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0811*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0711*(-delta1 - v*Kvec1 + WLz/6.));
+dr0712_dt = (-(gt*r0712) - (gt + g2)*r0712)/2. - i*(-(conj(Ep4a)*r0702)/(4.*rt6) - (conj(Ep3a)*r0706)/(4.*rt2) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0712 - (conj(Ep2a)*r0912)/(4.*rt6) + (conj(Em2a)*r1112)/(4.*rt6) + (conj(Ep3a)*r1312)/8. + (conj(Em3a)*r1512)/8. - r0713*((2*WLx)/3. + (2*i*WLy)/3.) + r0612*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0812*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0712*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0713_dt = (-(gt*r0713) - (gt + g2)*r0713)/2. - i*((conj(Em4a)*r0701)/(4.*rt6) - (conj(Ep4a)*r0703)/8. - (conj(Ep3a)*r0707)/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0713 - (conj(Ep2a)*r0913)/(4.*rt6) + (conj(Em2a)*r1113)/(4.*rt6) + (conj(Ep3a)*r1313)/8. + (conj(Em3a)*r1513)/8. - r0712*((2*WLx)/3. - (2*i*WLy)/3.) - r0714*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0613*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0813*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0713*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0714_dt = (-(gt*r0714) - (gt + g2)*r0714)/2. - i*(-(conj(Ep3a)*conj(r0807))/(8.*rt3) + (conj(Ep3a)*conj(r1413))/8. + (conj(Em4a)*r0702)/8. - (conj(Ep4a)*r0704)/8. - (conj(Em3a)*r0706)/(8.*rt3) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0714 - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0714 - (conj(Ep2a)*r0914)/(4.*rt6) + (conj(Em2a)*r1114)/(4.*rt6) + (conj(Em3a)*r1514)/8. - r0713*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0715*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0614*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0814*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0715_dt = (-(gt*r0715) - (gt + g2)*r0715)/2. - i*((conj(Ep3a)*conj(r1513))/8. + (conj(Em4a)*r0703)/8. - (conj(Ep4a)*r0705)/(4.*rt6) - (conj(Em3a)*r0707)/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0715 - (conj(Ep2a)*r0915)/(4.*rt6) + (conj(Em2a)*r1115)/(4.*rt6) + (conj(Em3a)*r1515)/8. - r0716*((2*WLx)/3. + (2*i*WLy)/3.) - r0714*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0615*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0815*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0715*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr0716_dt = (-(gt*r0716) - (gt + g2)*r0716)/2. - i*(-(conj(Em3a)*conj(r0807))/(4.*rt2) + (conj(Ep3a)*conj(r1613))/8. + (conj(Em3a)*conj(r1615))/8. + (conj(Em4a)*r0704)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0716 - (conj(Ep2a)*r0916)/(4.*rt6) + (conj(Em2a)*r1116)/(4.*rt6) - r0715*((2*WLx)/3. - (2*i*WLy)/3.) + r0616*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0816*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0716*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr0801_dt = -(gt*r0801) - i*(-(conj(Ep2a)*conj(r0110))/(4.*rt6) + (conj(Ep3a)*conj(r0114))/(8.*rt3) + (conj(Em3a)*conj(r0116))/(4.*rt2) - (Em1a*r0809)/4. + (Em4a*r0813)/(4.*rt6) - r0802*(WLx/2. + (i*WLy)/2.) + r0701*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0801*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0801*WLz);
+dr0802_dt = -(gt*r0802) - i*(-(conj(Ep2a)*conj(r0210))/(4.*rt6) + (conj(Ep3a)*conj(r0214))/(8.*rt3) + (conj(Em3a)*conj(r0216))/(4.*rt2) - (Em1a*r0810)/(4.*rt2) - (Ep4a*r0812)/(4.*rt6) + (Em4a*r0814)/8. - r0801*(WLx/2. - (i*WLy)/2.) - r0803*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0702*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0802*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - (r0802*WLz)/2.);
+dr0803_dt = -(gt*r0803) - i*(-(conj(Ep2a)*conj(r0310))/(4.*rt6) + (conj(Ep3a)*conj(r0314))/(8.*rt3) + (conj(Em3a)*conj(r0316))/(4.*rt2) - (Ep1a*r0809)/(4.*rt6) - (Em1a*r0811)/(4.*rt6) - (Ep4a*r0813)/8. + (Em4a*r0815)/8. - r0802*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0804*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0703*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0803*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0804_dt = -(gt*r0804) - i*(-(conj(Ep2a)*conj(r0410))/(4.*rt6) + (conj(Ep3a)*conj(r0414))/(8.*rt3) + (conj(Em3a)*conj(r0416))/(4.*rt2) - (Ep1a*r0810)/(4.*rt2) - (Ep4a*r0814)/8. + (Em4a*r0816)/(4.*rt6) - r0805*(WLx/2. + (i*WLy)/2.) - r0803*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0704*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0804*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) + (r0804*WLz)/2.);
+dr0805_dt = -(gt*r0805) - i*(-(conj(Ep2a)*conj(r0510))/(4.*rt6) + (conj(Ep3a)*conj(r0514))/(8.*rt3) + (conj(Em3a)*conj(r0516))/(4.*rt2) - (Ep1a*r0811)/4. - (Ep4a*r0815)/(4.*rt6) - r0804*(WLx/2. - (i*WLy)/2.) + r0705*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0805*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) + r0805*WLz);
+dr0806_dt = -(gt*r0806) - (g1*r1109)/12. + (g2*r1412)/(2.*rt6) + (g2*r1513)/4. + (g2*r1614)/(2.*rt6) - i*(-(conj(Ep2a)*conj(r0610))/(4.*rt6) + (conj(Ep3a)*conj(r0614))/(8.*rt3) + (conj(Em3a)*conj(r0616))/(4.*rt2) - (Em2a*r0810)/(4.*rt6) - (Ep3a*r0812)/(4.*rt2) - (Em3a*r0814)/(8.*rt3) + r0706*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0807*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0806*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + r0806*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0807_dt = -(gt*r0807) + (g1*r1009)/12. + (g2*r1413)/(4.*rt3) + (g2*r1514)/(2.*rt3) + (g2*r1615)/(2.*rt2) - i*(-(conj(Ep2a)*conj(r0710))/(4.*rt6) + (conj(Ep3a)*conj(r0714))/(8.*rt3) + (conj(Em3a)*conj(r0716))/(4.*rt2) - (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0807 + (Ep2a*r0809)/(4.*rt6) - (Em2a*r0811)/(4.*rt6) - (Ep3a*r0813)/8. - (Em3a*r0815)/8. + r0707*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0808*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0806*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0807*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0808_dt = gt/8. - gt*r0808 + (g1*r1010)/12. + (g1*r1111)/12. + (g2*r1414)/12. + (g2*r1515)/4. + (g2*r1616)/2. - i*(-(conj(Ep2a)*conj(r0810))/(4.*rt6) + (conj(Ep3a)*conj(r0814))/(8.*rt3) + (conj(Em3a)*conj(r0816))/(4.*rt2) + (Ep2a*r0810)/(4.*rt6) - (Ep3a*r0814)/(8.*rt3) - (Em3a*r0816)/(4.*rt2) + conj(r0807)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0807*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0809_dt = (-(gt*r0809) - (gt + g1)*r0809)/2. - i*((conj(Ep3a)*conj(r0914))/(8.*rt3) + (conj(Em3a)*conj(r0916))/(4.*rt2) - (conj(Em1a)*r0801)/4. - (conj(Ep1a)*r0803)/(4.*rt6) + (conj(Ep2a)*r0807)/(4.*rt6) - (conj(Ep2a)*r1009)/(4.*rt6) + r0709*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0810*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0809*(-delta1 - v*Kvec1 - WLz/6.) + r0809*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0810_dt = (-(gt*r0810) - (gt + g1)*r0810)/2. - i*((conj(Ep3a)*conj(r1014))/(8.*rt3) + (conj(Em3a)*conj(r1016))/(4.*rt2) - (conj(Em1a)*r0802)/(4.*rt2) - (conj(Ep1a)*r0804)/(4.*rt2) - (conj(Em2a)*r0806)/(4.*rt6) + (conj(Ep2a)*r0808)/(4.*rt6) + (delta1 + v*Kvec1)*r0810 - (conj(Ep2a)*r1010)/(4.*rt6) + r0710*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0811*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0809*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0810*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0811_dt = (-(gt*r0811) - (gt + g1)*r0811)/2. - i*(-(conj(Ep2a)*conj(r1110))/(4.*rt6) + (conj(Ep3a)*conj(r1114))/(8.*rt3) + (conj(Em3a)*conj(r1116))/(4.*rt2) - (conj(Em1a)*r0803)/(4.*rt6) - (conj(Ep1a)*r0805)/4. - (conj(Em2a)*r0807)/(4.*rt6) + r0711*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0810*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0811*(-delta1 - v*Kvec1 + WLz/6.) + r0811*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0812_dt = (-(gt*r0812) - (gt + g2)*r0812)/2. - i*(-(conj(Ep4a)*r0802)/(4.*rt6) - (conj(Ep3a)*r0806)/(4.*rt2) - (conj(Ep2a)*r1012)/(4.*rt6) + (conj(Ep3a)*r1412)/(8.*rt3) + (conj(Em3a)*r1612)/(4.*rt2) - r0813*((2*WLx)/3. + (2*i*WLy)/3.) + r0712*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0812*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0812*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0813_dt = (-(gt*r0813) - (gt + g2)*r0813)/2. - i*((conj(Em4a)*r0801)/(4.*rt6) - (conj(Ep4a)*r0803)/8. - (conj(Ep3a)*r0807)/8. - (conj(Ep2a)*r1013)/(4.*rt6) + (conj(Ep3a)*r1413)/(8.*rt3) + (conj(Em3a)*r1613)/(4.*rt2) - r0812*((2*WLx)/3. - (2*i*WLy)/3.) - r0814*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0713*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0813*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0813*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0814_dt = (-(gt*r0814) - (gt + g2)*r0814)/2. - i*((conj(Em4a)*r0802)/8. - (conj(Ep4a)*r0804)/8. - (conj(Em3a)*r0806)/(8.*rt3) - (conj(Ep3a)*r0808)/(8.*rt3) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0814 - (conj(Ep2a)*r1014)/(4.*rt6) + (conj(Ep3a)*r1414)/(8.*rt3) + (conj(Em3a)*r1614)/(4.*rt2) - r0813*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0815*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0714*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0814*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0815_dt = (-(gt*r0815) - (gt + g2)*r0815)/2. - i*((conj(Ep3a)*conj(r1514))/(8.*rt3) + (conj(Em4a)*r0803)/8. - (conj(Ep4a)*r0805)/(4.*rt6) - (conj(Em3a)*r0807)/8. - (conj(Ep2a)*r1015)/(4.*rt6) + (conj(Em3a)*r1615)/(4.*rt2) - r0816*((2*WLx)/3. + (2*i*WLy)/3.) - r0814*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0715*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0815*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0815*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0816_dt = (-(gt*r0816) - (gt + g2)*r0816)/2. - i*((conj(Ep3a)*conj(r1614))/(8.*rt3) + (conj(Em4a)*r0804)/(4.*rt6) - (conj(Em3a)*r0808)/(4.*rt2) - (conj(Ep2a)*r1016)/(4.*rt6) + (conj(Em3a)*r1616)/(4.*rt2) - r0815*((2*WLx)/3. - (2*i*WLy)/3.) + r0716*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0816*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0816*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0909_dt = -((gt + g1)*r0909) - i*(-(conj(Em1a)*conj(r0109))/4. - (conj(Ep1a)*conj(r0309))/(4.*rt6) + (conj(Ep2a)*conj(r0709))/(4.*rt6) + (Em1a*r0109)/4. + (Ep1a*r0309)/(4.*rt6) - (Ep2a*r0709)/(4.*rt6) - conj(r1009)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1009*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr0912_dt = (-((gt + g1)*r0912) - (gt + g2)*r0912)/2. - i*(-(conj(Ep4a)*conj(r0209))/(4.*rt6) - (conj(Ep3a)*conj(r0609))/(4.*rt2) + (Em1a*r0112)/4. + (Ep1a*r0312)/(4.*rt6) - (Ep2a*r0712)/(4.*rt6) - r0913*((2*WLx)/3. + (2*i*WLy)/3.) + r1012*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0912*(-delta1 - v*Kvec1 - WLz/6.) - r0912*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0913_dt = (-((gt + g1)*r0913) - (gt + g2)*r0913)/2. - i*((conj(Em4a)*conj(r0109))/(4.*rt6) - (conj(Ep4a)*conj(r0309))/8. - (conj(Ep3a)*conj(r0709))/8. + (Em1a*r0113)/4. + (Ep1a*r0313)/(4.*rt6) - (Ep2a*r0713)/(4.*rt6) - r0912*((2*WLx)/3. - (2*i*WLy)/3.) - r0914*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1013*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0913*(-delta1 - v*Kvec1 - WLz/6.) - r0913*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0914_dt = (-((gt + g1)*r0914) - (gt + g2)*r0914)/2. - i*((conj(Em4a)*conj(r0209))/8. - (conj(Ep4a)*conj(r0409))/8. - (conj(Em3a)*conj(r0609))/(8.*rt3) - (conj(Ep3a)*conj(r0809))/(8.*rt3) + (Em1a*r0114)/4. + (Ep1a*r0314)/(4.*rt6) - (Ep2a*r0714)/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0914 - r0913*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0915*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1014*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0914*(-delta1 - v*Kvec1 - WLz/6.));
+dr0915_dt = (-((gt + g1)*r0915) - (gt + g2)*r0915)/2. - i*((conj(Em4a)*conj(r0309))/8. - (conj(Ep4a)*conj(r0509))/(4.*rt6) - (conj(Em3a)*conj(r0709))/8. + (Em1a*r0115)/4. + (Ep1a*r0315)/(4.*rt6) - (Ep2a*r0715)/(4.*rt6) - r0916*((2*WLx)/3. + (2*i*WLy)/3.) - r0914*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1015*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0915*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0915*(-delta1 - v*Kvec1 - WLz/6.));
+dr0916_dt = (-((gt + g1)*r0916) - (gt + g2)*r0916)/2. - i*((conj(Em4a)*conj(r0409))/(4.*rt6) - (conj(Em3a)*conj(r0809))/(4.*rt2) + (Em1a*r0116)/4. + (Ep1a*r0316)/(4.*rt6) - (Ep2a*r0716)/(4.*rt6) - r0915*((2*WLx)/3. - (2*i*WLy)/3.) + r1016*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0916*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0916*(-delta1 - v*Kvec1 - WLz/6.));
+dr1009_dt = -((gt + g1)*r1009) - i*(-(conj(Em1a)*conj(r0110))/4. - (conj(Ep1a)*conj(r0310))/(4.*rt6) + (conj(Ep2a)*conj(r0710))/(4.*rt6) + (Em1a*r0209)/(4.*rt2) + (Ep1a*r0409)/(4.*rt2) + (Em2a*r0609)/(4.*rt6) - (Ep2a*r0809)/(4.*rt6) - (delta1 + v*Kvec1)*r1009 + r0909*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1010*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1009*(-delta1 - v*Kvec1 - WLz/6.));
+dr1010_dt = -((gt + g1)*r1010) - i*(-(conj(Em1a)*conj(r0210))/(4.*rt2) - (conj(Ep1a)*conj(r0410))/(4.*rt2) - (conj(Em2a)*conj(r0610))/(4.*rt6) + (conj(Ep2a)*conj(r0810))/(4.*rt6) + (Em1a*r0210)/(4.*rt2) + (Ep1a*r0410)/(4.*rt2) + (Em2a*r0610)/(4.*rt6) - (Ep2a*r0810)/(4.*rt6) + conj(r1009)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - conj(r1110)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1009*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r1110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr1012_dt = (-((gt + g1)*r1012) - (gt + g2)*r1012)/2. - i*(-(conj(Ep4a)*conj(r0210))/(4.*rt6) - (conj(Ep3a)*conj(r0610))/(4.*rt2) + (Em1a*r0212)/(4.*rt2) + (Ep1a*r0412)/(4.*rt2) + (Em2a*r0612)/(4.*rt6) - (Ep2a*r0812)/(4.*rt6) - (delta1 + v*Kvec1)*r1012 - r1013*((2*WLx)/3. + (2*i*WLy)/3.) + r0912*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1112*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1012*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1013_dt = (-((gt + g1)*r1013) - (gt + g2)*r1013)/2. - i*((conj(Em4a)*conj(r0110))/(4.*rt6) - (conj(Ep4a)*conj(r0310))/8. - (conj(Ep3a)*conj(r0710))/8. + (Em1a*r0213)/(4.*rt2) + (Ep1a*r0413)/(4.*rt2) + (Em2a*r0613)/(4.*rt6) - (Ep2a*r0813)/(4.*rt6) - (delta1 + v*Kvec1)*r1013 - r1012*((2*WLx)/3. - (2*i*WLy)/3.) - r1014*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0913*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1113*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1013*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1014_dt = (-((gt + g1)*r1014) - (gt + g2)*r1014)/2. - i*((conj(Em4a)*conj(r0210))/8. - (conj(Ep4a)*conj(r0410))/8. - (conj(Em3a)*conj(r0610))/(8.*rt3) - (conj(Ep3a)*conj(r0810))/(8.*rt3) + (Em1a*r0214)/(4.*rt2) + (Ep1a*r0414)/(4.*rt2) + (Em2a*r0614)/(4.*rt6) - (Ep2a*r0814)/(4.*rt6) - (delta1 + v*Kvec1)*r1014 - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1014 - r1013*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r1015*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0914*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1114*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr1015_dt = (-((gt + g1)*r1015) - (gt + g2)*r1015)/2. - i*((conj(Em4a)*conj(r0310))/8. - (conj(Ep4a)*conj(r0510))/(4.*rt6) - (conj(Em3a)*conj(r0710))/8. + (Em1a*r0215)/(4.*rt2) + (Ep1a*r0415)/(4.*rt2) + (Em2a*r0615)/(4.*rt6) - (Ep2a*r0815)/(4.*rt6) - (delta1 + v*Kvec1)*r1015 - r1016*((2*WLx)/3. + (2*i*WLy)/3.) - r1014*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0915*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1115*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1015*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr1016_dt = (-((gt + g1)*r1016) - (gt + g2)*r1016)/2. - i*((conj(Em4a)*conj(r0410))/(4.*rt6) - (conj(Em3a)*conj(r0810))/(4.*rt2) + (Em1a*r0216)/(4.*rt2) + (Ep1a*r0416)/(4.*rt2) + (Em2a*r0616)/(4.*rt6) - (Ep2a*r0816)/(4.*rt6) - (delta1 + v*Kvec1)*r1016 - r1015*((2*WLx)/3. - (2*i*WLy)/3.) + r0916*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1116*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1016*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr1109_dt = -((gt + g1)*r1109) - i*(-(conj(Em1a)*conj(r0111))/4. - (conj(Ep1a)*conj(r0311))/(4.*rt6) + (conj(Ep2a)*conj(r0711))/(4.*rt6) + (Em1a*r0309)/(4.*rt6) + (Ep1a*r0509)/4. + (Em2a*r0709)/(4.*rt6) + r1009*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1110*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1109*(-delta1 - v*Kvec1 - WLz/6.) + r1109*(-delta1 - v*Kvec1 + WLz/6.));
+dr1110_dt = -((gt + g1)*r1110) - i*(-(conj(Em1a)*conj(r0211))/(4.*rt2) - (conj(Ep1a)*conj(r0411))/(4.*rt2) - (conj(Em2a)*conj(r0611))/(4.*rt6) + (conj(Ep2a)*conj(r0811))/(4.*rt6) + (Em1a*r0310)/(4.*rt6) + (Ep1a*r0510)/4. + (Em2a*r0710)/(4.*rt6) + (delta1 + v*Kvec1)*r1110 + r1010*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1111*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r1110*(-delta1 - v*Kvec1 + WLz/6.));
+dr1111_dt = -((gt + g1)*r1111) - i*(-(conj(Em1a)*conj(r0311))/(4.*rt6) - (conj(Ep1a)*conj(r0511))/4. - (conj(Em2a)*conj(r0711))/(4.*rt6) + (Em1a*r0311)/(4.*rt6) + (Ep1a*r0511)/4. + (Em2a*r0711)/(4.*rt6) + conj(r1110)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr1112_dt = (-((gt + g1)*r1112) - (gt + g2)*r1112)/2. - i*(-(conj(Ep4a)*conj(r0211))/(4.*rt6) - (conj(Ep3a)*conj(r0611))/(4.*rt2) + (Em1a*r0312)/(4.*rt6) + (Ep1a*r0512)/4. + (Em2a*r0712)/(4.*rt6) - r1113*((2*WLx)/3. + (2*i*WLy)/3.) + r1012*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1112*(-delta1 - v*Kvec1 + WLz/6.) - r1112*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1113_dt = (-((gt + g1)*r1113) - (gt + g2)*r1113)/2. - i*((conj(Em4a)*conj(r0111))/(4.*rt6) - (conj(Ep4a)*conj(r0311))/8. - (conj(Ep3a)*conj(r0711))/8. + (Em1a*r0313)/(4.*rt6) + (Ep1a*r0513)/4. + (Em2a*r0713)/(4.*rt6) - r1112*((2*WLx)/3. - (2*i*WLy)/3.) - r1114*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1013*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1113*(-delta1 - v*Kvec1 + WLz/6.) - r1113*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1114_dt = (-((gt + g1)*r1114) - (gt + g2)*r1114)/2. - i*((conj(Em4a)*conj(r0211))/8. - (conj(Ep4a)*conj(r0411))/8. - (conj(Em3a)*conj(r0611))/(8.*rt3) - (conj(Ep3a)*conj(r0811))/(8.*rt3) + (Em1a*r0314)/(4.*rt6) + (Ep1a*r0514)/4. + (Em2a*r0714)/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1114 - r1113*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r1115*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1014*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1114*(-delta1 - v*Kvec1 + WLz/6.));
+dr1115_dt = (-((gt + g1)*r1115) - (gt + g2)*r1115)/2. - i*((conj(Em4a)*conj(r0311))/8. - (conj(Ep4a)*conj(r0511))/(4.*rt6) - (conj(Em3a)*conj(r0711))/8. + (Em1a*r0315)/(4.*rt6) + (Ep1a*r0515)/4. + (Em2a*r0715)/(4.*rt6) - r1116*((2*WLx)/3. + (2*i*WLy)/3.) - r1114*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1015*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1115*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r1115*(-delta1 - v*Kvec1 + WLz/6.));
+dr1116_dt = (-((gt + g1)*r1116) - (gt + g2)*r1116)/2. - i*((conj(Em4a)*conj(r0411))/(4.*rt6) - (conj(Em3a)*conj(r0811))/(4.*rt2) + (Em1a*r0316)/(4.*rt6) + (Ep1a*r0516)/4. + (Em2a*r0716)/(4.*rt6) - r1115*((2*WLx)/3. - (2*i*WLy)/3.) + r1016*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1116*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r1116*(-delta1 - v*Kvec1 + WLz/6.));
+dr1212_dt = -((gt + g2)*r1212) - i*(-(conj(Ep4a)*conj(r0212))/(4.*rt6) - (conj(Ep3a)*conj(r0612))/(4.*rt2) + (Ep4a*r0212)/(4.*rt6) + (Ep3a*r0612)/(4.*rt2) + r1312*((2*WLx)/3. - (2*i*WLy)/3.) - conj(r1312)*((2*WLx)/3. + (2*i*WLy)/3.));
+dr1312_dt = -((gt + g2)*r1312) - i*(-(conj(Ep4a)*conj(r0213))/(4.*rt6) - (conj(Ep3a)*conj(r0613))/(4.*rt2) - (Em4a*r0112)/(4.*rt6) + (Ep4a*r0312)/8. + (Ep3a*r0712)/8. + r1212*((2*WLx)/3. + (2*i*WLy)/3.) - r1313*((2*WLx)/3. + (2*i*WLy)/3.) + r1412*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - r1312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1313_dt = -((gt + g2)*r1313) - i*((conj(Em4a)*conj(r0113))/(4.*rt6) - (conj(Ep4a)*conj(r0313))/8. - (conj(Ep3a)*conj(r0713))/8. - (Em4a*r0113)/(4.*rt6) + (Ep4a*r0313)/8. + (Ep3a*r0713)/8. - r1312*((2*WLx)/3. - (2*i*WLy)/3.) + conj(r1312)*((2*WLx)/3. + (2*i*WLy)/3.) + r1413*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - conj(r1413)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy));
+dr1412_dt = -((gt + g2)*r1412) - i*(-(conj(Ep4a)*conj(r0214))/(4.*rt6) - (conj(Ep3a)*conj(r0614))/(4.*rt2) - (Em4a*r0212)/8. + (Ep4a*r0412)/8. + (Em3a*r0612)/(8.*rt3) + (Ep3a*r0812)/(8.*rt3) + (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1412 - r1413*((2*WLx)/3. + (2*i*WLy)/3.) + r1512*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1312*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1412*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1413_dt = -((gt + g2)*r1413) - i*((conj(Em4a)*conj(r0114))/(4.*rt6) - (conj(Ep4a)*conj(r0314))/8. - (conj(Ep3a)*conj(r0714))/8. - (Em4a*r0213)/8. + (Ep4a*r0413)/8. + (Em3a*r0613)/(8.*rt3) + (Ep3a*r0813)/(8.*rt3) + (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1413 - r1412*((2*WLx)/3. - (2*i*WLy)/3.) + r1513*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1313*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1414*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1413*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1414_dt = -((gt + g2)*r1414) - i*((conj(Em4a)*conj(r0214))/8. - (conj(Ep4a)*conj(r0414))/8. - (conj(Em3a)*conj(r0614))/(8.*rt3) - (conj(Ep3a)*conj(r0814))/(8.*rt3) - (Em4a*r0214)/8. + (Ep4a*r0414)/8. + (Em3a*r0614)/(8.*rt3) + (Ep3a*r0814)/(8.*rt3) - r1413*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1514*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + conj(r1413)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - conj(r1514)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy));
+dr1512_dt = -((gt + g2)*r1512) - i*(-(conj(Ep4a)*conj(r0215))/(4.*rt6) - (conj(Ep3a)*conj(r0615))/(4.*rt2) - (Em4a*r0312)/8. + (Ep4a*r0512)/(4.*rt6) + (Em3a*r0712)/8. + r1612*((2*WLx)/3. - (2*i*WLy)/3.) - r1513*((2*WLx)/3. + (2*i*WLy)/3.) + r1412*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r1512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1513_dt = -((gt + g2)*r1513) - i*((conj(Em4a)*conj(r0115))/(4.*rt6) - (conj(Ep4a)*conj(r0315))/8. - (conj(Ep3a)*conj(r0715))/8. - (Em4a*r0313)/8. + (Ep4a*r0513)/(4.*rt6) + (Em3a*r0713)/8. - r1512*((2*WLx)/3. - (2*i*WLy)/3.) + r1613*((2*WLx)/3. - (2*i*WLy)/3.) + r1413*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1514*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r1513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1514_dt = -((gt + g2)*r1514) - i*((conj(Em4a)*conj(r0215))/8. - (conj(Ep4a)*conj(r0415))/8. - (conj(Em3a)*conj(r0615))/(8.*rt3) - (conj(Ep3a)*conj(r0815))/(8.*rt3) - (Em4a*r0314)/8. + (Ep4a*r0514)/(4.*rt6) + (Em3a*r0714)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1514 + r1614*((2*WLx)/3. - (2*i*WLy)/3.) - r1513*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1414*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1515*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1514*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr1515_dt = -((gt + g2)*r1515) - i*((conj(Em4a)*conj(r0315))/8. - (conj(Ep4a)*conj(r0515))/(4.*rt6) - (conj(Em3a)*conj(r0715))/8. - (Em4a*r0315)/8. + (Ep4a*r0515)/(4.*rt6) + (Em3a*r0715)/8. + r1615*((2*WLx)/3. - (2*i*WLy)/3.) - conj(r1615)*((2*WLx)/3. + (2*i*WLy)/3.) - r1514*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + conj(r1514)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy));
+dr1612_dt = -((gt + g2)*r1612) - i*(-(conj(Ep4a)*conj(r0216))/(4.*rt6) - (conj(Ep3a)*conj(r0616))/(4.*rt2) - (Em4a*r0412)/(4.*rt6) + (Em3a*r0812)/(4.*rt2) + r1512*((2*WLx)/3. + (2*i*WLy)/3.) - r1613*((2*WLx)/3. + (2*i*WLy)/3.) + r1612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1613_dt = -((gt + g2)*r1613) - i*((conj(Em4a)*conj(r0116))/(4.*rt6) - (conj(Ep4a)*conj(r0316))/8. - (conj(Ep3a)*conj(r0716))/8. - (Em4a*r0413)/(4.*rt6) + (Em3a*r0813)/(4.*rt2) - r1612*((2*WLx)/3. - (2*i*WLy)/3.) + r1513*((2*WLx)/3. + (2*i*WLy)/3.) - r1614*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1614_dt = -((gt + g2)*r1614) - i*((conj(Em4a)*conj(r0216))/8. - (conj(Ep4a)*conj(r0416))/8. - (conj(Em3a)*conj(r0616))/(8.*rt3) - (conj(Ep3a)*conj(r0816))/(8.*rt3) - (Em4a*r0414)/(4.*rt6) + (Em3a*r0814)/(4.*rt2) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1614 + r1514*((2*WLx)/3. + (2*i*WLy)/3.) - r1613*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r1615*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1614*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr1615_dt = -((gt + g2)*r1615) - i*((conj(Em4a)*conj(r0316))/8. - (conj(Ep4a)*conj(r0516))/(4.*rt6) - (conj(Em3a)*conj(r0716))/8. - (Em4a*r0415)/(4.*rt6) + (Em3a*r0815)/(4.*rt2) + r1515*((2*WLx)/3. + (2*i*WLy)/3.) - r1616*((2*WLx)/3. + (2*i*WLy)/3.) - r1614*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr1616_dt = -((gt + g2)*r1616) - i*((conj(Em4a)*conj(r0416))/(4.*rt6) - (conj(Em3a)*conj(r0816))/(4.*rt2) - (Em4a*r0416)/(4.*rt6) + (Em3a*r0816)/(4.*rt2) - r1615*((2*WLx)/3. - (2*i*WLy)/3.) + conj(r1615)*((2*WLx)/3. + (2*i*WLy)/3.));
+//---------------- RbEquations.cdata ends  ------------------
+]]>
diff --git a/xmds2/realistic_Rb_and_fields/RbInits.cdata b/xmds2/realistic_Rb_and_fields/RbInits.cdata
new file mode 100644
index 0000000..0e04ec5
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/RbInits.cdata
@@ -0,0 +1,140 @@
+<![CDATA[
+//---------------- RbInits.cdata starts ------------------
+r0101 = 0.125;
+r0109 = 0;
+r0110 = 0;
+r0111 = 0;
+r0112 = 0;
+r0113 = 0;
+r0114 = 0;
+r0115 = 0;
+r0116 = 0;
+r0201 = 0;
+r0202 = 0.125;
+r0209 = 0;
+r0210 = 0;
+r0211 = 0;
+r0212 = 0;
+r0213 = 0;
+r0214 = 0;
+r0215 = 0;
+r0216 = 0;
+r0301 = 0;
+r0302 = 0;
+r0303 = 0.125;
+r0309 = 0;
+r0310 = 0;
+r0311 = 0;
+r0312 = 0;
+r0313 = 0;
+r0314 = 0;
+r0315 = 0;
+r0316 = 0;
+r0401 = 0;
+r0402 = 0;
+r0403 = 0;
+r0404 = 0.125;
+r0409 = 0;
+r0410 = 0;
+r0411 = 0;
+r0412 = 0;
+r0413 = 0;
+r0414 = 0;
+r0415 = 0;
+r0416 = 0;
+r0501 = 0;
+r0502 = 0;
+r0503 = 0;
+r0504 = 0;
+r0505 = 0.125;
+r0509 = 0;
+r0510 = 0;
+r0511 = 0;
+r0512 = 0;
+r0513 = 0;
+r0514 = 0;
+r0515 = 0;
+r0516 = 0;
+r0601 = 0;
+r0602 = 0;
+r0603 = 0;
+r0604 = 0;
+r0605 = 0;
+r0606 = 0.125;
+r0609 = 0;
+r0610 = 0;
+r0611 = 0;
+r0612 = 0;
+r0613 = 0;
+r0614 = 0;
+r0615 = 0;
+r0616 = 0;
+r0701 = 0;
+r0702 = 0;
+r0703 = 0;
+r0704 = 0;
+r0705 = 0;
+r0706 = 0;
+r0707 = 0.125;
+r0709 = 0;
+r0710 = 0;
+r0711 = 0;
+r0712 = 0;
+r0713 = 0;
+r0714 = 0;
+r0715 = 0;
+r0716 = 0;
+r0801 = 0;
+r0802 = 0;
+r0803 = 0;
+r0804 = 0;
+r0805 = 0;
+r0806 = 0;
+r0807 = 0;
+r0808 = 0.125;
+r0809 = 0;
+r0810 = 0;
+r0811 = 0;
+r0812 = 0;
+r0813 = 0;
+r0814 = 0;
+r0815 = 0;
+r0816 = 0;
+r0909 = 0;
+r0912 = 0;
+r0913 = 0;
+r0914 = 0;
+r0915 = 0;
+r0916 = 0;
+r1009 = 0;
+r1010 = 0;
+r1012 = 0;
+r1013 = 0;
+r1014 = 0;
+r1015 = 0;
+r1016 = 0;
+r1109 = 0;
+r1110 = 0;
+r1111 = 0;
+r1112 = 0;
+r1113 = 0;
+r1114 = 0;
+r1115 = 0;
+r1116 = 0;
+r1212 = 0;
+r1312 = 0;
+r1313 = 0;
+r1412 = 0;
+r1413 = 0;
+r1414 = 0;
+r1512 = 0;
+r1513 = 0;
+r1514 = 0;
+r1515 = 0;
+r1612 = 0;
+r1613 = 0;
+r1614 = 0;
+r1615 = 0;
+r1616 = 0;
+//---------------- RbInits.cdata ends  ------------------
+]]>
diff --git a/xmds2/realistic_Rb_and_fields/RbPropEquations.cdata b/xmds2/realistic_Rb_and_fields/RbPropEquations.cdata
new file mode 100644
index 0000000..f098f3d
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/RbPropEquations.cdata
@@ -0,0 +1,12 @@
+<![CDATA[
+//---------------- RbPropEquations.cdata starts ------------------
+dEp1_dz = -((i*Ndens*(rt2*conj(r0309) + rt6*(conj(r0410) + rt2*conj(r0511)))*eta1)/(rt2*rt6)) - Lt[Ep1];
+dEm1_dz = -((i*Ndens*(rt2*rt6*conj(r0109) + rt6*conj(r0210) + rt2*conj(r0311))*eta1)/(rt2*rt6)) - Lt[Em1];
+dEp2_dz = (i*Ndens*(conj(r0709) + conj(r0810))*eta1)/rt6 - Lt[Ep2];
+dEm2_dz = -((i*Ndens*(conj(r0610) + conj(r0711))*eta1)/rt6) - Lt[Em2];
+dEp3_dz = -((i*Ndens*(rt2*rt3*conj(r0612) + rt3*conj(r0713) + conj(r0814))*eta2)/rt3) - Lt[Ep3];
+dEm3_dz = -((i*Ndens*(conj(r0614) + rt3*(conj(r0715) + rt2*conj(r0816)))*eta2)/rt3) - Lt[Em3];
+dEp4_dz = -((i*Ndens*(rt2*conj(r0212) + rt3*conj(r0313) + rt3*conj(r0414) + rt2*conj(r0515))*eta2)/rt3) - Lt[Ep4];
+dEm4_dz = (i*Ndens*(rt2*conj(r0113) + rt3*conj(r0214) + rt3*conj(r0315) + rt2*conj(r0416))*eta2)/rt3 - Lt[Em4];
+//---------------- RbPropEquations.cdata ends  ------------------
+]]>
diff --git a/xmds2/realistic_Rb_and_fields/pp_I2.m b/xmds2/realistic_Rb_and_fields/pp_I2.m
new file mode 100644
index 0000000..c3c6932
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/pp_I2.m
@@ -0,0 +1,82 @@
+% suppress output of plots on display
+set (0, "defaultfigurevisible", "off") 
+
+realistic_Rb_and_fields
+
+%% field I2  propagation
+z_1=z_1*100; % z in cm
+t_1=t_1*1e6; % time now measured in uS
+figure(1)
+%set(gca,'fontsize',20); 
+imagesc(z_1, t_1, Ip2_out_1); colorbar
+tmin=-0.4;
+tmax= 0.4;
+ylim([tmin,tmax],'manual');	
+xlabel('z (cm)')
+ylabel('t (uS)')
+zlabel('I_p2')
+title('I_p2')
+print('-color','-depsc2', '-tight', '-S200,120', 'fields_propagation_Ip2.eps')
+
+figure(1)
+%set(gca,'fontsize',20); 
+imagesc(z_1, t_1, Im2_out_1); colorbar
+tmin=-0.4;
+tmax= 0.4;
+ylim([tmin,tmax],'manual');	
+xlabel('z (cm)')
+ylabel('t (uS)')
+zlabel('I_m2')
+title('I_m2')
+print('-color','-depsc2', '-tight', '-S200,120', 'fields_propagation_Im2.eps')
+
+
+%% field I4  propagation
+figure(3)
+
+imagesc(z_1, t_1, Ip4_out_1); colorbar
+tmin=-0.4;
+tmax= 0.4;
+ylim([tmin,tmax],'manual');	
+xlabel('z (cm)')
+ylabel('t (uS)')
+zlabel('I_p4')
+title('I_p4')
+print('-color','-depsc2', '-tight', '-S200,120', 'fields_propagation_Ip4.eps')
+
+figure(4)
+
+imagesc(z_1, t_1, Im4_out_1); colorbar
+tmin=-0.4;
+tmax= 0.4;
+ylim([tmin,tmax],'manual');	
+xlabel('z (cm)')
+ylabel('t (uS)')
+zlabel('I_m4')
+title('I_m4')
+print('-color','-depsc2', '-tight', '-S200,120', 'fields_propagation_Im4.eps')
+
+
+
+
+
+%% fields before and after the cell
+figure(5)
+%set(gca,'fontsize',30); 
+plot( ...
+	 t_1,Ip2_out_1(:,1),'.-;I_p2 before;', "linewidth", 4  ...
+	,t_1,Im2_out_1(:,1),'.-;I_m2 before;', "linewidth", 4  ...
+	,t_1,Ip2_out_1(:,end), '-;I_p2 after;', "linewidth", 4 ...
+	,t_1,Im2_out_1(:,end), '-;I_m2 after;', "linewidth", 4 ...
+	,t_1,Ip4_out_1(:,end), '-;I_p4 after;', "linewidth", 4 ...
+	,t_1,Im4_out_1(:,end), '-;I_m after;', "linewidth", 4 ...
+	)
+xlabel('t (uS)')
+ylabel('I (1/s)^2')
+title('Fields before and after cell')
+legend('location', 'northeast');
+print('-color','-depsc2', 'fields_before_after_cell.eps')
+
+
+fid_stamp=fopen ("pp_I2.stamp", "a+");
+fclose (fid_stamp);
diff --git a/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
new file mode 100644
index 0000000..33f7918
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/realistic_Rb_and_fields.xmds
@@ -0,0 +1,341 @@
+<?xml version="1.0"?>
+<!-- Below text defines necessary includes files generated by mathematica 
+		 and references to them -->
+<!DOCTYPE simulation [
+<!ENTITY RbAtomConstantsFile SYSTEM "RbAtomConstants.cdata" >
+<!ENTITY RbChosenRhoFile SYSTEM "RbChosenRho.txt" >
+<!ENTITY RbInitsFile SYSTEM "RbInits.cdata" >
+<!ENTITY RbEquationsFile SYSTEM "RbEquations.cdata" >
+<!ENTITY RbPropEquationsFile SYSTEM "RbPropEquations.cdata" >
+]>
+<simulation xmds-version="2">
+	<testing>
+		<arguments> --Ndens=1e15 --Lcell=10.0e-2  --Temperature=1e-3  --Pwidth=0.4e-6  --delta1=0 --delta2=0 --delta3=0  --Ep1o=1e4 --Ep2o=1e2 --Ep3o=1e1 --Ep4o=1e1 --Em1o=1e4 --Em2o=1e2 --Em3o=1e1 --Em4o=1e1 --WLx=0 --WLy=0 --WLz=0</arguments>
+		<xsil_file name="realistic_Rb_and_fields.xsil" expected="realistic_Rb_and_fields_expected.xsil" absolute_tolerance="1e-7" relative_tolerance="1e-5">
+			<moment_group number="0" absolute_tolerance="1e-7" relative_tolerance="1e-6" />
+		</xsil_file>
+	</testing>
+
+	<name>realistic_Rb_and_fields</name>
+
+	<author>Eugeniy Mikhailov</author>
+	<description>
+		License GPL.
+
+		Solving simplified Rb atom model
+		with fields propagation along spatial axis Z
+		with Doppler broadening.
+
+
+		We assume four-wave mixing condition when w3-w4=w2-w1 i.e. fields E3 and E4 drive the same
+		resonance as fields E2 and E1.
+
+
+		*              --------------- | F=1, 2P_3/2 >
+		*                \        \    
+		*                 \ E3_r   \    -------- | F=2, 2P_+1/2 >
+		*                  \   E4_r \   /    \
+		*                   \        \ / E2_l \ 
+		*                    \        /        \ E1_l
+		*   | F=2, 2S_1/2 > --------------      \
+		*                               \        \
+		*                                \        \
+		*                               ------------- | F=1, 2S_1/2 >
+		*            
+
+
+		We are solving 
+			dE/dz+(1/c)*dE/dt=i*eta*rho_ij,  where j level is higher than i.
+			Note that E is actually a Rabi frequency of electromagnetic field not the EM field
+		in xmds terms it looks like
+			dE_dz = i*eta*rhoij - 1/c*L[E], here we moved t dependence to Fourier space
+
+		VERY IMPORTANT: all Rabi frequency should be given in [1/s], if you want to
+		normalize it to something else look drho/dt equation.
+		No need to renormalizes eta as long as its express through
+		the upper level decay rate in the same units as Rabi frequency.
+	</description>
+
+	<features>
+		<globals>
+			<!--atom related constants-->
+			<!--read from Mathematica generated RbAtomConstants.cdata-->
+			&RbAtomConstantsFile;
+
+			<![CDATA[
+				// Some numerical constants
+				const double pi = M_PI; 
+
+				const double c=3.e8;
+				const double k_boltzmann= 1.3806505e-23; // Boltzmann knostant in [J/K]
+				const double lambda=794.7e-9; //wavelength in m
+				// Fields k-vector
+				const double Kvec = 2*M_PI/lambda;  
+				// Simplified k-vectors
+				const double Kvec1 = Kvec, Kvec2=Kvec, Kvec3=Kvec;
+
+				//  ---------  Atom and cell properties -------------------------
+				// range of Maxwell distribution atomic velocities
+				const double mass = (86.909180527 * 1.660538921e-27); // atom mass in [kg] 
+				// above mass expression is written as (expression is isotopic_mass * atomic_mass_unit)
+
+				// Average sqrt(v^2) in Maxwell distribution for one dimension
+				// Maxwell related parameters will be calculated in <arguments> section
+				double v_thermal_averaged=0;
+				// Maxwell distribution velocities range to take in account in [m/s]
+				double V_maxwell_min = 0, V_maxwell_max = 0;
+
+				// repopulation rate (atoms flying in/out the laser beam)  in [1/s]
+				const double gt=0.01 *(2*M_PI*1e6);
+
+				// inner use variables 
+				double probability_v; // will be used as p(v) in Maxwell distribution
+			]]>
+		</globals>
+		<validation kind="run-time"/> <!--allows to put ranges as variables-->
+		<benchmark />
+    <arguments>
+			<!-- Rabi frequency divided by 2 in [1/s] -->
+      <argument name="Ep1o" type="real" default_value="2*1.5*(2*M_PI*1e6)" />
+      <argument name="Em1o" type="real" default_value="2*1.5*(2*M_PI*1e6)" />
+      <argument name="Ep2o" type="real" default_value="0.05*(2*M_PI*1e6)" />
+      <argument name="Em2o" type="real" default_value="0.05*(2*M_PI*1e6)" />
+      <argument name="Ep3o" type="real" default_value="2*3.0*(2*M_PI*1e6)" />
+      <argument name="Em3o" type="real" default_value="2*3.0*(2*M_PI*1e6)" />
+      <argument name="Ep4o" type="real" default_value=".01*(2*M_PI*1e6)" />
+      <argument name="Em4o" type="real" default_value=".01*(2*M_PI*1e6)" />
+			<!-- Fields detuning in [1/s] -->
+      <argument name="delta1"  type="real" default_value="0.0" />
+      <argument name="delta2"  type="real" default_value="0.0" />
+      <argument name="delta3"  type="real" default_value="0.0" />
+			<!--Pulse duration/width [s] -->
+			<argument name="Pwidth"  type="real" default_value="0.1e-6" />
+			<!--  Atom and cell properties -->
+			<!--Cell length [m] -->
+			<argument name="Lcell"  type="real" default_value="1.5e-2" />
+			<!--Density of atoms [1/m^3] -->
+			<argument name="Ndens"  type="real" default_value="1e15" />
+			<!-- Projections of magnetic field in Larmor frequency units [1/s] -->
+			<argument name="WLx"  type="real" default_value="0" />
+			<argument name="WLy"  type="real" default_value="0" />
+			<argument name="WLz"  type="real" default_value="0" />
+			<!--Atoms temperature [K] -->
+			<!--TODO: looks like Temperature > 10 K knocks solver, 
+					 I am guessing detunings are too large and thus it became a stiff equation-->
+			<!--! make sure it is not equal to zero!-->
+			<argument name="Temperature"  type="real" default_value="5" />
+			<!-- This will be executed after arguments/parameters are parsed -->
+			<!-- Read the code Luke: took me a while of reading the xmds2 sources to find it -->
+			<![CDATA[
+				// Average sqrt(v^2) in Maxwell distribution for one dimension
+				if (Temperature == 0)
+					_LOG(_ERROR_LOG_LEVEL, "ERROR: Temperature should be >0 to provide range for Maxwell velocity distribution\n");
+				v_thermal_averaged=sqrt(k_boltzmann*Temperature/mass); 
+				// Maxwell distribution velocities range to take in account in [m/s]
+				// there is almost zero probability for higher velocity p(4*v_av) = 3.3e-04 * p(0)
+				V_maxwell_min = -4*v_thermal_averaged; V_maxwell_max = -V_maxwell_min; 
+			]]>
+    </arguments>
+		<bing />
+		<diagnostics /> 
+		<fftw plan="estimate" threads="1" />
+		<!--<fftw plan="patient" threads="1" />-->
+		<!-- I don't see any speed up on 6 core CPU even if use threads="6" -->
+		<!--<openmp />-->
+		<auto_vectorise />
+		<halt_non_finite />
+	</features>
+
+	<!-- 'z', 't', and 'v'  to have dimensions [m], [s], and [m/s]   -->
+	<geometry>
+		<propagation_dimension> z </propagation_dimension>
+		<transverse_dimensions>
+			<!-- IMPORTANT: looks like having a lot of points in time helps with convergence.
+					 I suspect that time spacing should be small enough to catch
+					 all pulse harmonics and more importantly 1/dt should be larger than
+					 the largest detuning (including Doppler shifts).
+					 Unfortunately calculation time is proportional to lattice size
+					 so we cannot just blindly increase it.
+					 Some rules of thumb:  
+						* lattice="1000"   domain="(-1e-6, 1e-6)" 
+							was good enough detunings up to 155 MHz (980 rad/s) notice that 1/dt=500 MHz
+						* lattice="10000"   domain="(-1e-6, 1e-6)" 
+							works for Doppler averaging in up to 400K for Rb when lasers are zero detuned
+			 -->
+			<dimension name="t"   lattice="10000"   domain="(-1e-6, 1e-6)" />
+			<dimension name="v"   lattice="2"   domain="(V_maxwell_min, V_maxwell_max)" />
+		</transverse_dimensions>
+	</geometry>
+
+	<!-- Rabi frequency --> 
+	<vector name="E_field" type="complex" initial_space="t">
+		 <!--plus/minus circular polarization components-->
+		<components>Ep1 Em1 Ep2 Em2 Ep3 Em3 Ep4 Em4</components>
+		<initialisation>
+			<![CDATA[
+			// Initial (at starting 'z' position) electromagnetic field does not depend on detuning
+			// as well as time
+			Ep1=Ep1o;
+			Em1=Em1o;
+			Ep2=Ep2o*exp(-pow( ((t-0.0)/Pwidth),2) );
+			Em2=Em2o*exp(-pow( ((t-0.0)/Pwidth),2) );
+			Ep3=Ep3o;
+			Em3=Em3o;
+			Ep4=Ep4o;
+			Em4=Em4o;
+			]]>
+		</initialisation>
+	</vector>
+
+	<!--Maxwell distribution probability p(v)-->
+	<vector name="Maxwell_distribution_probabilities" dimensions="v" type="real">
+		<components>probability_v</components>
+		<initialisation>
+			<![CDATA[
+			// TODO: move to the global space/function. This reevaluated many times since it called from dependency requests but it never changes during  the script lifetime since 'v' is fixed.
+			probability_v=1.0/(v_thermal_averaged*sqrt(2*M_PI)) * exp( - mod2(v/v_thermal_averaged)/2.0 ); 
+			]]>
+		</initialisation>
+	</vector>
+
+	<!--Maxwell distribution norm sum(p(v))
+			 Needed since we sum over the grid instead of true integral,
+			 we also have finite cut off velocities-->
+	<vector name="Maxwell_distribution_probabilities_norm" dimensions="" type="real">
+		<components>probability_v_norm</components>
+		<initialisation>
+			<dependencies basis="v">Maxwell_distribution_probabilities</dependencies>
+			<![CDATA[
+			// TODO: move to the global space/function. This reevaluated many times since it called from dependency requests but it never changes during  the script lifetime since 'v' is fixed.
+			probability_v_norm=probability_v;
+			]]>
+		</initialisation>
+	</vector>
+
+
+	<!-- Averaged across Maxwell distribution fields amplitudes -->
+	<computed_vector name="E_field_avgd" dimensions="t" type="complex">
+		<components>Ep1a Em1a Ep2a Em2a Ep3a Em3a Ep4a Em4a</components>
+		<evaluation>
+			<dependencies basis="v">E_field Maxwell_distribution_probabilities Maxwell_distribution_probabilities_norm</dependencies>
+			<![CDATA[
+			double prob_v_normalized=probability_v/probability_v_norm;
+			Ep1a=Ep1*prob_v_normalized;
+			Em1a=Em1*prob_v_normalized;
+			Ep2a=Ep2*prob_v_normalized;
+			Em2a=Em2*prob_v_normalized;
+			Ep3a=Ep3*prob_v_normalized;
+			Em3a=Em3*prob_v_normalized;
+			Ep4a=Ep4*prob_v_normalized;
+			Em4a=Em4*prob_v_normalized;
+			]]>
+		</evaluation>
+	</computed_vector>
+
+	<vector name="density_matrix" type="complex" initial_space="t">
+		<components>
+			<!-- read from Mathematica generated RbChosenRho.txt -->
+			&RbChosenRhoFile;
+		</components>
+		<initialisation>
+			<!--This sets boundary condition at all times and left border of z (i.e. z=0)-->
+			<![CDATA[
+			// Note: 
+			// convergence is really slow if all populations concentrated at the bottom level |1>
+			// this is because if r11=1, everything else is 0 and then every small increment 
+			// seems to be huge and adaptive solver makes smaller and smaller steps.
+			// As quick and dirty fix I reshuffle initial population  
+			// so some of the population sits at the  second ground level |2>
+			// TODO: Fix above. Make the equation of motion for r11 
+			//       and express other level, let's say r44
+			//       through population normalization
+			]]>
+			<!--read from Mathematica generated RbInits.cdata-->
+			&RbInitsFile;
+		</initialisation>
+	</vector>
+
+	<sequence>
+		<!--For this set of conditions ARK45 is faster than ARK89-->
+		<!--ARK45 is good for small detuning when all frequency like term are close to zero-->
+		<integrate algorithm="ARK45" tolerance="1e-5" interval="Lcell"> 
+		<!--<integrate algorithm="SI" steps="200" interval="Lcell"> -->
+		<!--RK4 is good for large detunings when frequency like term are big, it does not try to be too smart about adaptive step which ARK seems to make too small-->
+		<!--When ARK45 works it about 3 times faster than RK4 with 1000 steps-->
+		<!--<integrate algorithm="RK4" steps="100" interval="1.5e-2">-->
+		<!--SIC algorithm seems to be much slower and needs fine 'z'  step tuning and much finer time grid-->
+		<!--For example I had to quadruple the time grid from 1000 to 4000 when increased z distance from 0.02 to 0.04-->
+
+		<!--<integrate algorithm="SIC" interval="4e-2" steps="200">-->
+
+			<samples>100</samples>
+			<!--<samples>100 100</samples>-->
+			<!--Use the next line for debuging to see velocity dependence. Uncomment/switch on output groups 3,4-->
+			<!--<samples>100 100 100 100</samples>--> 
+			<operators>
+        <operator kind="cross_propagation" algorithm="SI" propagation_dimension="t">
+					<integration_vectors>density_matrix</integration_vectors>
+          <dependencies>E_field_avgd</dependencies>
+          <boundary_condition kind="left">
+						<!--This set boundary condition at all 'z'  and left border of 't' (i.e. min(t))-->
+						<!--
+            <![CDATA[
+							r11 = 0; r22 = 1; r33 = 0; r44 = 0;
+							r12 = 0; r13 = 0; r14 = 0;
+							r23 = 0; r24 = 0;
+							r34 = 0;
+							printf("z= %g, t= %g\n", z, t);
+            ]]>
+						-->
+          </boundary_condition>
+					<!-- Equations of motions according to Simon's mathematica code -->
+					<!-- read from Mathematica generated RbEquations.cdata -->
+					&RbEquationsFile;
+        </operator>
+				<!--
+							 According to xmds2 docs operator kind="ip" should be faster
+							 but our codes runs about 5% to 10% slower with it.
+							 Maybe because we very close to the stiff condition so I use "ex" kind
+							 <operator kind="ip" constant="yes">
+					 -->
+				<operator kind="ex" constant="yes" type="imaginary">
+					<operator_names>Lt</operator_names>
+					<![CDATA[
+					Lt = -i/c*kt;
+					]]>
+				</operator>
+        <integration_vectors>E_field</integration_vectors>
+				<dependencies>density_matrix</dependencies>
+				<!-- read from Mathematica generated RbPropEquations.cdata-->
+				&RbPropEquationsFile;
+			</operators>
+		</integrate>
+	</sequence>
+
+
+
+	<!-- The output to generate -->
+	<output format="binary" filename="realistic_Rb_and_fields.xsil">
+		<group>
+      <sampling basis="t(1000) " initial_sample="yes">
+				<dependencies>E_field_avgd</dependencies>
+				<moments>Ip1_out Im1_out Ip2_out Im2_out Ip3_out Im3_out Ip4_out Im4_out</moments>
+				<![CDATA[
+				Ip1_out = mod2(Ep1a);
+				Im1_out = mod2(Em1a);
+				Ip2_out = mod2(Ep2a);
+				Im2_out = mod2(Em2a);
+				Ip3_out = mod2(Ep3a);
+				Im3_out = mod2(Em3a);
+				Ip4_out = mod2(Ep4a);
+				Im4_out = mod2(Em4a);
+				]]>
+			</sampling>
+		</group>
+	</output>
+
+</simulation>
+	
+<!-- 
+vim: ts=2 sw=2 foldmethod=indent: 
+-->
diff --git a/xmds2/realistic_Rb_and_fields/tests/run_tests.py b/xmds2/realistic_Rb_and_fields/tests/run_tests.py
new file mode 100755
index 0000000..61f4eea
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/tests/run_tests.py
@@ -0,0 +1,350 @@
+#!/usr/bin/env python
+# encoding: utf-8
+"""
+run_tests.py
+
+Created by Graham Dennis on 2008-06-15.
+
+Copyright (c) 2008-2012, Graham Dennis
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 2 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+"""
+
+import xpdeint.Python24Support
+
+import os
+import re
+import sys
+import getopt
+import shutil
+import hashlib
+import unittest
+import subprocess
+
+from xml.dom import minidom
+import xpdeint.minidom_extras
+from xpdeint import CodeParser
+
+from xpdeint.XSILFile import XSILFile
+
+import numpy
+
+help_message = '''
+The help message goes here.
+'''
+
+
+class Usage(Exception):
+  def __init__(self, msg):
+    self.msg = msg
+
+def pass_nan_test(array1, array2):
+    """Return `True` if isNaN(`array1`) == isNaN(`array2`)"""
+    # NaN test. array2 is allowed to be NaN at an index if array1 is also NaN there.
+    nanTestPassed = numpy.equal(numpy.isnan(array1), numpy.isnan(array2)).all()
+    return nanTestPassed
+
+def array_approx_equal(array1, array2, absTol, relTol):
+  """Return `True` if all of (`array1` - `array2`) <= `absTol` or (`array1` - `array2`) <= `relTol` * `array2`"""
+  diff = array1-array2
+  # NaN values would fail this test. So we have to exclude them. But only exclude them if array2 (the expected results)
+  # have a NaN
+  return numpy.logical_or(numpy.logical_or(numpy.abs(diff) <= 0.5 * relTol * (numpy.abs(array2) + numpy.abs(array1)), numpy.abs(diff) <= absTol), numpy.isnan(array2)).all()
+
+def scriptTestingFunction(root, scriptName, testDir, absPath, self):
+  if not os.path.exists(testDir):
+    os.makedirs(testDir)
+  
+  proc = subprocess.Popen('xmds2 --no-version ' + absPath,
+                          shell=True,
+                          stdout=subprocess.PIPE,
+                          stderr=subprocess.PIPE,
+                          cwd=testDir)
+  (stdout, stderr) = proc.communicate()
+  returnCode = proc.wait()
+  
+  message = ''.join(["\n%(handleName)s:\n%(content)s" % locals() for handleName, content in [('stdout', stdout), ('stderr', stderr)] if content])
+  
+  # A few tests require XMDS1. If XMDS1 isn't present we should just
+  # skip that test rather than failing.
+  # The skip functionality for the unittest class is only available
+  # in python 2.7 and later, so check for that too.
+  if returnCode != 0 and sys.version_info[:2] >= (2, 7):
+    if re.search(r'^The missing \w+ feature\(s\) were: .*xmds.*', message, re.MULTILINE):
+      self.skipTest("Skipping test as XMDS1 is required and not installed")
+
+  # A few tests require specific features.  If it isn't available, skip the test
+  # rather than failing.
+  # The skip functionality for the unittest class is only available
+  # in python 2.7 and later, so check for that too.
+  if returnCode != 0 and sys.version_info[:2] >= (2, 7):
+    if re.search(r'^The missing \w+ feature\(s\) were:', message, re.MULTILINE):
+      self.skipTest("Skipping test as feature required is not installed")
+
+  self.assert_(returnCode == 0, ("Failed to compile." % locals()) + message)
+  
+  xmlDocument = minidom.parse(absPath)
+  simulationElement = xmlDocument.getChildElementByTagName('simulation')
+  nameElement = simulationElement.getChildElementByTagName('name')
+  testingElement = simulationElement.getChildElementByTagName('testing')
+  
+  simulationName = nameElement.innerText()
+  
+  # If the source is the same as the last known good, then we don't need to compile or execute the simulation.
+  sourceFilePath = os.path.join(testDir, simulationName + '.cc')
+  checksumFilePath = os.path.join(testDir, simulationName + '_last_known_good.checksum')
+  sourceContents = file(sourceFilePath).read()
+  h = hashlib.sha1()
+  h.update(sourceContents)
+  currentChecksum = h.hexdigest()
+  
+  if os.path.exists(checksumFilePath):
+    lastKnownGoodChecksum = file(checksumFilePath).read()
+    
+    if lastKnownGoodChecksum == currentChecksum:
+      # The checksums check out, so we don't need to go any further
+      return
+  
+  # Now we have compiled, we need to copy any input data needed and then run the simulation
+  inputXSILElements = testingElement.getChildElementsByTagName('input_xsil_file', optional=True)
+  
+  filesToCopy = []
+  
+  for inputXSILElement in inputXSILElements:
+    name = inputXSILElement.getAttribute('name').strip()
+    filesToCopy.append(name)
+    inputXSILFile = XSILFile(os.path.join(os.path.split(absPath)[0], name), loadData=False)
+    filesToCopy.extend([os.path.join(os.path.split(name)[0], xsil.data.filename) for xsil in inputXSILFile.xsilObjects if hasattr(xsil.data, 'filename')])
+  
+  for fileToCopy in filesToCopy:
+    sourceFile = os.path.join(os.path.split(absPath)[0], fileToCopy)
+    shutil.copy(sourceFile, testDir)
+  
+  # Allow command-line arguments to be specified for the simulation
+  commandLineElement = testingElement.getChildElementByTagName('command_line', optional=True)
+  argumentsElement = testingElement.getChildElementByTagName('arguments', optional=True)
+  commandLineString = './' + simulationName
+  if commandLineElement:
+    # The command line element overrides the prefix
+    commandLineString = commandLineElement.innerText().strip()
+  if argumentsElement:
+    commandLineString += ' ' + argumentsElement.innerText().strip()
+  
+  simulationProc = subprocess.Popen(commandLineString,
+                                    shell=True,
+                                    stdout=subprocess.PIPE,
+                                    stderr=subprocess.PIPE,
+                                    cwd=testDir)
+  (stdout, stderr) = simulationProc.communicate()
+  returnCode = simulationProc.wait()
+  
+  self.assert_(returnCode == 0, "Failed to execute compiled simulation correctly." % locals())
+  
+  # The next thing to check is that the generated data agrees with the expected data to within the set error margins.
+  xsilFileElements = testingElement.getChildElementsByTagName('xsil_file', optional=True)
+  for xsilFileElement in xsilFileElements:
+    sourceFile = xsilFileElement.getAttribute('name').strip()
+    expectedResultsFile = xsilFileElement.getAttribute('expected').strip()
+    # Defaults
+    absoluteTolerance = 0 
+    relativeTolerance = 1e-9
+    
+    if xsilFileElement.hasAttribute('absolute_tolerance'):
+      absoluteTolerance = float(xsilFileElement.getAttribute('absolute_tolerance'))
+    if xsilFileElement.hasAttribute('relative_tolerance'):
+      relativeTolerance = float(xsilFileElement.getAttribute('relative_tolerance'))
+    
+    resultsFullPath = os.path.join(testDir, sourceFile)
+    results = XSILFile(resultsFullPath)
+    expectedResultsFullPath = os.path.join(os.path.split(absPath)[0], expectedResultsFile)
+    if not os.path.exists(expectedResultsFullPath):
+      print >> sys.stderr, "Expected results file '%(expectedResultsFile)s' missing. Using current. " % locals()
+      
+      # If there are any NaN's in the results, issue a warning.
+      for mgNum, o in enumerate(results.xsilObjects):
+        for v in o.independentVariables:
+          if numpy.isnan(v['array']).any():
+            print >> sys.stderr, "Warning: Coordinate '%s' in moment group %i of file '%s' contains a NaN." % (v['name'], mgNum+1, sourceFile)
+        for v in o.dependentVariables:
+          if numpy.isnan(v['array']).any():
+            print >> sys.stderr, "Warning: Dependent variable '%s' in moment group %i of file '%s' contains a NaN." % (v['name'], mgNum+1, sourceFile)
+      
+      resultsFileContents = file(resultsFullPath).read()
+      
+      for xsilObject in results.xsilObjects:
+        if hasattr(xsilObject.data, 'filename'):
+          # If the moment group has a data file name, then we need to copy it to the expected results file
+          newDataFilename = xsilObject.data.filename.replace(os.path.splitext(sourceFile)[0], os.path.splitext(expectedResultsFile)[0], 1)
+          
+          resultsFileContents = resultsFileContents.replace(xsilObject.data.filename, newDataFilename)
+          
+          shutil.copyfile(os.path.join(testDir, xsilObject.data.filename),
+                          os.path.join(os.path.split(absPath)[0], newDataFilename))
+      
+      file(expectedResultsFullPath, 'w').write(resultsFileContents)
+    else:
+      expectedResults = XSILFile(expectedResultsFullPath)
+      
+      self.assert_(len(results.xsilObjects) == len(expectedResults.xsilObjects))
+      
+      momentGroupElements = xsilFileElement.getChildElementsByTagName('moment_group', optional=True)
+      if momentGroupElements:
+        self.assert_(len(momentGroupElements) == len(results.xsilObjects))
+      else:
+        momentGroupElements = [None]*len(results.xsilObjects)
+      
+      for mgNum, (o1, o2, mgElem) in enumerate(zip(results.xsilObjects, expectedResults.xsilObjects, momentGroupElements)):
+        currentAbsoluteTolerance = absoluteTolerance
+        currentRelativeTolerance = relativeTolerance
+        self.assert_(len(o1.independentVariables) == len(o2.independentVariables),
+                     "The number of independent variables in moment group %(mgNum)i doesn't match." % locals())
+        self.assert_(len(o1.dependentVariables) == len(o2.dependentVariables),
+                     "The number of dependent variables in moment group %(mgNum)i doesn't match." % locals())
+        
+        if mgElem:
+          if mgElem.hasAttribute('absolute_tolerance'):
+            currentAbsoluteTolerance = float(mgElem.getAttribute('absolute_tolerance'))
+          if mgElem.hasAttribute('relative_tolerance'):
+            currentRelativeTolerance = float(mgElem.getAttribute('relative_tolerance'))
+        
+        self.assert_(currentAbsoluteTolerance != None and currentRelativeTolerance != None, "An absolute and a relative tolerance must be specified.")
+        
+        for v1, v2 in zip(o1.independentVariables, o2.independentVariables):
+          self.assert_(v1['name'] == v2['name'])
+          self.assert_(v1['length'] == v2['length'])
+          # These are the coordinates, we just specify a constant absolute and relative tolerance.
+          # No-one should need to change these
+          self.assert_(array_approx_equal(v1['array'], v2['array'], 1e-7, 1e-6),
+                      "Coordinate '%s' in moment group %i of file '%s' didn't pass tolerance criteria." % (v1['name'], mgNum+1, sourceFile))
+        
+        for v1, v2 in zip(o1.dependentVariables, o2.dependentVariables):
+          self.assert_(v1['name'] == v2['name'])
+          self.assert_(pass_nan_test(v1['array'], v2['array']),
+                       "Dependent variable '%s' in moment group %i of file '%s' had a NaN where the expected results didn't (or vice-versa)." % (v1['name'], mgNum+1, sourceFile))
+          self.assert_(array_approx_equal(v1['array'], v2['array'], currentAbsoluteTolerance, currentRelativeTolerance),
+                       "Dependent variable '%s' in moment group %i of file '%s' failed to pass tolerance criteria." % (v1['name'], mgNum+1, sourceFile))
+  
+  # Test has succeeded, so save our checksum for the source file and copy the source file
+  file(checksumFilePath, 'w').write(currentChecksum)
+  
+  lastKnownGoodSourcePath = os.path.join(testDir, simulationName + '_last_known_good.cc')
+  file(lastKnownGoodSourcePath, 'w').write(sourceContents)
+
+def partial(func, *args, **keywords):
+  def newfunc(*fargs, **fkeywords):
+    newkeywords = keywords.copy()
+    newkeywords.update(fkeywords)
+    return func(*(args + fargs), **newkeywords)
+  return newfunc
+
+
+def main(argv=None):
+  if argv is None:
+    argv = sys.argv
+  try:
+    try:
+      opts, args = getopt.getopt(argv[1:], "ho:v", ["help", "output="])
+    except getopt.error, msg:
+      raise Usage(msg)
+  
+    # option processing
+    for option, value in opts:
+      if option == "-v":
+        verbose = True
+      if option in ("-h", "--help"):
+        raise Usage(help_message)
+      if option in ("-o", "--output"):
+        output = value
+  
+  except Usage, err:
+    print >> sys.stderr, sys.argv[0].split("/")[-1] + ": " + str(err.msg)
+    print >> sys.stderr, "\t for help use --help"
+    return 2
+  
+  basePath = os.path.dirname(__file__)
+  
+  resultsPath = os.path.join(basePath, 'testsuite_results')
+  if not os.path.exists(resultsPath):
+    os.mkdir(resultsPath)
+  resultsPath = os.path.abspath(resultsPath)
+  
+  print "Saving test results in %(resultsPath)s" % locals()
+  
+  testsuites = {}
+  baseSuiteName = 'testsuite'
+  baseSuitePath = os.path.join(basePath, baseSuiteName)
+  
+  for root, dirs, files in os.walk(baseSuitePath):
+    # First remove directories we don't want to traverse
+    for dirName in ['.svn']:
+      if dirName in dirs:
+        dirs.remove(dirName)
+    # Remove the 'testsuite/' part of the path
+    dirRelativeToBase = root[(len(baseSuitePath)+1):]
+    if dirRelativeToBase:
+      testSuiteName = os.path.join(baseSuiteName, dirRelativeToBase)
+    else:
+      testSuiteName = baseSuiteName
+    
+    # If we have .xmds files in this path, then create a TestCase subclass
+    xmdsTestScripts = [filename for filename in files if os.path.splitext(filename)[1].lower() == '.xmds']
+    
+    if xmdsTestScripts:
+      class ScriptTestCase(unittest.TestCase):
+        # Create test functions for each test script using 'scriptTestingFunction'
+        # These test function names are of the form 'test_ScriptName'
+        for scriptName in xmdsTestScripts:
+          prefix = os.path.splitext(scriptName)[0]
+          absPath = os.path.abspath(os.path.join(root, scriptName))
+          testDir = os.path.join(resultsPath, dirRelativeToBase)
+          locals()['test_' + prefix] = partial(scriptTestingFunction, root, scriptName, testDir, absPath)
+          locals()['test_' + prefix].__doc__ = os.path.join(dirRelativeToBase, scriptName)
+      
+      # Create a TestSuite from that class
+      suite = unittest.defaultTestLoader.loadTestsFromTestCase(ScriptTestCase)
+      testsuites[testSuiteName] = suite
+    
+    if not testSuiteName in testsuites:
+      testsuites[testSuiteName] = unittest.TestSuite()
+    
+    suite = testsuites[testSuiteName]
+    # Add our TestSuite as a sub-suite of all parent suites
+    head = testSuiteName
+    while True:
+      head, tail = os.path.split(head)
+      if not head or not tail:
+        break
+      testsuites[head].addTest(suite)
+  
+  
+  suitesToRun = list()
+  if len(args):
+    for suiteName in args:
+      fullSuiteName = os.path.join(baseSuiteName, suiteName)
+      if fullSuiteName in testsuites:
+        suitesToRun.append(testsuites[fullSuiteName])
+      else:
+        print >> sys.stderr, "Unable to find test '%(suiteName)s'" % locals()
+  else:
+    suitesToRun.append(testsuites[baseSuiteName])
+  suitesToRun.append(unittest.defaultTestLoader.loadTestsFromModule(CodeParser))
+  
+  fullSuite = unittest.TestSuite(tests=suitesToRun)
+  
+  return not unittest.TextTestRunner().run(fullSuite).wasSuccessful()
+
+
+if __name__ == "__main__":
+  sys.exit(main())
diff --git a/xmds2/realistic_Rb_and_fields/tests/testsuite/realistic_Rb_and_fields_expected.xsil b/xmds2/realistic_Rb_and_fields/tests/testsuite/realistic_Rb_and_fields_expected.xsil
new file mode 100644
index 0000000..c09460c
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/tests/testsuite/realistic_Rb_and_fields_expected.xsil
@@ -0,0 +1,676 @@
+<?xml version="1.0"?>
+<simulation xmds-version="2">
+        <testing>
+                <arguments> --Ndens=1e15 --Lcell=10.0e-2  --Temperature=1e-3  --Pwidth=0.4e-6  --delta1=0 --delta2=0 --delta3=0  --Ep1o=1e4 --Ep2o=1e2 --Ep3o=1e1 --Ep4o=1e1 --Em1o=1e4 --Em2o=1e2 --Em3o=1e1 --Em4o=1e1 --WLx=0 --WLy=0 --WLz=0</arguments>
+                <xsil_file name="realistic_Rb_and_fields.xsil" expected="realistic_Rb_and_fields_expected.xsil" absolute_tolerance="1e-7" relative_tolerance="1e-5">
+                        <moment_group number="0" absolute_tolerance="1e-7" relative_tolerance="1e-6" />
+                </xsil_file>
+        </testing>
+
+        <name>realistic_Rb_and_fields</name>
+
+        <author>Eugeniy Mikhailov</author>
+        <description>
+                License GPL.
+
+                Solving simplified Rb atom model
+                with fields propagation along spatial axis Z
+                with Doppler broadening.
+
+
+                We assume four-wave mixing condition when w3-w4=w2-w1 i.e. fields E3 and E4 drive the same
+                resonance as fields E2 and E1.
+
+
+                *              --------------- | F=1, 2P_3/2 >
+                *                \        \    
+                *                 \ E3_r   \    -------- | F=2, 2P_+1/2 >
+                *                  \   E4_r \   /    \
+                *                   \        \ / E2_l \ 
+                *                    \        /        \ E1_l
+                *   | F=2, 2S_1/2 > --------------      \
+                *                               \        \
+                *                                \        \
+                *                               ------------- | F=1, 2S_1/2 >
+                *            
+
+
+                We are solving 
+                        dE/dz+(1/c)*dE/dt=i*eta*rho_ij,  where j level is higher than i.
+                        Note that E is actually a Rabi frequency of electromagnetic field not the EM field
+                in xmds terms it looks like
+                        dE_dz = i*eta*rhoij - 1/c*L[E], here we moved t dependence to Fourier space
+
+                VERY IMPORTANT: all Rabi frequency should be given in [1/s], if you want to
+                normalize it to something else look drho/dt equation.
+                No need to renormalizes eta as long as its express through
+                the upper level decay rate in the same units as Rabi frequency.
+        </description>
+
+        <features>
+                <globals>
+                        <![CDATA[
+                                // Some numerical constants
+                                const double pi = M_PI; 
+
+                                // atom related constants
+                                //read from Mathematica generated Constants.txt
+//---------------- Constants.txt starts ------------------
+const double ha0 = 2.1471788680034824e10;
+const double ha1 = 2.558764384495815e9;
+const double g1 = 3.612847284945266e7;
+const double ha2 = 5.323020344462938e8;
+const double hb2 = 7.85178251911697e7;
+const double g2 = 3.8117309832741246e7;
+const double lambda1 = 7.949788511562656e-7;
+const double lambda2 = 7.802412096860509e-7;
+const double eta1 = 5.450949336831401e-6;
+const double eta2 = 5.5397657647874e-6;
+const double rt6 = 2.449489742783178;
+const double rt3 = 1.7320508075688772;
+const double rt2 = 1.4142135623730951;
+//---------------- Constants.txt ends   ------------------
+
+                                const double c=3.e8;
+                                const double k_boltzmann= 1.3806505e-23; // Boltzmann knostant in [J/K]
+                                const double lambda=794.7e-9; //wavelength in m
+                                // Fields k-vector
+                                const double Kvec = 2*M_PI/lambda;  
+                                // Simplified k-vectors
+                                const double Kvec1 = Kvec, Kvec2=Kvec, Kvec3=Kvec;
+
+                                //  ---------  Atom and cell properties -------------------------
+                                // range of Maxwell distribution atomic velocities
+                                const double mass = (86.909180527 * 1.660538921e-27); // atom mass in [kg] 
+                                // above mass expression is written as (expression is isotopic_mass * atomic_mass_unit)
+
+                                // Average sqrt(v^2) in Maxwell distribution for one dimension
+                                // Maxwell related parameters will be calculated in <arguments> section
+                                double v_thermal_averaged=0;
+                                // Maxwell distribution velocities range to take in account in [m/s]
+                                double V_maxwell_min = 0, V_maxwell_max = 0;
+
+                                // repopulation rate (atoms flying in/out the laser beam)  in [1/s]
+                                const double gt=0.01 *(2*M_PI*1e6);
+
+                                // inner use variables 
+                                double probability_v; // will be used as p(v) in Maxwell distribution
+
+                        ]]>
+                </globals>
+                <validation kind="run-time"/> <!--allows to put ranges as variables-->
+                <benchmark />
+    <arguments>
+                        <!-- Rabi frequency divided by 2 in [1/s] -->
+      <argument name="Ep1o" type="real" default_value="2*1.5*(2*M_PI*1e6)" />
+      <argument name="Em1o" type="real" default_value="2*1.5*(2*M_PI*1e6)" />
+      <argument name="Ep2o" type="real" default_value="0.05*(2*M_PI*1e6)" />
+      <argument name="Em2o" type="real" default_value="0.05*(2*M_PI*1e6)" />
+      <argument name="Ep3o" type="real" default_value="2*3.0*(2*M_PI*1e6)" />
+      <argument name="Em3o" type="real" default_value="2*3.0*(2*M_PI*1e6)" />
+      <argument name="Ep4o" type="real" default_value=".01*(2*M_PI*1e6)" />
+      <argument name="Em4o" type="real" default_value=".01*(2*M_PI*1e6)" />
+                        <!-- Fields detuning in [1/s] -->
+      <argument name="delta1"  type="real" default_value="0.0" />
+      <argument name="delta2"  type="real" default_value="0.0" />
+      <argument name="delta3"  type="real" default_value="0.0" />
+                        <!--Pulse duration/width [s] -->
+                        <argument name="Pwidth"  type="real" default_value="0.1e-6" />
+                        <!--  Atom and cell properties -->
+                        <!--Cell length [m] -->
+                        <argument name="Lcell"  type="real" default_value="1.5e-2" />
+                        <!--Density of atoms [1/m^3] -->
+                        <argument name="Ndens"  type="real" default_value="1e15" />
+                        <!-- Projections of magnetic field in Larmor frequency units [1/s] -->
+                        <argument name="WLx"  type="real" default_value="0" />
+                        <argument name="WLy"  type="real" default_value="0" />
+                        <argument name="WLz"  type="real" default_value="0" />
+                        <!--Atoms temperature [K] -->
+                        <!--TODO: looks like Temperature > 10 K knocks solver, 
+                                         I am guessing detunings are too large and thus it became a stiff equation-->
+                        <!--! make sure it is not equal to zero!-->
+                        <argument name="Temperature"  type="real" default_value="5" />
+                        <!-- This will be executed after arguments/parameters are parsed -->
+                        <!-- Read the code Luke: took me a while of reading the xmds2 sources to find it -->
+                        <![CDATA[
+                                // Average sqrt(v^2) in Maxwell distribution for one dimension
+                                if (Temperature == 0)
+                                        _LOG(_ERROR_LOG_LEVEL, "ERROR: Temperature should be >0 to provide range for Maxwell velocity distribution\n");
+                                v_thermal_averaged=sqrt(k_boltzmann*Temperature/mass); 
+                                // Maxwell distribution velocities range to take in account in [m/s]
+                                // there is almost zero probability for higher velocity p(4*v_av) = 3.3e-04 * p(0)
+                                V_maxwell_min = -4*v_thermal_averaged; V_maxwell_max = -V_maxwell_min; 
+                        ]]>
+    </arguments>
+                <bing />
+                <diagnostics /> 
+                <fftw plan="estimate" threads="1" />
+                <!--<fftw plan="patient" threads="1" />-->
+                <!-- I don't see any speed up on 6 core CPU even if use threads="6" -->
+                <!--<openmp />-->
+                <auto_vectorise />
+                <halt_non_finite />
+        </features>
+
+        <!-- 'z', 't', and 'v'  to have dimensions [m], [s], and [m/s]   -->
+        <geometry>
+                <propagation_dimension> z </propagation_dimension>
+                <transverse_dimensions>
+                        <!-- IMPORTANT: looks like having a lot of points in time helps with convergence.
+                                         I suspect that time spacing should be small enough to catch
+                                         all pulse harmonics and more importantly 1/dt should be larger than
+                                         the largest detuning (including Doppler shifts).
+                                         Unfortunately calculation time is proportional to lattice size
+                                         so we cannot just blindly increase it.
+                                         Some rules of thumb:  
+                                                * lattice="1000"   domain="(-1e-6, 1e-6)" 
+                                                        was good enough detunings up to 155 MHz (980 rad/s) notice that 1/dt=500 MHz
+                                                * lattice="10000"   domain="(-1e-6, 1e-6)" 
+                                                        works for Doppler averaging in up to 400K for Rb when lasers are zero detuned
+                         -->
+                        <dimension name="t"   lattice="10000"   domain="(-1e-6, 1e-6)" />
+                        <dimension name="v"   lattice="2"   domain="(V_maxwell_min, V_maxwell_max)" />
+                </transverse_dimensions>
+        </geometry>
+
+        <!-- Rabi frequency --> 
+        <vector name="E_field" type="complex" initial_space="t">
+                 <!--plus/minus circular polarization components-->
+                <components>Ep1 Em1 Ep2 Em2 Ep3 Em3 Ep4 Em4</components>
+                <initialisation>
+                        <![CDATA[
+                        // Initial (at starting 'z' position) electromagnetic field does not depend on detuning
+                        // as well as time
+                        Ep1=Ep1o;
+                        Em1=Em1o;
+                        Ep2=Ep2o*exp(-pow( ((t-0.0)/Pwidth),2) );
+                        Em2=Em2o*exp(-pow( ((t-0.0)/Pwidth),2) );
+                        Ep3=Ep3o;
+                        Em3=Em3o;
+                        Ep4=Ep4o;
+                        Em4=Em4o;
+                        ]]>
+                </initialisation>
+        </vector>
+
+        <!--Maxwell distribution probability p(v)-->
+        <computed_vector name="Maxwell_distribution_probabilities" dimensions="v" type="real">
+                <components>probability_v</components>
+                <evaluation>
+                        <![CDATA[
+                        // TODO: move to the global space/function. This reevaluated many times since it called from dependency requests but it never changes during  the script lifetime since 'v' is fixed.
+                        probability_v=1.0/(v_thermal_averaged*sqrt(2*M_PI)) * exp( - mod2(v/v_thermal_averaged)/2.0 ); 
+                        ]]>
+                </evaluation>
+        </computed_vector>
+
+        <!--Maxwell distribution norm sum(p(v))
+                         Needed since we sum over the grid instead of true integral,
+                         we also have finite cut off velocities-->
+        <computed_vector name="Maxwell_distribution_probabilities_norm" dimensions="" type="real">
+                <components>probability_v_norm</components>
+                <evaluation>
+                        <dependencies basis="v">Maxwell_distribution_probabilities</dependencies>
+                        <![CDATA[
+                        // TODO: move to the global space/function. This reevaluated many times since it called from dependency requests but it never changes during  the script lifetime since 'v' is fixed.
+                        probability_v_norm=probability_v;
+                        ]]>
+                </evaluation>
+        </computed_vector>
+
+
+        <!-- Averaged across Maxwell distribution fields amplitudes -->
+        <computed_vector name="E_field_avgd" dimensions="t" type="complex">
+                <components>Ep1a Em1a Ep2a Em2a Ep3a Em3a Ep4a Em4a</components>
+                <evaluation>
+                        <dependencies basis="v">E_field Maxwell_distribution_probabilities Maxwell_distribution_probabilities_norm</dependencies>
+                        <![CDATA[
+                        double prob_v_normalized=probability_v/probability_v_norm;
+                        Ep1a=Ep1*prob_v_normalized;
+                        Em1a=Em1*prob_v_normalized;
+                        Ep2a=Ep2*prob_v_normalized;
+                        Em2a=Em2*prob_v_normalized;
+                        Ep3a=Ep3*prob_v_normalized;
+                        Em3a=Em3*prob_v_normalized;
+                        Ep4a=Ep4*prob_v_normalized;
+                        Em4a=Em4*prob_v_normalized;
+                        ]]>
+                </evaluation>
+        </computed_vector>
+
+        <vector name="density_matrix" type="complex" initial_space="t">
+                <components>
+                        <!-- read from Mathematica generated RbChosenRho.txt -->
+<!-- ############### RbChosenRho.txt starts ################ -->
+r0101 r0109 r0110 r0111 r0112 r0113 r0114 r0115 r0116 r0201 r0202 r0209 r0210 r0211 r0212 r0213 r0214 r0215 r0216 r0301 r0302 r0303 r0309 r0310 r0311 r0312 r0313 r0314 r0315 r0316 r0401 r0402 r0403 r0404 r0409 r0410 r0411 r0412 r0413 r0414 r0415 r0416 r0501 r0502 r0503 r0504 r0505 r0509 r0510 r0511 r0512 r0513 r0514 r0515 r0516 r0601 r0602 r0603 r0604 r0605 r0606 r0609 r0610 r0611 r0612 r0613 r0614 r0615 r0616 r0701 r0702 r0703 r0704 r0705 r0706 r0707 r0709 r0710 r0711 r0712 r0713 r0714 r0715 r0716 r0801 r0802 r0803 r0804 r0805 r0806 r0807 r0808 r0809 r0810 r0811 r0812 r0813 r0814 r0815 r0816 r0909 r0912 r0913 r0914 r0915 r0916 r1009 r1010 r1012 r1013 r1014 r1015 r1016 r1109 r1110 r1111 r1112 r1113 r1114 r1115 r1116 r1212 r1312 r1313 r1412 r1413 r1414 r1512 r1513 r1514 r1515 r1612 r1613 r1614 r1615 r1616 
+<!-- ############### RbChosenRho.txt ends  ################# -->
+                </components>
+                <initialisation>
+                        <!--This sets boundary condition at all times and left border of z (i.e. z=0)-->
+                        <![CDATA[
+                        // Note: 
+                        // convergence is really slow if all populations concentrated at the bottom level |1>
+                        // this is because if r11=1, everything else is 0 and then every small increment 
+                        // seems to be huge and adaptive solver makes smaller and smaller steps.
+                        // As quick and dirty fix I reshuffle initial population  
+                        // so some of the population sits at the  second ground level |2>
+                        // TODO: Fix above. Make the equation of motion for r11 
+                        //       and express other level, let's say r44
+                        //       through population normalization
+
+                        //read from Mathematica generated RbInits.txt
+//---------------- RbInits.txt starts ------------------
+r0101 = 0.125;
+r0109 = 0;
+r0110 = 0;
+r0111 = 0;
+r0112 = 0;
+r0113 = 0;
+r0114 = 0;
+r0115 = 0;
+r0116 = 0;
+r0201 = 0;
+r0202 = 0.125;
+r0209 = 0;
+r0210 = 0;
+r0211 = 0;
+r0212 = 0;
+r0213 = 0;
+r0214 = 0;
+r0215 = 0;
+r0216 = 0;
+r0301 = 0;
+r0302 = 0;
+r0303 = 0.125;
+r0309 = 0;
+r0310 = 0;
+r0311 = 0;
+r0312 = 0;
+r0313 = 0;
+r0314 = 0;
+r0315 = 0;
+r0316 = 0;
+r0401 = 0;
+r0402 = 0;
+r0403 = 0;
+r0404 = 0.125;
+r0409 = 0;
+r0410 = 0;
+r0411 = 0;
+r0412 = 0;
+r0413 = 0;
+r0414 = 0;
+r0415 = 0;
+r0416 = 0;
+r0501 = 0;
+r0502 = 0;
+r0503 = 0;
+r0504 = 0;
+r0505 = 0.125;
+r0509 = 0;
+r0510 = 0;
+r0511 = 0;
+r0512 = 0;
+r0513 = 0;
+r0514 = 0;
+r0515 = 0;
+r0516 = 0;
+r0601 = 0;
+r0602 = 0;
+r0603 = 0;
+r0604 = 0;
+r0605 = 0;
+r0606 = 0.125;
+r0609 = 0;
+r0610 = 0;
+r0611 = 0;
+r0612 = 0;
+r0613 = 0;
+r0614 = 0;
+r0615 = 0;
+r0616 = 0;
+r0701 = 0;
+r0702 = 0;
+r0703 = 0;
+r0704 = 0;
+r0705 = 0;
+r0706 = 0;
+r0707 = 0.125;
+r0709 = 0;
+r0710 = 0;
+r0711 = 0;
+r0712 = 0;
+r0713 = 0;
+r0714 = 0;
+r0715 = 0;
+r0716 = 0;
+r0801 = 0;
+r0802 = 0;
+r0803 = 0;
+r0804 = 0;
+r0805 = 0;
+r0806 = 0;
+r0807 = 0;
+r0808 = 0.125;
+r0809 = 0;
+r0810 = 0;
+r0811 = 0;
+r0812 = 0;
+r0813 = 0;
+r0814 = 0;
+r0815 = 0;
+r0816 = 0;
+r0909 = 0;
+r0912 = 0;
+r0913 = 0;
+r0914 = 0;
+r0915 = 0;
+r0916 = 0;
+r1009 = 0;
+r1010 = 0;
+r1012 = 0;
+r1013 = 0;
+r1014 = 0;
+r1015 = 0;
+r1016 = 0;
+r1109 = 0;
+r1110 = 0;
+r1111 = 0;
+r1112 = 0;
+r1113 = 0;
+r1114 = 0;
+r1115 = 0;
+r1116 = 0;
+r1212 = 0;
+r1312 = 0;
+r1313 = 0;
+r1412 = 0;
+r1413 = 0;
+r1414 = 0;
+r1512 = 0;
+r1513 = 0;
+r1514 = 0;
+r1515 = 0;
+r1612 = 0;
+r1613 = 0;
+r1614 = 0;
+r1615 = 0;
+r1616 = 0;
+//---------------- RbInits.txt ends  ------------------
+                        ]]>
+                </initialisation>
+        </vector>
+
+        <sequence>
+                <!--For this set of conditions ARK45 is faster than ARK89-->
+                <!--ARK45 is good for small detuning when all frequency like term are close to zero-->
+                <integrate algorithm="ARK45" tolerance="1e-5" interval="Lcell"> 
+                <!--<integrate algorithm="SI" steps="200" interval="Lcell"> -->
+                <!--RK4 is good for large detunings when frequency like term are big, it does not try to be too smart about adaptive step which ARK seems to make too small-->
+                <!--When ARK45 works it about 3 times faster than RK4 with 1000 steps-->
+                <!--<integrate algorithm="RK4" steps="100" interval="1.5e-2">-->
+                <!--SIC algorithm seems to be much slower and needs fine 'z'  step tuning and much finer time grid-->
+                <!--For example I had to quadruple the time grid from 1000 to 4000 when increased z distance from 0.02 to 0.04-->
+
+                <!--<integrate algorithm="SIC" interval="4e-2" steps="200">-->
+
+                        <samples>100</samples>
+                        <!--<samples>100 100</samples>-->
+                        <!--Use the next line for debuging to see velocity dependence. Uncomment/switch on output groups 3,4-->
+                        <!--<samples>100 100 100 100</samples>--> 
+                        <operators>
+        <operator kind="cross_propagation" algorithm="SI" propagation_dimension="t">
+                                        <integration_vectors>density_matrix</integration_vectors>
+          <dependencies>E_field_avgd</dependencies>
+          <boundary_condition kind="left">
+                                                <!--This set boundary condition at all 'z'  and left border of 't' (i.e. min(t))-->
+                                                <!--
+            <![CDATA[
+                                                        r11 = 0; r22 = 1; r33 = 0; r44 = 0;
+                                                        r12 = 0; r13 = 0; r14 = 0;
+                                                        r23 = 0; r24 = 0;
+                                                        r34 = 0;
+                                                        printf("z= %g, t= %g\n", z, t);
+            ]]>
+                                                -->
+          </boundary_condition>
+                                        <![CDATA[
+                                                // Equations of motions according to Simon's mathematica code
+                                                //read from Mathematica generated RbEquations.txt
+//---------------- RbEquations.txt starts ------------------
+dr0101_dt = gt/8. - gt*r0101 + (g1*r0909)/2. + (g2*r1212)/3. + (g2*r1313)/6. - i*((conj(Em1a)*conj(r0109))/4. - (conj(Em4a)*conj(r0113))/(4.*rt6) - (Em1a*r0109)/4. + (Em4a*r0113)/(4.*rt6) + r0201*(WLx/2. - (i*WLy)/2.) - conj(r0201)*(WLx/2. + (i*WLy)/2.));
+dr0109_dt = (-(gt*r0109) - (gt + g1)*r0109)/2. - i*(-(conj(Ep1a)*conj(r0301))/(4.*rt6) + (conj(Ep2a)*conj(r0701))/(4.*rt6) - (conj(Em4a)*conj(r0913))/(4.*rt6) - (conj(Em1a)*r0101)/4. + (conj(Em1a)*r0909)/4. + r0209*(WLx/2. - (i*WLy)/2.) - r0110*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0109*(-delta1 - v*Kvec1 - WLz/6.) + r0109*WLz);
+dr0110_dt = (-(gt*r0110) - (gt + g1)*r0110)/2. - i*(-(conj(Em1a)*conj(r0201))/(4.*rt2) - (conj(Ep1a)*conj(r0401))/(4.*rt2) - (conj(Em2a)*conj(r0601))/(4.*rt6) + (conj(Ep2a)*conj(r0801))/(4.*rt6) + (conj(Em1a)*conj(r1009))/4. - (conj(Em4a)*conj(r1013))/(4.*rt6) + (delta1 + v*Kvec1)*r0110 + r0210*(WLx/2. - (i*WLy)/2.) - r0111*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0110*WLz);
+dr0111_dt = (-(gt*r0111) - (gt + g1)*r0111)/2. - i*(-(conj(Em1a)*conj(r0301))/(4.*rt6) - (conj(Ep1a)*conj(r0501))/4. - (conj(Em2a)*conj(r0701))/(4.*rt6) + (conj(Em1a)*conj(r1109))/4. - (conj(Em4a)*conj(r1113))/(4.*rt6) + r0211*(WLx/2. - (i*WLy)/2.) - r0110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0111*(-delta1 - v*Kvec1 + WLz/6.) + r0111*WLz);
+dr0112_dt = (-(gt*r0112) - (gt + g2)*r0112)/2. - i*(-(conj(Ep4a)*conj(r0201))/(4.*rt6) - (conj(Ep3a)*conj(r0601))/(4.*rt2) + (conj(Em1a)*r0912)/4. - (conj(Em4a)*r1312)/(4.*rt6) + r0212*(WLx/2. - (i*WLy)/2.) - r0113*((2*WLx)/3. + (2*i*WLy)/3.) + r0112*WLz - r0112*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0113_dt = (-(gt*r0113) - (gt + g2)*r0113)/2. - i*(-(conj(Ep4a)*conj(r0301))/8. - (conj(Ep3a)*conj(r0701))/8. + (conj(Em4a)*r0101)/(4.*rt6) + (conj(Em1a)*r0913)/4. - (conj(Em4a)*r1313)/(4.*rt6) - r0112*((2*WLx)/3. - (2*i*WLy)/3.) + r0213*(WLx/2. - (i*WLy)/2.) - r0114*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r0113*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) + r0113*WLz);
+dr0114_dt = (-(gt*r0114) - (gt + g2)*r0114)/2. - i*((conj(Em4a)*conj(r0201))/8. - (conj(Ep4a)*conj(r0401))/8. - (conj(Em3a)*conj(r0601))/(8.*rt3) - (conj(Ep3a)*conj(r0801))/(8.*rt3) - (conj(Em4a)*conj(r1413))/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0114 + (conj(Em1a)*r0914)/4. + r0214*(WLx/2. - (i*WLy)/2.) - r0113*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0115*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0114*WLz);
+dr0115_dt = (-(gt*r0115) - (gt + g2)*r0115)/2. - i*((conj(Em4a)*conj(r0301))/8. - (conj(Ep4a)*conj(r0501))/(4.*rt6) - (conj(Em3a)*conj(r0701))/8. - (conj(Em4a)*conj(r1513))/(4.*rt6) + (conj(Em1a)*r0915)/4. + r0215*(WLx/2. - (i*WLy)/2.) - r0116*((2*WLx)/3. + (2*i*WLy)/3.) - r0114*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0115*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0115*WLz);
+dr0116_dt = (-(gt*r0116) - (gt + g2)*r0116)/2. - i*((conj(Em4a)*conj(r0401))/(4.*rt6) - (conj(Em3a)*conj(r0801))/(4.*rt2) - (conj(Em4a)*conj(r1613))/(4.*rt6) + (conj(Em1a)*r0916)/4. - r0115*((2*WLx)/3. - (2*i*WLy)/3.) + r0216*(WLx/2. - (i*WLy)/2.) - r0116*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0116*WLz);
+dr0201_dt = -(gt*r0201) + (g1*r1009)/(2.*rt2) + (g2*r1312)/6. + (g2*r1413)/(2.*rt6) - i*((conj(Em1a)*conj(r0110))/(4.*rt2) + (conj(Ep4a)*conj(r0112))/(4.*rt6) - (conj(Em4a)*conj(r0114))/8. - (Em1a*r0209)/4. + (Em4a*r0213)/(4.*rt6) + r0101*(WLx/2. + (i*WLy)/2.) - r0202*(WLx/2. + (i*WLy)/2.) + r0301*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - (r0201*WLz)/2.);
+dr0202_dt = gt/8. - gt*r0202 + (g1*r0909)/4. + (g1*r1010)/4. + (g2*r1212)/6. + (g2*r1313)/12. + (g2*r1414)/4. - i*((conj(Em1a)*conj(r0210))/(4.*rt2) + (conj(Ep4a)*conj(r0212))/(4.*rt6) - (conj(Em4a)*conj(r0214))/8. - (Em1a*r0210)/(4.*rt2) - (Ep4a*r0212)/(4.*rt6) + (Em4a*r0214)/8. - r0201*(WLx/2. - (i*WLy)/2.) + conj(r0201)*(WLx/2. + (i*WLy)/2.) + r0302*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - conj(r0302)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0209_dt = (-(gt*r0209) - (gt + g1)*r0209)/2. - i*(-(conj(Ep1a)*conj(r0302))/(4.*rt6) + (conj(Ep2a)*conj(r0702))/(4.*rt6) + (conj(Ep4a)*conj(r0912))/(4.*rt6) - (conj(Em4a)*conj(r0914))/8. - (conj(Em1a)*r0201)/4. + (conj(Em1a)*r1009)/(4.*rt2) + r0109*(WLx/2. + (i*WLy)/2.) + r0309*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0210*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0209*(-delta1 - v*Kvec1 - WLz/6.) + (r0209*WLz)/2.);
+dr0210_dt = (-(gt*r0210) - (gt + g1)*r0210)/2. - i*(-(conj(Ep1a)*conj(r0402))/(4.*rt2) - (conj(Em2a)*conj(r0602))/(4.*rt6) + (conj(Ep2a)*conj(r0802))/(4.*rt6) + (conj(Ep4a)*conj(r1012))/(4.*rt6) - (conj(Em4a)*conj(r1014))/8. - (conj(Em1a)*r0202)/(4.*rt2) + (delta1 + v*Kvec1)*r0210 + (conj(Em1a)*r1010)/(4.*rt2) + r0110*(WLx/2. + (i*WLy)/2.) + r0310*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0211*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0209*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + (r0210*WLz)/2.);
+dr0211_dt = (-(gt*r0211) - (gt + g1)*r0211)/2. - i*(-(conj(Em1a)*conj(r0302))/(4.*rt6) - (conj(Ep1a)*conj(r0502))/4. - (conj(Em2a)*conj(r0702))/(4.*rt6) + (conj(Em1a)*conj(r1110))/(4.*rt2) + (conj(Ep4a)*conj(r1112))/(4.*rt6) - (conj(Em4a)*conj(r1114))/8. + r0111*(WLx/2. + (i*WLy)/2.) + r0311*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0210*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0211*(-delta1 - v*Kvec1 + WLz/6.) + (r0211*WLz)/2.);
+dr0212_dt = (-(gt*r0212) - (gt + g2)*r0212)/2. - i*(-(conj(Ep3a)*conj(r0602))/(4.*rt2) - (conj(Ep4a)*r0202)/(4.*rt6) + (conj(Em1a)*r1012)/(4.*rt2) + (conj(Ep4a)*r1212)/(4.*rt6) - (conj(Em4a)*r1412)/8. + r0112*(WLx/2. + (i*WLy)/2.) - r0213*((2*WLx)/3. + (2*i*WLy)/3.) + r0312*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + (r0212*WLz)/2. - r0212*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0213_dt = (-(gt*r0213) - (gt + g2)*r0213)/2. - i*(-(conj(Ep4a)*conj(r0302))/8. - (conj(Ep3a)*conj(r0702))/8. + (conj(Ep4a)*conj(r1312))/(4.*rt6) + (conj(Em4a)*r0201)/(4.*rt6) + (conj(Em1a)*r1013)/(4.*rt2) - (conj(Em4a)*r1413)/8. - r0212*((2*WLx)/3. - (2*i*WLy)/3.) + r0113*(WLx/2. + (i*WLy)/2.) - r0214*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0313*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0213*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) + (r0213*WLz)/2.);
+dr0214_dt = (-(gt*r0214) - (gt + g2)*r0214)/2. - i*(-(conj(Ep4a)*conj(r0402))/8. - (conj(Em3a)*conj(r0602))/(8.*rt3) - (conj(Ep3a)*conj(r0802))/(8.*rt3) + (conj(Ep4a)*conj(r1412))/(4.*rt6) + (conj(Em4a)*r0202)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0214 + (conj(Em1a)*r1014)/(4.*rt2) - (conj(Em4a)*r1414)/8. + r0114*(WLx/2. + (i*WLy)/2.) - r0213*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0215*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0314*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + (r0214*WLz)/2.);
+dr0215_dt = (-(gt*r0215) - (gt + g2)*r0215)/2. - i*((conj(Em4a)*conj(r0302))/8. - (conj(Ep4a)*conj(r0502))/(4.*rt6) - (conj(Em3a)*conj(r0702))/8. + (conj(Ep4a)*conj(r1512))/(4.*rt6) - (conj(Em4a)*conj(r1514))/8. + (conj(Em1a)*r1015)/(4.*rt2) + r0115*(WLx/2. + (i*WLy)/2.) - r0216*((2*WLx)/3. + (2*i*WLy)/3.) - r0214*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0315*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0215*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + (r0215*WLz)/2.);
+dr0216_dt = (-(gt*r0216) - (gt + g2)*r0216)/2. - i*((conj(Em4a)*conj(r0402))/(4.*rt6) - (conj(Em3a)*conj(r0802))/(4.*rt2) + (conj(Ep4a)*conj(r1612))/(4.*rt6) - (conj(Em4a)*conj(r1614))/8. + (conj(Em1a)*r1016)/(4.*rt2) - r0215*((2*WLx)/3. - (2*i*WLy)/3.) + r0116*(WLx/2. + (i*WLy)/2.) + r0316*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0216*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + (r0216*WLz)/2.);
+dr0301_dt = -(gt*r0301) + (g1*r1109)/(2.*rt6) + (g2*r1513)/(2.*rt6) - i*((conj(Ep1a)*conj(r0109))/(4.*rt6) + (conj(Em1a)*conj(r0111))/(4.*rt6) + (conj(Ep4a)*conj(r0113))/8. - (conj(Em4a)*conj(r0115))/8. - (Em1a*r0309)/4. + (Em4a*r0313)/(4.*rt6) - r0302*(WLx/2. + (i*WLy)/2.) + r0401*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0201*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0301*WLz);
+dr0302_dt = -(gt*r0302) + (g1*r1009)/(2.*rt3) + (g1*r1110)/(4.*rt3) + (g2*r1312)/(2.*rt6) + (g2*r1514)/4. - i*((conj(Ep1a)*conj(r0209))/(4.*rt6) + (conj(Em1a)*conj(r0211))/(4.*rt6) + (conj(Ep4a)*conj(r0213))/8. - (conj(Em4a)*conj(r0215))/8. - (Em1a*r0310)/(4.*rt2) - (Ep4a*r0312)/(4.*rt6) + (Em4a*r0314)/8. - r0301*(WLx/2. - (i*WLy)/2.) + r0402*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0202*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0303*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0302*WLz)/2.);
+dr0303_dt = gt/8. - gt*r0303 + (g1*r0909)/12. + (g1*r1010)/3. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1515)/4. - i*((conj(Ep1a)*conj(r0309))/(4.*rt6) + (conj(Em1a)*conj(r0311))/(4.*rt6) + (conj(Ep4a)*conj(r0313))/8. - (conj(Em4a)*conj(r0315))/8. - (Ep1a*r0309)/(4.*rt6) - (Em1a*r0311)/(4.*rt6) - (Ep4a*r0313)/8. + (Em4a*r0315)/8. - r0302*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0403*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + conj(r0302)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - conj(r0403)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0309_dt = (-(gt*r0309) - (gt + g1)*r0309)/2. - i*((conj(Ep2a)*conj(r0703))/(4.*rt6) + (conj(Ep4a)*conj(r0913))/8. - (conj(Em4a)*conj(r0915))/8. - (conj(Em1a)*r0301)/4. - (conj(Ep1a)*r0303)/(4.*rt6) + (conj(Ep1a)*r0909)/(4.*rt6) + (conj(Em1a)*r1109)/(4.*rt6) + r0409*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0209*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0310*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0309*(-delta1 - v*Kvec1 - WLz/6.));
+dr0310_dt = (-(gt*r0310) - (gt + g1)*r0310)/2. - i*(-(conj(Ep1a)*conj(r0403))/(4.*rt2) - (conj(Em2a)*conj(r0603))/(4.*rt6) + (conj(Ep2a)*conj(r0803))/(4.*rt6) + (conj(Ep1a)*conj(r1009))/(4.*rt6) + (conj(Ep4a)*conj(r1013))/8. - (conj(Em4a)*conj(r1015))/8. - (conj(Em1a)*r0302)/(4.*rt2) + (delta1 + v*Kvec1)*r0310 + (conj(Em1a)*r1110)/(4.*rt6) + r0410*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0210*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0311*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0309*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr0311_dt = (-(gt*r0311) - (gt + g1)*r0311)/2. - i*(-(conj(Ep1a)*conj(r0503))/4. - (conj(Em2a)*conj(r0703))/(4.*rt6) + (conj(Ep1a)*conj(r1109))/(4.*rt6) + (conj(Ep4a)*conj(r1113))/8. - (conj(Em4a)*conj(r1115))/8. - (conj(Em1a)*r0303)/(4.*rt6) + (conj(Em1a)*r1111)/(4.*rt6) + r0411*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0211*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0310*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0311*(-delta1 - v*Kvec1 + WLz/6.));
+dr0312_dt = (-(gt*r0312) - (gt + g2)*r0312)/2. - i*(-(conj(Ep3a)*conj(r0603))/(4.*rt2) - (conj(Ep4a)*r0302)/(4.*rt6) + (conj(Ep1a)*r0912)/(4.*rt6) + (conj(Em1a)*r1112)/(4.*rt6) + (conj(Ep4a)*r1312)/8. - (conj(Em4a)*r1512)/8. - r0313*((2*WLx)/3. + (2*i*WLy)/3.) + r0412*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0212*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0313_dt = (-(gt*r0313) - (gt + g2)*r0313)/2. - i*(-(conj(Ep3a)*conj(r0703))/8. + (conj(Em4a)*r0301)/(4.*rt6) - (conj(Ep4a)*r0303)/8. + (conj(Ep1a)*r0913)/(4.*rt6) + (conj(Em1a)*r1113)/(4.*rt6) + (conj(Ep4a)*r1313)/8. - (conj(Em4a)*r1513)/8. - r0312*((2*WLx)/3. - (2*i*WLy)/3.) - r0314*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0413*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0213*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0313*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0314_dt = (-(gt*r0314) - (gt + g2)*r0314)/2. - i*(-(conj(Ep4a)*conj(r0403))/8. - (conj(Em3a)*conj(r0603))/(8.*rt3) - (conj(Ep3a)*conj(r0803))/(8.*rt3) + (conj(Ep4a)*conj(r1413))/8. + (conj(Em4a)*r0302)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0314 + (conj(Ep1a)*r0914)/(4.*rt6) + (conj(Em1a)*r1114)/(4.*rt6) - (conj(Em4a)*r1514)/8. - r0313*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0315*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0414*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0214*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0315_dt = (-(gt*r0315) - (gt + g2)*r0315)/2. - i*(-(conj(Ep4a)*conj(r0503))/(4.*rt6) - (conj(Em3a)*conj(r0703))/8. + (conj(Ep4a)*conj(r1513))/8. + (conj(Em4a)*r0303)/8. + (conj(Ep1a)*r0915)/(4.*rt6) + (conj(Em1a)*r1115)/(4.*rt6) - (conj(Em4a)*r1515)/8. - r0316*((2*WLx)/3. + (2*i*WLy)/3.) - r0314*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0415*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0215*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0315*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr0316_dt = (-(gt*r0316) - (gt + g2)*r0316)/2. - i*((conj(Em4a)*conj(r0403))/(4.*rt6) - (conj(Em3a)*conj(r0803))/(4.*rt2) + (conj(Ep4a)*conj(r1613))/8. - (conj(Em4a)*conj(r1615))/8. + (conj(Ep1a)*r0916)/(4.*rt6) + (conj(Em1a)*r1116)/(4.*rt6) - r0315*((2*WLx)/3. - (2*i*WLy)/3.) + r0416*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0216*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0316*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr0401_dt = -(gt*r0401) - (g2*r1512)/6. + (g2*r1613)/6. - i*((conj(Ep1a)*conj(r0110))/(4.*rt2) + (conj(Ep4a)*conj(r0114))/8. - (conj(Em4a)*conj(r0116))/(4.*rt6) - (Em1a*r0409)/4. + (Em4a*r0413)/(4.*rt6) + r0501*(WLx/2. - (i*WLy)/2.) - r0402*(WLx/2. + (i*WLy)/2.) + r0301*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (3*r0401*WLz)/2.);
+dr0402_dt = -(gt*r0402) + (g1*r1109)/4. + (g2*r1412)/(2.*rt6) - (g2*r1513)/12. + (g2*r1614)/(2.*rt6) - i*((conj(Ep1a)*conj(r0210))/(4.*rt2) + (conj(Ep4a)*conj(r0214))/8. - (conj(Em4a)*conj(r0216))/(4.*rt6) - (Em1a*r0410)/(4.*rt2) - (Ep4a*r0412)/(4.*rt6) + (Em4a*r0414)/8. - r0401*(WLx/2. - (i*WLy)/2.) + r0502*(WLx/2. - (i*WLy)/2.) + r0302*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0403*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0402*WLz);
+dr0403_dt = -(gt*r0403) + (g1*r1009)/(4.*rt3) + (g1*r1110)/(2.*rt3) + (g2*r1413)/4. + (g2*r1615)/(2.*rt6) - i*((conj(Ep1a)*conj(r0310))/(4.*rt2) + (conj(Ep4a)*conj(r0314))/8. - (conj(Em4a)*conj(r0316))/(4.*rt6) - (Ep1a*r0409)/(4.*rt6) - (Em1a*r0411)/(4.*rt6) - (Ep4a*r0413)/8. + (Em4a*r0415)/8. + r0503*(WLx/2. - (i*WLy)/2.) - r0402*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0303*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0404*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0403*WLz)/2.);
+dr0404_dt = gt/8. - gt*r0404 + (g1*r1010)/4. + (g1*r1111)/4. + (g2*r1414)/4. + (g2*r1515)/12. + (g2*r1616)/6. - i*((conj(Ep1a)*conj(r0410))/(4.*rt2) + (conj(Ep4a)*conj(r0414))/8. - (conj(Em4a)*conj(r0416))/(4.*rt6) - (Ep1a*r0410)/(4.*rt2) - (Ep4a*r0414)/8. + (Em4a*r0416)/(4.*rt6) + r0504*(WLx/2. - (i*WLy)/2.) - conj(r0504)*(WLx/2. + (i*WLy)/2.) - r0403*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + conj(r0403)*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.));
+dr0409_dt = (-(gt*r0409) - (gt + g1)*r0409)/2. - i*((conj(Ep2a)*conj(r0704))/(4.*rt6) + (conj(Ep4a)*conj(r0914))/8. - (conj(Em4a)*conj(r0916))/(4.*rt6) - (conj(Em1a)*r0401)/4. - (conj(Ep1a)*r0403)/(4.*rt6) + (conj(Ep1a)*r1009)/(4.*rt2) + r0509*(WLx/2. - (i*WLy)/2.) + r0309*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0410*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0409*(-delta1 - v*Kvec1 - WLz/6.) - (r0409*WLz)/2.);
+dr0410_dt = (-(gt*r0410) - (gt + g1)*r0410)/2. - i*(-(conj(Em2a)*conj(r0604))/(4.*rt6) + (conj(Ep2a)*conj(r0804))/(4.*rt6) + (conj(Ep4a)*conj(r1014))/8. - (conj(Em4a)*conj(r1016))/(4.*rt6) - (conj(Em1a)*r0402)/(4.*rt2) - (conj(Ep1a)*r0404)/(4.*rt2) + (delta1 + v*Kvec1)*r0410 + (conj(Ep1a)*r1010)/(4.*rt2) + r0510*(WLx/2. - (i*WLy)/2.) + r0310*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0411*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0409*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - (r0410*WLz)/2.);
+dr0411_dt = (-(gt*r0411) - (gt + g1)*r0411)/2. - i*(-(conj(Ep1a)*conj(r0504))/4. - (conj(Em2a)*conj(r0704))/(4.*rt6) + (conj(Ep1a)*conj(r1110))/(4.*rt2) + (conj(Ep4a)*conj(r1114))/8. - (conj(Em4a)*conj(r1116))/(4.*rt6) - (conj(Em1a)*r0403)/(4.*rt6) + r0511*(WLx/2. - (i*WLy)/2.) + r0311*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0410*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0411*(-delta1 - v*Kvec1 + WLz/6.) - (r0411*WLz)/2.);
+dr0412_dt = (-(gt*r0412) - (gt + g2)*r0412)/2. - i*(-(conj(Ep3a)*conj(r0604))/(4.*rt2) - (conj(Ep4a)*r0402)/(4.*rt6) + (conj(Ep1a)*r1012)/(4.*rt2) + (conj(Ep4a)*r1412)/8. - (conj(Em4a)*r1612)/(4.*rt6) + r0512*(WLx/2. - (i*WLy)/2.) - r0413*((2*WLx)/3. + (2*i*WLy)/3.) + r0312*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0412*WLz)/2. - r0412*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0413_dt = (-(gt*r0413) - (gt + g2)*r0413)/2. - i*(-(conj(Ep3a)*conj(r0704))/8. + (conj(Em4a)*r0401)/(4.*rt6) - (conj(Ep4a)*r0403)/8. + (conj(Ep1a)*r1013)/(4.*rt2) + (conj(Ep4a)*r1413)/8. - (conj(Em4a)*r1613)/(4.*rt6) - r0412*((2*WLx)/3. - (2*i*WLy)/3.) + r0513*(WLx/2. - (i*WLy)/2.) - r0414*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0313*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0413*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - (r0413*WLz)/2.);
+dr0414_dt = (-(gt*r0414) - (gt + g2)*r0414)/2. - i*(-(conj(Em3a)*conj(r0604))/(8.*rt3) - (conj(Ep3a)*conj(r0804))/(8.*rt3) + (conj(Em4a)*r0402)/8. - (conj(Ep4a)*r0404)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0414 + (conj(Ep1a)*r1014)/(4.*rt2) + (conj(Ep4a)*r1414)/8. - (conj(Em4a)*r1614)/(4.*rt6) + r0514*(WLx/2. - (i*WLy)/2.) - r0413*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0415*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0314*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (r0414*WLz)/2.);
+dr0415_dt = (-(gt*r0415) - (gt + g2)*r0415)/2. - i*(-(conj(Ep4a)*conj(r0504))/(4.*rt6) - (conj(Em3a)*conj(r0704))/8. + (conj(Ep4a)*conj(r1514))/8. + (conj(Em4a)*r0403)/8. + (conj(Ep1a)*r1015)/(4.*rt2) - (conj(Em4a)*r1615)/(4.*rt6) + r0515*(WLx/2. - (i*WLy)/2.) - r0416*((2*WLx)/3. + (2*i*WLy)/3.) - r0414*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0315*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0415*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - (r0415*WLz)/2.);
+dr0416_dt = (-(gt*r0416) - (gt + g2)*r0416)/2. - i*(-(conj(Em3a)*conj(r0804))/(4.*rt2) + (conj(Ep4a)*conj(r1614))/8. + (conj(Em4a)*r0404)/(4.*rt6) + (conj(Ep1a)*r1016)/(4.*rt2) - (conj(Em4a)*r1616)/(4.*rt6) - r0415*((2*WLx)/3. - (2*i*WLy)/3.) + r0516*(WLx/2. - (i*WLy)/2.) + r0316*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0416*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - (r0416*WLz)/2.);
+dr0501_dt = -(gt*r0501) - (g2*r1612)/3. - i*((conj(Ep1a)*conj(r0111))/4. + (conj(Ep4a)*conj(r0115))/(4.*rt6) - (Em1a*r0509)/4. + (Em4a*r0513)/(4.*rt6) + r0401*(WLx/2. + (i*WLy)/2.) - r0502*(WLx/2. + (i*WLy)/2.) - 2*r0501*WLz);
+dr0502_dt = -(gt*r0502) + (g2*r1512)/6. - (g2*r1613)/6. - i*((conj(Ep1a)*conj(r0211))/4. + (conj(Ep4a)*conj(r0215))/(4.*rt6) - (Em1a*r0510)/(4.*rt2) - (Ep4a*r0512)/(4.*rt6) + (Em4a*r0514)/8. - r0501*(WLx/2. - (i*WLy)/2.) + r0402*(WLx/2. + (i*WLy)/2.) - r0503*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - (3*r0502*WLz)/2.);
+dr0503_dt = -(gt*r0503) + (g1*r1109)/(2.*rt6) + (g2*r1513)/(2.*rt6) - i*((conj(Ep1a)*conj(r0311))/4. + (conj(Ep4a)*conj(r0315))/(4.*rt6) - (Ep1a*r0509)/(4.*rt6) - (Em1a*r0511)/(4.*rt6) - (Ep4a*r0513)/8. + (Em4a*r0515)/8. + r0403*(WLx/2. + (i*WLy)/2.) - r0502*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0504*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) - r0503*WLz);
+dr0504_dt = -(gt*r0504) + (g1*r1110)/(2.*rt2) + (g2*r1514)/(2.*rt6) + (g2*r1615)/6. - i*((conj(Ep1a)*conj(r0411))/4. + (conj(Ep4a)*conj(r0415))/(4.*rt6) - (Ep1a*r0510)/(4.*rt2) - (Ep4a*r0514)/8. + (Em4a*r0516)/(4.*rt6) + r0404*(WLx/2. + (i*WLy)/2.) - r0505*(WLx/2. + (i*WLy)/2.) - r0503*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - (r0504*WLz)/2.);
+dr0505_dt = gt/8. - gt*r0505 + (g1*r1111)/2. + (g2*r1515)/6. + (g2*r1616)/3. - i*((conj(Ep1a)*conj(r0511))/4. + (conj(Ep4a)*conj(r0515))/(4.*rt6) - (Ep1a*r0511)/4. - (Ep4a*r0515)/(4.*rt6) - r0504*(WLx/2. - (i*WLy)/2.) + conj(r0504)*(WLx/2. + (i*WLy)/2.));
+dr0509_dt = (-(gt*r0509) - (gt + g1)*r0509)/2. - i*((conj(Ep2a)*conj(r0705))/(4.*rt6) + (conj(Ep4a)*conj(r0915))/(4.*rt6) - (conj(Em1a)*r0501)/4. - (conj(Ep1a)*r0503)/(4.*rt6) + (conj(Ep1a)*r1109)/4. + r0409*(WLx/2. + (i*WLy)/2.) - r0510*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0509*(-delta1 - v*Kvec1 - WLz/6.) - r0509*WLz);
+dr0510_dt = (-(gt*r0510) - (gt + g1)*r0510)/2. - i*(-(conj(Em2a)*conj(r0605))/(4.*rt6) + (conj(Ep2a)*conj(r0805))/(4.*rt6) + (conj(Ep4a)*conj(r1015))/(4.*rt6) - (conj(Em1a)*r0502)/(4.*rt2) - (conj(Ep1a)*r0504)/(4.*rt2) + (delta1 + v*Kvec1)*r0510 + (conj(Ep1a)*r1110)/4. + r0410*(WLx/2. + (i*WLy)/2.) - r0511*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0509*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0510*WLz);
+dr0511_dt = (-(gt*r0511) - (gt + g1)*r0511)/2. - i*(-(conj(Em2a)*conj(r0705))/(4.*rt6) + (conj(Ep4a)*conj(r1115))/(4.*rt6) - (conj(Em1a)*r0503)/(4.*rt6) - (conj(Ep1a)*r0505)/4. + (conj(Ep1a)*r1111)/4. + r0411*(WLx/2. + (i*WLy)/2.) - r0510*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0511*(-delta1 - v*Kvec1 + WLz/6.) - r0511*WLz);
+dr0512_dt = (-(gt*r0512) - (gt + g2)*r0512)/2. - i*(-(conj(Ep3a)*conj(r0605))/(4.*rt2) - (conj(Ep4a)*r0502)/(4.*rt6) + (conj(Ep1a)*r1112)/4. + (conj(Ep4a)*r1512)/(4.*rt6) + r0412*(WLx/2. + (i*WLy)/2.) - r0513*((2*WLx)/3. + (2*i*WLy)/3.) - r0512*WLz - r0512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0513_dt = (-(gt*r0513) - (gt + g2)*r0513)/2. - i*(-(conj(Ep3a)*conj(r0705))/8. + (conj(Em4a)*r0501)/(4.*rt6) - (conj(Ep4a)*r0503)/8. + (conj(Ep1a)*r1113)/4. + (conj(Ep4a)*r1513)/(4.*rt6) - r0512*((2*WLx)/3. - (2*i*WLy)/3.) + r0413*(WLx/2. + (i*WLy)/2.) - r0514*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r0513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - r0513*WLz);
+dr0514_dt = (-(gt*r0514) - (gt + g2)*r0514)/2. - i*(-(conj(Em3a)*conj(r0605))/(8.*rt3) - (conj(Ep3a)*conj(r0805))/(8.*rt3) + (conj(Em4a)*r0502)/8. - (conj(Ep4a)*r0504)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0514 + (conj(Ep1a)*r1114)/4. + (conj(Ep4a)*r1514)/(4.*rt6) + r0414*(WLx/2. + (i*WLy)/2.) - r0513*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0515*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r0514*WLz);
+dr0515_dt = (-(gt*r0515) - (gt + g2)*r0515)/2. - i*(-(conj(Em3a)*conj(r0705))/8. + (conj(Em4a)*r0503)/8. - (conj(Ep4a)*r0505)/(4.*rt6) + (conj(Ep1a)*r1115)/4. + (conj(Ep4a)*r1515)/(4.*rt6) + r0415*(WLx/2. + (i*WLy)/2.) - r0516*((2*WLx)/3. + (2*i*WLy)/3.) - r0514*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0515*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r0515*WLz);
+dr0516_dt = (-(gt*r0516) - (gt + g2)*r0516)/2. - i*(-(conj(Em3a)*conj(r0805))/(4.*rt2) + (conj(Ep4a)*conj(r1615))/(4.*rt6) + (conj(Em4a)*r0504)/(4.*rt6) + (conj(Ep1a)*r1116)/4. - r0515*((2*WLx)/3. - (2*i*WLy)/3.) + r0416*(WLx/2. + (i*WLy)/2.) - r0516*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r0516*WLz);
+dr0601_dt = -(gt*r0601) - i*((conj(Em2a)*conj(r0110))/(4.*rt6) + (conj(Ep3a)*conj(r0112))/(4.*rt2) + (conj(Em3a)*conj(r0114))/(8.*rt3) - (Em1a*r0609)/4. + (Em4a*r0613)/(4.*rt6) - r0602*(WLx/2. + (i*WLy)/2.) + r0701*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0601*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0601*WLz);
+dr0602_dt = -(gt*r0602) - i*((conj(Em2a)*conj(r0210))/(4.*rt6) + (conj(Ep3a)*conj(r0212))/(4.*rt2) + (conj(Em3a)*conj(r0214))/(8.*rt3) - (Em1a*r0610)/(4.*rt2) - (Ep4a*r0612)/(4.*rt6) + (Em4a*r0614)/8. - r0601*(WLx/2. - (i*WLy)/2.) - r0603*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0702*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0602*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - (r0602*WLz)/2.);
+dr0603_dt = -(gt*r0603) - i*((conj(Em2a)*conj(r0310))/(4.*rt6) + (conj(Ep3a)*conj(r0312))/(4.*rt2) + (conj(Em3a)*conj(r0314))/(8.*rt3) - (Ep1a*r0609)/(4.*rt6) - (Em1a*r0611)/(4.*rt6) - (Ep4a*r0613)/8. + (Em4a*r0615)/8. - r0602*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0604*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0703*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0603*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0604_dt = -(gt*r0604) - i*((conj(Em2a)*conj(r0410))/(4.*rt6) + (conj(Ep3a)*conj(r0412))/(4.*rt2) + (conj(Em3a)*conj(r0414))/(8.*rt3) - (Ep1a*r0610)/(4.*rt2) - (Ep4a*r0614)/8. + (Em4a*r0616)/(4.*rt6) - r0605*(WLx/2. + (i*WLy)/2.) - r0603*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0704*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0604*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + (r0604*WLz)/2.);
+dr0605_dt = -(gt*r0605) - i*((conj(Em2a)*conj(r0510))/(4.*rt6) + (conj(Ep3a)*conj(r0512))/(4.*rt2) + (conj(Em3a)*conj(r0514))/(8.*rt3) - (Ep1a*r0611)/4. - (Ep4a*r0615)/(4.*rt6) - r0604*(WLx/2. - (i*WLy)/2.) + r0705*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0605*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + r0605*WLz);
+dr0606_dt = gt/8. - gt*r0606 + (g1*r0909)/12. + (g1*r1010)/12. + (g2*r1212)/2. + (g2*r1313)/4. + (g2*r1414)/12. - i*((conj(Em2a)*conj(r0610))/(4.*rt6) + (conj(Ep3a)*conj(r0612))/(4.*rt2) + (conj(Em3a)*conj(r0614))/(8.*rt3) - (Em2a*r0610)/(4.*rt6) - (Ep3a*r0612)/(4.*rt2) - (Em3a*r0614)/(8.*rt3) - conj(r0706)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0706*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0609_dt = (-(gt*r0609) - (gt + g1)*r0609)/2. - i*((conj(Ep2a)*conj(r0706))/(4.*rt6) + (conj(Ep3a)*conj(r0912))/(4.*rt2) + (conj(Em3a)*conj(r0914))/(8.*rt3) - (conj(Em1a)*r0601)/4. - (conj(Ep1a)*r0603)/(4.*rt6) + (conj(Em2a)*r1009)/(4.*rt6) - r0610*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r0709*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0609*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0609*(-delta1 - v*Kvec1 - WLz/6.));
+dr0610_dt = (-(gt*r0610) - (gt + g1)*r0610)/2. - i*((conj(Ep2a)*conj(r0806))/(4.*rt6) + (conj(Ep3a)*conj(r1012))/(4.*rt2) + (conj(Em3a)*conj(r1014))/(8.*rt3) - (conj(Em1a)*r0602)/(4.*rt2) - (conj(Ep1a)*r0604)/(4.*rt2) - (conj(Em2a)*r0606)/(4.*rt6) + (delta1 + v*Kvec1)*r0610 + (conj(Em2a)*r1010)/(4.*rt6) - r0611*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0609*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0710*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0610*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0611_dt = (-(gt*r0611) - (gt + g1)*r0611)/2. - i*(-(conj(Em2a)*conj(r0706))/(4.*rt6) + (conj(Em2a)*conj(r1110))/(4.*rt6) + (conj(Ep3a)*conj(r1112))/(4.*rt2) + (conj(Em3a)*conj(r1114))/(8.*rt3) - (conj(Em1a)*r0603)/(4.*rt6) - (conj(Ep1a)*r0605)/4. - r0610*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0711*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0611*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0611*(-delta1 - v*Kvec1 + WLz/6.));
+dr0612_dt = (-(gt*r0612) - (gt + g2)*r0612)/2. - i*(-(conj(Ep4a)*r0602)/(4.*rt6) - (conj(Ep3a)*r0606)/(4.*rt2) + (conj(Em2a)*r1012)/(4.*rt6) + (conj(Ep3a)*r1212)/(4.*rt2) + (conj(Em3a)*r1412)/(8.*rt3) - r0613*((2*WLx)/3. + (2*i*WLy)/3.) + r0712*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0612*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0613_dt = (-(gt*r0613) - (gt + g2)*r0613)/2. - i*(-(conj(Ep3a)*conj(r0706))/8. + (conj(Ep3a)*conj(r1312))/(4.*rt2) + (conj(Em4a)*r0601)/(4.*rt6) - (conj(Ep4a)*r0603)/8. + (conj(Em2a)*r1013)/(4.*rt6) + (conj(Em3a)*r1413)/(8.*rt3) - r0612*((2*WLx)/3. - (2*i*WLy)/3.) - r0614*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0713*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0613*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) - r0613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0614_dt = (-(gt*r0614) - (gt + g2)*r0614)/2. - i*(-(conj(Ep3a)*conj(r0806))/(8.*rt3) + (conj(Ep3a)*conj(r1412))/(4.*rt2) + (conj(Em4a)*r0602)/8. - (conj(Ep4a)*r0604)/8. - (conj(Em3a)*r0606)/(8.*rt3) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0614 + (conj(Em2a)*r1014)/(4.*rt6) + (conj(Em3a)*r1414)/(8.*rt3) - r0613*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0615*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0714*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0614*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0615_dt = (-(gt*r0615) - (gt + g2)*r0615)/2. - i*(-(conj(Em3a)*conj(r0706))/8. + (conj(Ep3a)*conj(r1512))/(4.*rt2) + (conj(Em3a)*conj(r1514))/(8.*rt3) + (conj(Em4a)*r0603)/8. - (conj(Ep4a)*r0605)/(4.*rt6) + (conj(Em2a)*r1015)/(4.*rt6) - r0616*((2*WLx)/3. + (2*i*WLy)/3.) - r0614*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0715*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0615*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0616_dt = (-(gt*r0616) - (gt + g2)*r0616)/2. - i*(-(conj(Em3a)*conj(r0806))/(4.*rt2) + (conj(Ep3a)*conj(r1612))/(4.*rt2) + (conj(Em3a)*conj(r1614))/(8.*rt3) + (conj(Em4a)*r0604)/(4.*rt6) + (conj(Em2a)*r1016)/(4.*rt6) - r0615*((2*WLx)/3. - (2*i*WLy)/3.) + r0716*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0616*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0616*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0701_dt = -(gt*r0701) - i*(-(conj(Ep2a)*conj(r0109))/(4.*rt6) + (conj(Em2a)*conj(r0111))/(4.*rt6) + (conj(Ep3a)*conj(r0113))/8. + (conj(Em3a)*conj(r0115))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0701 - (Em1a*r0709)/4. + (Em4a*r0713)/(4.*rt6) - r0702*(WLx/2. + (i*WLy)/2.) + r0601*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0801*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0701*WLz);
+dr0702_dt = -(gt*r0702) - i*(-(conj(Ep2a)*conj(r0209))/(4.*rt6) + (conj(Em2a)*conj(r0211))/(4.*rt6) + (conj(Ep3a)*conj(r0213))/8. + (conj(Em3a)*conj(r0215))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0702 - (Em1a*r0710)/(4.*rt2) - (Ep4a*r0712)/(4.*rt6) + (Em4a*r0714)/8. - r0701*(WLx/2. - (i*WLy)/2.) - r0703*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0602*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0802*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - (r0702*WLz)/2.);
+dr0703_dt = -(gt*r0703) - i*(-(conj(Ep2a)*conj(r0309))/(4.*rt6) + (conj(Em2a)*conj(r0311))/(4.*rt6) + (conj(Ep3a)*conj(r0313))/8. + (conj(Em3a)*conj(r0315))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0703 - (Ep1a*r0709)/(4.*rt6) - (Em1a*r0711)/(4.*rt6) - (Ep4a*r0713)/8. + (Em4a*r0715)/8. - r0702*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0704*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0603*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0803*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0704_dt = -(gt*r0704) - i*(-(conj(Ep2a)*conj(r0409))/(4.*rt6) + (conj(Em2a)*conj(r0411))/(4.*rt6) + (conj(Ep3a)*conj(r0413))/8. + (conj(Em3a)*conj(r0415))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0704 - (Ep1a*r0710)/(4.*rt2) - (Ep4a*r0714)/8. + (Em4a*r0716)/(4.*rt6) - r0705*(WLx/2. + (i*WLy)/2.) - r0703*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0604*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0804*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + (r0704*WLz)/2.);
+dr0705_dt = -(gt*r0705) - i*(-(conj(Ep2a)*conj(r0509))/(4.*rt6) + (conj(Em2a)*conj(r0511))/(4.*rt6) + (conj(Ep3a)*conj(r0513))/8. + (conj(Em3a)*conj(r0515))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0705 - (Ep1a*r0711)/4. - (Ep4a*r0715)/(4.*rt6) - r0704*(WLx/2. - (i*WLy)/2.) + r0605*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0805*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0705*WLz);
+dr0706_dt = -(gt*r0706) + (g1*r1110)/12. + (g2*r1312)/(2.*rt2) + (g2*r1413)/(2.*rt3) + (g2*r1514)/(4.*rt3) - i*(-(conj(Ep2a)*conj(r0609))/(4.*rt6) + (conj(Em2a)*conj(r0611))/(4.*rt6) + (conj(Ep3a)*conj(r0613))/8. + (conj(Em3a)*conj(r0615))/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0706 - (Em2a*r0710)/(4.*rt6) - (Ep3a*r0712)/(4.*rt2) - (Em3a*r0714)/(8.*rt3) + r0606*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0707*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0806*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0706*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.));
+dr0707_dt = gt/8. - gt*r0707 + (g1*r0909)/12. + (g1*r1111)/12. + (g2*r1313)/4. + (g2*r1414)/3. + (g2*r1515)/4. - i*(-(conj(Ep2a)*conj(r0709))/(4.*rt6) + (conj(Em2a)*conj(r0711))/(4.*rt6) + (conj(Ep3a)*conj(r0713))/8. + (conj(Em3a)*conj(r0715))/8. + (Ep2a*r0709)/(4.*rt6) - (Em2a*r0711)/(4.*rt6) - (Ep3a*r0713)/8. - (Em3a*r0715)/8. + conj(r0706)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - conj(r0807)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0706*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0807*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0709_dt = (-(gt*r0709) - (gt + g1)*r0709)/2. - i*((conj(Ep3a)*conj(r0913))/8. + (conj(Em3a)*conj(r0915))/8. - (conj(Em1a)*r0701)/4. - (conj(Ep1a)*r0703)/(4.*rt6) + (conj(Ep2a)*r0707)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0709 - (conj(Ep2a)*r0909)/(4.*rt6) + (conj(Em2a)*r1109)/(4.*rt6) + r0609*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0710*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r0809*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0709*(-delta1 - v*Kvec1 - WLz/6.));
+dr0710_dt = (-(gt*r0710) - (gt + g1)*r0710)/2. - i*((conj(Ep2a)*conj(r0807))/(4.*rt6) - (conj(Ep2a)*conj(r1009))/(4.*rt6) + (conj(Ep3a)*conj(r1013))/8. + (conj(Em3a)*conj(r1015))/8. - (conj(Em1a)*r0702)/(4.*rt2) - (conj(Ep1a)*r0704)/(4.*rt2) - (conj(Em2a)*r0706)/(4.*rt6) + (delta1 + v*Kvec1)*r0710 + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0710 + (conj(Em2a)*r1110)/(4.*rt6) + r0610*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0711*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0709*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0810*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0711_dt = (-(gt*r0711) - (gt + g1)*r0711)/2. - i*(-(conj(Ep2a)*conj(r1109))/(4.*rt6) + (conj(Ep3a)*conj(r1113))/8. + (conj(Em3a)*conj(r1115))/8. - (conj(Em1a)*r0703)/(4.*rt6) - (conj(Ep1a)*r0705)/4. - (conj(Em2a)*r0707)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0711 + (conj(Em2a)*r1111)/(4.*rt6) + r0611*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0710*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0811*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0711*(-delta1 - v*Kvec1 + WLz/6.));
+dr0712_dt = (-(gt*r0712) - (gt + g2)*r0712)/2. - i*(-(conj(Ep4a)*r0702)/(4.*rt6) - (conj(Ep3a)*r0706)/(4.*rt2) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0712 - (conj(Ep2a)*r0912)/(4.*rt6) + (conj(Em2a)*r1112)/(4.*rt6) + (conj(Ep3a)*r1312)/8. + (conj(Em3a)*r1512)/8. - r0713*((2*WLx)/3. + (2*i*WLy)/3.) + r0612*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0812*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0712*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0713_dt = (-(gt*r0713) - (gt + g2)*r0713)/2. - i*((conj(Em4a)*r0701)/(4.*rt6) - (conj(Ep4a)*r0703)/8. - (conj(Ep3a)*r0707)/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0713 - (conj(Ep2a)*r0913)/(4.*rt6) + (conj(Em2a)*r1113)/(4.*rt6) + (conj(Ep3a)*r1313)/8. + (conj(Em3a)*r1513)/8. - r0712*((2*WLx)/3. - (2*i*WLy)/3.) - r0714*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0613*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0813*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0713*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0714_dt = (-(gt*r0714) - (gt + g2)*r0714)/2. - i*(-(conj(Ep3a)*conj(r0807))/(8.*rt3) + (conj(Ep3a)*conj(r1413))/8. + (conj(Em4a)*r0702)/8. - (conj(Ep4a)*r0704)/8. - (conj(Em3a)*r0706)/(8.*rt3) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0714 - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0714 - (conj(Ep2a)*r0914)/(4.*rt6) + (conj(Em2a)*r1114)/(4.*rt6) + (conj(Em3a)*r1514)/8. - r0713*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0715*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0614*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0814*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0715_dt = (-(gt*r0715) - (gt + g2)*r0715)/2. - i*((conj(Ep3a)*conj(r1513))/8. + (conj(Em4a)*r0703)/8. - (conj(Ep4a)*r0705)/(4.*rt6) - (conj(Em3a)*r0707)/8. + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0715 - (conj(Ep2a)*r0915)/(4.*rt6) + (conj(Em2a)*r1115)/(4.*rt6) + (conj(Em3a)*r1515)/8. - r0716*((2*WLx)/3. + (2*i*WLy)/3.) - r0714*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0615*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0815*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0715*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr0716_dt = (-(gt*r0716) - (gt + g2)*r0716)/2. - i*(-(conj(Em3a)*conj(r0807))/(4.*rt2) + (conj(Ep3a)*conj(r1613))/8. + (conj(Em3a)*conj(r1615))/8. + (conj(Em4a)*r0704)/(4.*rt6) + (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0716 - (conj(Ep2a)*r0916)/(4.*rt6) + (conj(Em2a)*r1116)/(4.*rt6) - r0715*((2*WLx)/3. - (2*i*WLy)/3.) + r0616*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0816*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) - r0716*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr0801_dt = -(gt*r0801) - i*(-(conj(Ep2a)*conj(r0110))/(4.*rt6) + (conj(Ep3a)*conj(r0114))/(8.*rt3) + (conj(Em3a)*conj(r0116))/(4.*rt2) - (Em1a*r0809)/4. + (Em4a*r0813)/(4.*rt6) - r0802*(WLx/2. + (i*WLy)/2.) + r0701*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0801*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0801*WLz);
+dr0802_dt = -(gt*r0802) - i*(-(conj(Ep2a)*conj(r0210))/(4.*rt6) + (conj(Ep3a)*conj(r0214))/(8.*rt3) + (conj(Em3a)*conj(r0216))/(4.*rt2) - (Em1a*r0810)/(4.*rt2) - (Ep4a*r0812)/(4.*rt6) + (Em4a*r0814)/8. - r0801*(WLx/2. - (i*WLy)/2.) - r0803*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0702*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0802*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - (r0802*WLz)/2.);
+dr0803_dt = -(gt*r0803) - i*(-(conj(Ep2a)*conj(r0310))/(4.*rt6) + (conj(Ep3a)*conj(r0314))/(8.*rt3) + (conj(Em3a)*conj(r0316))/(4.*rt2) - (Ep1a*r0809)/(4.*rt6) - (Em1a*r0811)/(4.*rt6) - (Ep4a*r0813)/8. + (Em4a*r0815)/8. - r0802*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) - r0804*((sqrt(1.5)*WLx)/2. + (sqrt(1.5)*i*WLy)/2.) + r0703*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0803*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0804_dt = -(gt*r0804) - i*(-(conj(Ep2a)*conj(r0410))/(4.*rt6) + (conj(Ep3a)*conj(r0414))/(8.*rt3) + (conj(Em3a)*conj(r0416))/(4.*rt2) - (Ep1a*r0810)/(4.*rt2) - (Ep4a*r0814)/8. + (Em4a*r0816)/(4.*rt6) - r0805*(WLx/2. + (i*WLy)/2.) - r0803*((sqrt(1.5)*WLx)/2. - (sqrt(1.5)*i*WLy)/2.) + r0704*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0804*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) + (r0804*WLz)/2.);
+dr0805_dt = -(gt*r0805) - i*(-(conj(Ep2a)*conj(r0510))/(4.*rt6) + (conj(Ep3a)*conj(r0514))/(8.*rt3) + (conj(Em3a)*conj(r0516))/(4.*rt2) - (Ep1a*r0811)/4. - (Ep4a*r0815)/(4.*rt6) - r0804*(WLx/2. - (i*WLy)/2.) + r0705*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0805*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) + r0805*WLz);
+dr0806_dt = -(gt*r0806) - (g1*r1109)/12. + (g2*r1412)/(2.*rt6) + (g2*r1513)/4. + (g2*r1614)/(2.*rt6) - i*(-(conj(Ep2a)*conj(r0610))/(4.*rt6) + (conj(Ep3a)*conj(r0614))/(8.*rt3) + (conj(Em3a)*conj(r0616))/(4.*rt2) - (Em2a*r0810)/(4.*rt6) - (Ep3a*r0812)/(4.*rt2) - (Em3a*r0814)/(8.*rt3) + r0706*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0807*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0806*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 - WLz/2.) + r0806*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0807_dt = -(gt*r0807) + (g1*r1009)/12. + (g2*r1413)/(4.*rt3) + (g2*r1514)/(2.*rt3) + (g2*r1615)/(2.*rt2) - i*(-(conj(Ep2a)*conj(r0710))/(4.*rt6) + (conj(Ep3a)*conj(r0714))/(8.*rt3) + (conj(Em3a)*conj(r0716))/(4.*rt2) - (-delta1 + delta2 - v*Kvec1 + v*Kvec2)*r0807 + (Ep2a*r0809)/(4.*rt6) - (Em2a*r0811)/(4.*rt6) - (Ep3a*r0813)/8. - (Em3a*r0815)/8. + r0707*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0808*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0806*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)) + r0807*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0808_dt = gt/8. - gt*r0808 + (g1*r1010)/12. + (g1*r1111)/12. + (g2*r1414)/12. + (g2*r1515)/4. + (g2*r1616)/2. - i*(-(conj(Ep2a)*conj(r0810))/(4.*rt6) + (conj(Ep3a)*conj(r0814))/(8.*rt3) + (conj(Em3a)*conj(r0816))/(4.*rt2) + (Ep2a*r0810)/(4.*rt6) - (Ep3a*r0814)/(8.*rt3) - (Em3a*r0816)/(4.*rt2) + conj(r0807)*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0807*(-WLx/(2.*rt2) + (i*WLy)/(2.*rt2)));
+dr0809_dt = (-(gt*r0809) - (gt + g1)*r0809)/2. - i*((conj(Ep3a)*conj(r0914))/(8.*rt3) + (conj(Em3a)*conj(r0916))/(4.*rt2) - (conj(Em1a)*r0801)/4. - (conj(Ep1a)*r0803)/(4.*rt6) + (conj(Ep2a)*r0807)/(4.*rt6) - (conj(Ep2a)*r1009)/(4.*rt6) + r0709*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0810*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0809*(-delta1 - v*Kvec1 - WLz/6.) + r0809*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0810_dt = (-(gt*r0810) - (gt + g1)*r0810)/2. - i*((conj(Ep3a)*conj(r1014))/(8.*rt3) + (conj(Em3a)*conj(r1016))/(4.*rt2) - (conj(Em1a)*r0802)/(4.*rt2) - (conj(Ep1a)*r0804)/(4.*rt2) - (conj(Em2a)*r0806)/(4.*rt6) + (conj(Ep2a)*r0808)/(4.*rt6) + (delta1 + v*Kvec1)*r0810 - (conj(Ep2a)*r1010)/(4.*rt6) + r0710*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0811*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r0809*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0810*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0811_dt = (-(gt*r0811) - (gt + g1)*r0811)/2. - i*(-(conj(Ep2a)*conj(r1110))/(4.*rt6) + (conj(Ep3a)*conj(r1114))/(8.*rt3) + (conj(Em3a)*conj(r1116))/(4.*rt2) - (conj(Em1a)*r0803)/(4.*rt6) - (conj(Ep1a)*r0805)/4. - (conj(Em2a)*r0807)/(4.*rt6) + r0711*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0810*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0811*(-delta1 - v*Kvec1 + WLz/6.) + r0811*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0812_dt = (-(gt*r0812) - (gt + g2)*r0812)/2. - i*(-(conj(Ep4a)*r0802)/(4.*rt6) - (conj(Ep3a)*r0806)/(4.*rt2) - (conj(Ep2a)*r1012)/(4.*rt6) + (conj(Ep3a)*r1412)/(8.*rt3) + (conj(Em3a)*r1612)/(4.*rt2) - r0813*((2*WLx)/3. + (2*i*WLy)/3.) + r0712*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0812*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0812*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0813_dt = (-(gt*r0813) - (gt + g2)*r0813)/2. - i*((conj(Em4a)*r0801)/(4.*rt6) - (conj(Ep4a)*r0803)/8. - (conj(Ep3a)*r0807)/8. - (conj(Ep2a)*r1013)/(4.*rt6) + (conj(Ep3a)*r1413)/(8.*rt3) + (conj(Em3a)*r1613)/(4.*rt2) - r0812*((2*WLx)/3. - (2*i*WLy)/3.) - r0814*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0713*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0813*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.) - r0813*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0814_dt = (-(gt*r0814) - (gt + g2)*r0814)/2. - i*((conj(Em4a)*r0802)/8. - (conj(Ep4a)*r0804)/8. - (conj(Em3a)*r0806)/(8.*rt3) - (conj(Ep3a)*r0808)/(8.*rt3) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0814 - (conj(Ep2a)*r1014)/(4.*rt6) + (conj(Ep3a)*r1414)/(8.*rt3) + (conj(Em3a)*r1614)/(4.*rt2) - r0813*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0815*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0714*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) + r0814*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0815_dt = (-(gt*r0815) - (gt + g2)*r0815)/2. - i*((conj(Ep3a)*conj(r1514))/(8.*rt3) + (conj(Em4a)*r0803)/8. - (conj(Ep4a)*r0805)/(4.*rt6) - (conj(Em3a)*r0807)/8. - (conj(Ep2a)*r1015)/(4.*rt6) + (conj(Em3a)*r1615)/(4.*rt2) - r0816*((2*WLx)/3. + (2*i*WLy)/3.) - r0814*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0715*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0815*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0815*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0816_dt = (-(gt*r0816) - (gt + g2)*r0816)/2. - i*((conj(Ep3a)*conj(r1614))/(8.*rt3) + (conj(Em4a)*r0804)/(4.*rt6) - (conj(Em3a)*r0808)/(4.*rt2) - (conj(Ep2a)*r1016)/(4.*rt6) + (conj(Em3a)*r1616)/(4.*rt2) - r0815*((2*WLx)/3. - (2*i*WLy)/3.) + r0716*(-WLx/(2.*rt2) - (i*WLy)/(2.*rt2)) - r0816*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0816*(-delta1 + delta2 - v*Kvec1 + v*Kvec2 + WLz/2.));
+dr0909_dt = -((gt + g1)*r0909) - i*(-(conj(Em1a)*conj(r0109))/4. - (conj(Ep1a)*conj(r0309))/(4.*rt6) + (conj(Ep2a)*conj(r0709))/(4.*rt6) + (Em1a*r0109)/4. + (Ep1a*r0309)/(4.*rt6) - (Ep2a*r0709)/(4.*rt6) - conj(r1009)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1009*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr0912_dt = (-((gt + g1)*r0912) - (gt + g2)*r0912)/2. - i*(-(conj(Ep4a)*conj(r0209))/(4.*rt6) - (conj(Ep3a)*conj(r0609))/(4.*rt2) + (Em1a*r0112)/4. + (Ep1a*r0312)/(4.*rt6) - (Ep2a*r0712)/(4.*rt6) - r0913*((2*WLx)/3. + (2*i*WLy)/3.) + r1012*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0912*(-delta1 - v*Kvec1 - WLz/6.) - r0912*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr0913_dt = (-((gt + g1)*r0913) - (gt + g2)*r0913)/2. - i*((conj(Em4a)*conj(r0109))/(4.*rt6) - (conj(Ep4a)*conj(r0309))/8. - (conj(Ep3a)*conj(r0709))/8. + (Em1a*r0113)/4. + (Ep1a*r0313)/(4.*rt6) - (Ep2a*r0713)/(4.*rt6) - r0912*((2*WLx)/3. - (2*i*WLy)/3.) - r0914*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1013*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0913*(-delta1 - v*Kvec1 - WLz/6.) - r0913*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr0914_dt = (-((gt + g1)*r0914) - (gt + g2)*r0914)/2. - i*((conj(Em4a)*conj(r0209))/8. - (conj(Ep4a)*conj(r0409))/8. - (conj(Em3a)*conj(r0609))/(8.*rt3) - (conj(Ep3a)*conj(r0809))/(8.*rt3) + (Em1a*r0114)/4. + (Ep1a*r0314)/(4.*rt6) - (Ep2a*r0714)/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r0914 - r0913*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r0915*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1014*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r0914*(-delta1 - v*Kvec1 - WLz/6.));
+dr0915_dt = (-((gt + g1)*r0915) - (gt + g2)*r0915)/2. - i*((conj(Em4a)*conj(r0309))/8. - (conj(Ep4a)*conj(r0509))/(4.*rt6) - (conj(Em3a)*conj(r0709))/8. + (Em1a*r0115)/4. + (Ep1a*r0315)/(4.*rt6) - (Ep2a*r0715)/(4.*rt6) - r0916*((2*WLx)/3. + (2*i*WLy)/3.) - r0914*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1015*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0915*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r0915*(-delta1 - v*Kvec1 - WLz/6.));
+dr0916_dt = (-((gt + g1)*r0916) - (gt + g2)*r0916)/2. - i*((conj(Em4a)*conj(r0409))/(4.*rt6) - (conj(Em3a)*conj(r0809))/(4.*rt2) + (Em1a*r0116)/4. + (Ep1a*r0316)/(4.*rt6) - (Ep2a*r0716)/(4.*rt6) - r0915*((2*WLx)/3. - (2*i*WLy)/3.) + r1016*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r0916*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r0916*(-delta1 - v*Kvec1 - WLz/6.));
+dr1009_dt = -((gt + g1)*r1009) - i*(-(conj(Em1a)*conj(r0110))/4. - (conj(Ep1a)*conj(r0310))/(4.*rt6) + (conj(Ep2a)*conj(r0710))/(4.*rt6) + (Em1a*r0209)/(4.*rt2) + (Ep1a*r0409)/(4.*rt2) + (Em2a*r0609)/(4.*rt6) - (Ep2a*r0809)/(4.*rt6) - (delta1 + v*Kvec1)*r1009 + r0909*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1010*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1009*(-delta1 - v*Kvec1 - WLz/6.));
+dr1010_dt = -((gt + g1)*r1010) - i*(-(conj(Em1a)*conj(r0210))/(4.*rt2) - (conj(Ep1a)*conj(r0410))/(4.*rt2) - (conj(Em2a)*conj(r0610))/(4.*rt6) + (conj(Ep2a)*conj(r0810))/(4.*rt6) + (Em1a*r0210)/(4.*rt2) + (Ep1a*r0410)/(4.*rt2) + (Em2a*r0610)/(4.*rt6) - (Ep2a*r0810)/(4.*rt6) + conj(r1009)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - conj(r1110)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1009*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r1110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr1012_dt = (-((gt + g1)*r1012) - (gt + g2)*r1012)/2. - i*(-(conj(Ep4a)*conj(r0210))/(4.*rt6) - (conj(Ep3a)*conj(r0610))/(4.*rt2) + (Em1a*r0212)/(4.*rt2) + (Ep1a*r0412)/(4.*rt2) + (Em2a*r0612)/(4.*rt6) - (Ep2a*r0812)/(4.*rt6) - (delta1 + v*Kvec1)*r1012 - r1013*((2*WLx)/3. + (2*i*WLy)/3.) + r0912*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1112*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1012*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1013_dt = (-((gt + g1)*r1013) - (gt + g2)*r1013)/2. - i*((conj(Em4a)*conj(r0110))/(4.*rt6) - (conj(Ep4a)*conj(r0310))/8. - (conj(Ep3a)*conj(r0710))/8. + (Em1a*r0213)/(4.*rt2) + (Ep1a*r0413)/(4.*rt2) + (Em2a*r0613)/(4.*rt6) - (Ep2a*r0813)/(4.*rt6) - (delta1 + v*Kvec1)*r1013 - r1012*((2*WLx)/3. - (2*i*WLy)/3.) - r1014*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0913*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1113*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1013*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1014_dt = (-((gt + g1)*r1014) - (gt + g2)*r1014)/2. - i*((conj(Em4a)*conj(r0210))/8. - (conj(Ep4a)*conj(r0410))/8. - (conj(Em3a)*conj(r0610))/(8.*rt3) - (conj(Ep3a)*conj(r0810))/(8.*rt3) + (Em1a*r0214)/(4.*rt2) + (Ep1a*r0414)/(4.*rt2) + (Em2a*r0614)/(4.*rt6) - (Ep2a*r0814)/(4.*rt6) - (delta1 + v*Kvec1)*r1014 - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1014 - r1013*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r1015*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r0914*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1114*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr1015_dt = (-((gt + g1)*r1015) - (gt + g2)*r1015)/2. - i*((conj(Em4a)*conj(r0310))/8. - (conj(Ep4a)*conj(r0510))/(4.*rt6) - (conj(Em3a)*conj(r0710))/8. + (Em1a*r0215)/(4.*rt2) + (Ep1a*r0415)/(4.*rt2) + (Em2a*r0615)/(4.*rt6) - (Ep2a*r0815)/(4.*rt6) - (delta1 + v*Kvec1)*r1015 - r1016*((2*WLx)/3. + (2*i*WLy)/3.) - r1014*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r0915*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1115*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1015*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr1016_dt = (-((gt + g1)*r1016) - (gt + g2)*r1016)/2. - i*((conj(Em4a)*conj(r0410))/(4.*rt6) - (conj(Em3a)*conj(r0810))/(4.*rt2) + (Em1a*r0216)/(4.*rt2) + (Ep1a*r0416)/(4.*rt2) + (Em2a*r0616)/(4.*rt6) - (Ep2a*r0816)/(4.*rt6) - (delta1 + v*Kvec1)*r1016 - r1015*((2*WLx)/3. - (2*i*WLy)/3.) + r0916*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1116*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) - r1016*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr1109_dt = -((gt + g1)*r1109) - i*(-(conj(Em1a)*conj(r0111))/4. - (conj(Ep1a)*conj(r0311))/(4.*rt6) + (conj(Ep2a)*conj(r0711))/(4.*rt6) + (Em1a*r0309)/(4.*rt6) + (Ep1a*r0509)/4. + (Em2a*r0709)/(4.*rt6) + r1009*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1110*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1109*(-delta1 - v*Kvec1 - WLz/6.) + r1109*(-delta1 - v*Kvec1 + WLz/6.));
+dr1110_dt = -((gt + g1)*r1110) - i*(-(conj(Em1a)*conj(r0211))/(4.*rt2) - (conj(Ep1a)*conj(r0411))/(4.*rt2) - (conj(Em2a)*conj(r0611))/(4.*rt6) + (conj(Ep2a)*conj(r0811))/(4.*rt6) + (Em1a*r0310)/(4.*rt6) + (Ep1a*r0510)/4. + (Em2a*r0710)/(4.*rt6) + (delta1 + v*Kvec1)*r1110 + r1010*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1111*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1109*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)) + r1110*(-delta1 - v*Kvec1 + WLz/6.));
+dr1111_dt = -((gt + g1)*r1111) - i*(-(conj(Em1a)*conj(r0311))/(4.*rt6) - (conj(Ep1a)*conj(r0511))/4. - (conj(Em2a)*conj(r0711))/(4.*rt6) + (Em1a*r0311)/(4.*rt6) + (Ep1a*r0511)/4. + (Em2a*r0711)/(4.*rt6) + conj(r1110)*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1110*(-WLx/(6.*rt2) + (i*WLy)/(6.*rt2)));
+dr1112_dt = (-((gt + g1)*r1112) - (gt + g2)*r1112)/2. - i*(-(conj(Ep4a)*conj(r0211))/(4.*rt6) - (conj(Ep3a)*conj(r0611))/(4.*rt2) + (Em1a*r0312)/(4.*rt6) + (Ep1a*r0512)/4. + (Em2a*r0712)/(4.*rt6) - r1113*((2*WLx)/3. + (2*i*WLy)/3.) + r1012*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1112*(-delta1 - v*Kvec1 + WLz/6.) - r1112*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1113_dt = (-((gt + g1)*r1113) - (gt + g2)*r1113)/2. - i*((conj(Em4a)*conj(r0111))/(4.*rt6) - (conj(Ep4a)*conj(r0311))/8. - (conj(Ep3a)*conj(r0711))/8. + (Em1a*r0313)/(4.*rt6) + (Ep1a*r0513)/4. + (Em2a*r0713)/(4.*rt6) - r1112*((2*WLx)/3. - (2*i*WLy)/3.) - r1114*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1013*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1113*(-delta1 - v*Kvec1 + WLz/6.) - r1113*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1114_dt = (-((gt + g1)*r1114) - (gt + g2)*r1114)/2. - i*((conj(Em4a)*conj(r0211))/8. - (conj(Ep4a)*conj(r0411))/8. - (conj(Em3a)*conj(r0611))/(8.*rt3) - (conj(Ep3a)*conj(r0811))/(8.*rt3) + (Em1a*r0314)/(4.*rt6) + (Ep1a*r0514)/4. + (Em2a*r0714)/(4.*rt6) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1114 - r1113*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r1115*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1014*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) + r1114*(-delta1 - v*Kvec1 + WLz/6.));
+dr1115_dt = (-((gt + g1)*r1115) - (gt + g2)*r1115)/2. - i*((conj(Em4a)*conj(r0311))/8. - (conj(Ep4a)*conj(r0511))/(4.*rt6) - (conj(Em3a)*conj(r0711))/8. + (Em1a*r0315)/(4.*rt6) + (Ep1a*r0515)/4. + (Em2a*r0715)/(4.*rt6) - r1116*((2*WLx)/3. + (2*i*WLy)/3.) - r1114*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1015*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1115*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) + r1115*(-delta1 - v*Kvec1 + WLz/6.));
+dr1116_dt = (-((gt + g1)*r1116) - (gt + g2)*r1116)/2. - i*((conj(Em4a)*conj(r0411))/(4.*rt6) - (conj(Em3a)*conj(r0811))/(4.*rt2) + (Em1a*r0316)/(4.*rt6) + (Ep1a*r0516)/4. + (Em2a*r0716)/(4.*rt6) - r1115*((2*WLx)/3. - (2*i*WLy)/3.) + r1016*(-WLx/(6.*rt2) - (i*WLy)/(6.*rt2)) - r1116*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) + r1116*(-delta1 - v*Kvec1 + WLz/6.));
+dr1212_dt = -((gt + g2)*r1212) - i*(-(conj(Ep4a)*conj(r0212))/(4.*rt6) - (conj(Ep3a)*conj(r0612))/(4.*rt2) + (Ep4a*r0212)/(4.*rt6) + (Ep3a*r0612)/(4.*rt2) + r1312*((2*WLx)/3. - (2*i*WLy)/3.) - conj(r1312)*((2*WLx)/3. + (2*i*WLy)/3.));
+dr1312_dt = -((gt + g2)*r1312) - i*(-(conj(Ep4a)*conj(r0213))/(4.*rt6) - (conj(Ep3a)*conj(r0613))/(4.*rt2) - (Em4a*r0112)/(4.*rt6) + (Ep4a*r0312)/8. + (Ep3a*r0712)/8. + r1212*((2*WLx)/3. + (2*i*WLy)/3.) - r1313*((2*WLx)/3. + (2*i*WLy)/3.) + r1412*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.) - r1312*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1313_dt = -((gt + g2)*r1313) - i*((conj(Em4a)*conj(r0113))/(4.*rt6) - (conj(Ep4a)*conj(r0313))/8. - (conj(Ep3a)*conj(r0713))/8. - (Em4a*r0113)/(4.*rt6) + (Ep4a*r0313)/8. + (Ep3a*r0713)/8. - r1312*((2*WLx)/3. - (2*i*WLy)/3.) + conj(r1312)*((2*WLx)/3. + (2*i*WLy)/3.) + r1413*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - conj(r1413)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy));
+dr1412_dt = -((gt + g2)*r1412) - i*(-(conj(Ep4a)*conj(r0214))/(4.*rt6) - (conj(Ep3a)*conj(r0614))/(4.*rt2) - (Em4a*r0212)/8. + (Ep4a*r0412)/8. + (Em3a*r0612)/(8.*rt3) + (Ep3a*r0812)/(8.*rt3) + (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1412 - r1413*((2*WLx)/3. + (2*i*WLy)/3.) + r1512*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1312*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1412*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1413_dt = -((gt + g2)*r1413) - i*((conj(Em4a)*conj(r0114))/(4.*rt6) - (conj(Ep4a)*conj(r0314))/8. - (conj(Ep3a)*conj(r0714))/8. - (Em4a*r0213)/8. + (Ep4a*r0413)/8. + (Em3a*r0613)/(8.*rt3) + (Ep3a*r0813)/(8.*rt3) + (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1413 - r1412*((2*WLx)/3. - (2*i*WLy)/3.) + r1513*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1313*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1414*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1413*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1414_dt = -((gt + g2)*r1414) - i*((conj(Em4a)*conj(r0214))/8. - (conj(Ep4a)*conj(r0414))/8. - (conj(Em3a)*conj(r0614))/(8.*rt3) - (conj(Ep3a)*conj(r0814))/(8.*rt3) - (Em4a*r0214)/8. + (Ep4a*r0414)/8. + (Em3a*r0614)/(8.*rt3) + (Ep3a*r0814)/(8.*rt3) - r1413*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1514*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + conj(r1413)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - conj(r1514)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy));
+dr1512_dt = -((gt + g2)*r1512) - i*(-(conj(Ep4a)*conj(r0215))/(4.*rt6) - (conj(Ep3a)*conj(r0615))/(4.*rt2) - (Em4a*r0312)/8. + (Ep4a*r0512)/(4.*rt6) + (Em3a*r0712)/8. + r1612*((2*WLx)/3. - (2*i*WLy)/3.) - r1513*((2*WLx)/3. + (2*i*WLy)/3.) + r1412*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r1512*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1513_dt = -((gt + g2)*r1513) - i*((conj(Em4a)*conj(r0115))/(4.*rt6) - (conj(Ep4a)*conj(r0315))/8. - (conj(Ep3a)*conj(r0715))/8. - (Em4a*r0313)/8. + (Ep4a*r0513)/(4.*rt6) + (Em3a*r0713)/8. - r1512*((2*WLx)/3. - (2*i*WLy)/3.) + r1613*((2*WLx)/3. - (2*i*WLy)/3.) + r1413*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1514*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.) - r1513*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1514_dt = -((gt + g2)*r1514) - i*((conj(Em4a)*conj(r0215))/8. - (conj(Ep4a)*conj(r0415))/8. - (conj(Em3a)*conj(r0615))/(8.*rt3) - (conj(Ep3a)*conj(r0815))/(8.*rt3) - (Em4a*r0314)/8. + (Ep4a*r0514)/(4.*rt6) + (Em3a*r0714)/8. - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1514 + r1614*((2*WLx)/3. - (2*i*WLy)/3.) - r1513*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1414*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) - r1515*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1514*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr1515_dt = -((gt + g2)*r1515) - i*((conj(Em4a)*conj(r0315))/8. - (conj(Ep4a)*conj(r0515))/(4.*rt6) - (conj(Em3a)*conj(r0715))/8. - (Em4a*r0315)/8. + (Ep4a*r0515)/(4.*rt6) + (Em3a*r0715)/8. + r1615*((2*WLx)/3. - (2*i*WLy)/3.) - conj(r1615)*((2*WLx)/3. + (2*i*WLy)/3.) - r1514*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + conj(r1514)*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy));
+dr1612_dt = -((gt + g2)*r1612) - i*(-(conj(Ep4a)*conj(r0216))/(4.*rt6) - (conj(Ep3a)*conj(r0616))/(4.*rt2) - (Em4a*r0412)/(4.*rt6) + (Em3a*r0812)/(4.*rt2) + r1512*((2*WLx)/3. + (2*i*WLy)/3.) - r1613*((2*WLx)/3. + (2*i*WLy)/3.) + r1612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1612*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (4*WLz)/3.));
+dr1613_dt = -((gt + g2)*r1613) - i*((conj(Em4a)*conj(r0116))/(4.*rt6) - (conj(Ep4a)*conj(r0316))/8. - (conj(Ep3a)*conj(r0716))/8. - (Em4a*r0413)/(4.*rt6) + (Em3a*r0813)/(4.*rt2) - r1612*((2*WLx)/3. - (2*i*WLy)/3.) + r1513*((2*WLx)/3. + (2*i*WLy)/3.) - r1614*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1613*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 + (2*WLz)/3.));
+dr1614_dt = -((gt + g2)*r1614) - i*((conj(Em4a)*conj(r0216))/8. - (conj(Ep4a)*conj(r0416))/8. - (conj(Em3a)*conj(r0616))/(8.*rt3) - (conj(Ep3a)*conj(r0816))/(8.*rt3) - (Em4a*r0414)/(4.*rt6) + (Em3a*r0814)/(4.*rt2) - (-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3)*r1614 + r1514*((2*WLx)/3. + (2*i*WLy)/3.) - r1613*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) - r1615*(sqrt(0.6666666666666666)*WLx + sqrt(0.6666666666666666)*i*WLy) + r1614*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.));
+dr1615_dt = -((gt + g2)*r1615) - i*((conj(Em4a)*conj(r0316))/8. - (conj(Ep4a)*conj(r0516))/(4.*rt6) - (conj(Em3a)*conj(r0716))/8. - (Em4a*r0415)/(4.*rt6) + (Em3a*r0815)/(4.*rt2) + r1515*((2*WLx)/3. + (2*i*WLy)/3.) - r1616*((2*WLx)/3. + (2*i*WLy)/3.) - r1614*(sqrt(0.6666666666666666)*WLx - sqrt(0.6666666666666666)*i*WLy) + r1615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (4*WLz)/3.) - r1615*(-delta1 + delta2 - delta3 - v*Kvec1 + v*Kvec2 - v*Kvec3 - (2*WLz)/3.));
+dr1616_dt = -((gt + g2)*r1616) - i*((conj(Em4a)*conj(r0416))/(4.*rt6) - (conj(Em3a)*conj(r0816))/(4.*rt2) - (Em4a*r0416)/(4.*rt6) + (Em3a*r0816)/(4.*rt2) - r1615*((2*WLx)/3. - (2*i*WLy)/3.) + conj(r1615)*((2*WLx)/3. + (2*i*WLy)/3.));
+//---------------- RbEquations.txt ends  ------------------
+                                        ]]>
+        </operator>
+                                <!--
+                                                         According to xmds2 docs operator kind="ip" should be faster
+                                                         but our codes runs about 5% to 10% slower with it.
+                                                         Maybe because we very close to the stiff condition so I use "ex" kind
+                                                         <operator kind="ip" constant="yes">
+                                         -->
+                                <operator kind="ex" constant="yes" type="imaginary">
+                                        <operator_names>Lt</operator_names>
+                                        <![CDATA[
+                                        Lt = -i/c*kt;
+                                        ]]>
+                                </operator>
+        <integration_vectors>E_field</integration_vectors>
+                                <dependencies>density_matrix</dependencies>
+                                <![CDATA[
+                                //read from Mathematica generated RbPropEquations.txt
+//---------------- RbPropEquations.txt starts ------------------
+dEp1_dz = -((i*Ndens*(rt2*conj(r0309) + rt6*(conj(r0410) + rt2*conj(r0511)))*eta1)/(rt2*rt6)) - Lt[Ep1];
+dEm1_dz = -((i*Ndens*(rt2*rt6*conj(r0109) + rt6*conj(r0210) + rt2*conj(r0311))*eta1)/(rt2*rt6)) - Lt[Em1];
+dEp2_dz = (i*Ndens*(conj(r0709) + conj(r0810))*eta1)/rt6 - Lt[Ep2];
+dEm2_dz = -((i*Ndens*(conj(r0610) + conj(r0711))*eta1)/rt6) - Lt[Em2];
+dEp3_dz = -((i*Ndens*(rt2*rt3*conj(r0612) + rt3*conj(r0713) + conj(r0814))*eta2)/rt3) - Lt[Ep3];
+dEm3_dz = -((i*Ndens*(conj(r0614) + rt3*(conj(r0715) + rt2*conj(r0816)))*eta2)/rt3) - Lt[Em3];
+dEp4_dz = -((i*Ndens*(rt2*conj(r0212) + rt3*conj(r0313) + rt3*conj(r0414) + rt2*conj(r0515))*eta2)/rt3) - Lt[Ep4];
+dEm4_dz = (i*Ndens*(rt2*conj(r0113) + rt3*conj(r0214) + rt3*conj(r0315) + rt2*conj(r0416))*eta2)/rt3 - Lt[Em4];
+//---------------- RbPropEquations.txt ends  ------------------
+                                ]]>
+                        </operators>
+                </integrate>
+        </sequence>
+
+
+
+        <!-- The output to generate -->
+        <output format="binary" filename="realistic_Rb_and_fields.xsil">
+                <group>
+      <sampling basis="t(1000) " initial_sample="yes">
+                                <dependencies>E_field_avgd</dependencies>
+                                <moments>Ip1_out Im1_out Ip2_out Im2_out Ip3_out Im3_out Ip4_out Im4_out</moments>
+                                <![CDATA[
+                                Ip1_out = mod2(Ep1a);
+                                Im1_out = mod2(Em1a);
+                                Ip2_out = mod2(Ep2a);
+                                Im2_out = mod2(Em2a);
+                                Ip3_out = mod2(Ep3a);
+                                Im3_out = mod2(Em3a);
+                                Ip4_out = mod2(Ep4a);
+                                Im4_out = mod2(Em4a);
+                                ]]>
+                        </sampling>
+                </group>
+        </output>
+
+
+<info>
+Script compiled with XMDS2 version VERSION_PLACEHOLDER (SUBVERSION_REVISION_PLACEHOLDER)
+See http://www.xmds.org for more information.
+
+Variables that can be specified on the command line:
+  Command line argument Ep1o = 1.000000e+04
+  Command line argument Em1o = 1.000000e+04
+  Command line argument Ep2o = 1.000000e+02
+  Command line argument Em2o = 1.000000e+02
+  Command line argument Ep3o = 1.000000e+01
+  Command line argument Em3o = 1.000000e+01
+  Command line argument Ep4o = 1.000000e+01
+  Command line argument Em4o = 1.000000e+01
+  Command line argument delta1 = 0.000000e+00
+  Command line argument delta2 = 0.000000e+00
+  Command line argument delta3 = 0.000000e+00
+  Command line argument Pwidth = 4.000000e-07
+  Command line argument Lcell = 1.000000e-01
+  Command line argument Ndens = 1.000000e+15
+  Command line argument WLx = 0.000000e+00
+  Command line argument WLy = 0.000000e+00
+  Command line argument WLz = 0.000000e+00
+  Command line argument Temperature = 1.000000e-03
+</info>
+
+<XSIL Name="moment_group_1">
+  <Param Name="n_independent">2</Param>
+  <Array Name="variables" Type="Text">
+    <Dim>10</Dim>
+    <Stream><Metalink Format="Text" Delimiter=" \n"/>
+z t Ip1_out Im1_out Ip2_out Im2_out Ip3_out Im3_out Ip4_out Im4_out 
+    </Stream>
+  </Array>
+  <Array Name="data" Type="double">
+    <Dim>101</Dim>
+    <Dim>1000</Dim>
+    <Dim>10</Dim>
+    <Stream><Metalink Format="Binary" UnsignedLong="uint32" precision="double" Type="Remote" Encoding="LittleEndian"/>
+realistic_Rb_and_fields_expected_mg0.dat
+    </Stream>
+  </Array>
+</XSIL>
+</simulation>
diff --git a/xmds2/realistic_Rb_and_fields/tests/testsuite/realistic_Rb_and_fields_expected_mg0.dat b/xmds2/realistic_Rb_and_fields/tests/testsuite/realistic_Rb_and_fields_expected_mg0.dat
new file mode 100644
index 0000000..c301bc7
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/tests/testsuite/realistic_Rb_and_fields_expected_mg0.dat
diff --git a/xmds2/realistic_Rb_and_fields/two_field_circular_eit_cold.params b/xmds2/realistic_Rb_and_fields/two_field_circular_eit_cold.params
new file mode 100644
index 0000000..325be02
--- /dev/null
+++ b/xmds2/realistic_Rb_and_fields/two_field_circular_eit_cold.params
@@ -0,0 +1,10 @@
+
+PARAMS =  \
+	  --Ndens=1e15 \
+	  --Lcell=10.0e-2 \
+	  --Temperature=1e-3 \
+          --WLx=0 --WLy=0 --WLz=0 \
+	  --Pwidth=0.4e-6 \
+	  --delta1=0 --delta2=0 --delta3=0 \
+          --Ep1o=5e7 --Ep2o=1e2 --Ep3o=0 --Ep4o=0 --Em1o=0 --Em2o=0 --Em3o=0 --Em4o=0
+