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Update to v0.2:

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Added: Comparison of the energy for two different potentials that
  share the same scattering length and integral (new figure).

  Added: Lee-Huang-Yang prediction in figures.

  Fixed: Wrong exponent in definition of correlation function.

  Added: More precise comparison of the big equation prediction for the
  hard core potential (new figure).

  Changed: Miscellaneous minor fixes and clarifications.
This commit is contained in:
Ian Jauslin
2021-03-01 16:51:33 -05:00
parent 201099f9d0
commit 6a019dc4f9
14 changed files with 291 additions and 62 deletions
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36
figs/compare_pots.fig/Makefile Normal file
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@ -0,0 +1,36 @@
PROJECTNAME=compare_pots
SIMPLEQ=simpleq
DATS=bigeq_tent.dat bigeq_exp.dat
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME))
all: $(PDFS)
$(PDFS): $(DATS)
gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@)
pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
bigeq_tent.dat:
julia -p 8 $(SIMPLEQ)/main.jl -p "N=12;P=8;J=10;maxiter=100;v_a=32;minlrho=-4;nlrho=100;maxlrho=4;eq=bigeq" -U tent -M medeq energy_rho > $@
bigeq_exp.dat:
# rescale rho by beta^3~324.860
julia -p 8 $(SIMPLEQ)/main.jl -p "N=12;P=8;J=10;maxiter=100;v_a=19.1968;minlrho=-6.512;nlrho=100;maxlrho=1.488;eq=bigeq" -M medeq energy_rho > $@
install: $(PDFS)
cp $^ $(INSTALLDIR)/
clean-aux:
rm -f $(addsuffix .tikz.tex, $(PROJECTNAME))
rm -f $(addsuffix .aux, $(PROJECTNAME))
rm -f $(addsuffix .log, $(PROJECTNAME))
clean-dat:
rm -f $(DATS)
clean-tex:
rm -f $(PDFS)
clean: clean-aux clean-tex

39
figs/compare_pots.fig/compare_pots.gnuplot Normal file
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@ -0,0 +1,39 @@
set ylabel "$\\frac{e}{\\rho}$" norotate
set xlabel "$\\rho$"
set xtics 1e-4, 100, 10000
set xtics add ("$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100, "$10^4$" 10000)
unset mxtics
set xrange [1e-5:1e4]
#set ytics 0.8, 0.05, 1.1
set yrange [0:40]
# default output canvas size: 12.5cm x 8.75cm
set term lua tikz size 8,6 standalone
set key top left box linetype rgbcolor"#999999" width 0.3 height 0.3 spacing 1.3
# set linestyle
set style line 1 linetype rgbcolor "#FF3399" linewidth 2
set style line 2 linetype rgbcolor "#DC143C" linewidth 2
set style line 3 linetype rgbcolor "#DC143C" linewidth 2
set style line 4 linetype rgbcolor "#4B0082" linewidth 2 dashtype "."
set style line 5 linetype rgbcolor "#DAA520" linewidth 2
set style line 6 linetype rgbcolor "#999999" linewidth 1.5 dashtype (1,5)
set pointsize 1
set logscale x
a=0.597754
beta=6.87436
plot \
"bigeq_tent.dat" using 1:($2/$1) with lines ls 4 title "big $v_{32}^{(0)}$",\
"bigeq_exp.dat" using ($1*beta**3):($2/$1/beta) with lines ls 5 title "big $\\Phi$",\
"2021-02-16+tent32.dat" u 1:($2/$1) ls 1 title "QMC $v_{32}^{(0)}$",\
"2021-02-16+19.dat" u ($1*beta**3):($2/$1/beta) ls 2 title "QMC $\\Phi$",\
2*pi*a*(1+128./15/sqrt(pi)*sqrt(x*a**3)) ls 6 title "LHY"

8
figs/condensate.fig/condensate05.gnuplot
View File

@ -8,7 +8,7 @@ unset mxtics
#set ytics 0.6, 0.1
set mytics 2
set xrange [4e-7:100]
set xrange [4e-8:100]
set yrange [:0.06]
@ -24,14 +24,18 @@ set style line 2 linetype rgbcolor "#DC143C" linewidth 2
set style line 3 linetype rgbcolor "#32CD32" linewidth 2 dashtype "-"
set style line 4 linetype rgbcolor "#4B0082" linewidth 2
set style line 5 linetype rgbcolor "#DAA520" linewidth 2
set style line 6 linetype rgbcolor "#999999" linewidth 1.5 dashtype (1,5)
set pointsize 1
set logscale x
a=0.7666858699084325
plot \
"simpleq0.5.dat" using 1:($3<1e-5 ? $2 : 1/0) with lines ls 1 title "simple",\
"mueq0.5.dat" using 1:($3<1e-5 ? $2 : 1/0) with lines ls 3 title "med",\
"bigeq0.5.dat" using 1:($3<1e-5 ? $2 : 1/0) with lines ls 5 title "big",\
"2020-08-27+0.5.dat" using 1:(1-$3) with points ls 2 title "QMC"
"2020-08-27+0.5.dat" using 1:(1-$3) with points ls 2 title "QMC" ,\
8./(3*sqrt(pi))*sqrt(x*a**3) ls 6 title "Bog"

7
figs/condensate.fig/condensate16.gnuplot
View File

@ -10,6 +10,7 @@ set mytics 2
set xrange [1e-7:100]
set yrange [:1.2]
# default output canvas size: 12.5cm x 8.75cm
set term lua tikz size 8,6 standalone
@ -23,14 +24,18 @@ set style line 2 linetype rgbcolor "#DC143C" linewidth 2
set style line 3 linetype rgbcolor "#32CD32" linewidth 2 dashtype "-"
set style line 4 linetype rgbcolor "#4B0082" linewidth 2
set style line 5 linetype rgbcolor "#DAA520" linewidth 2
set style line 6 linetype rgbcolor "#999999" linewidth 1.5 dashtype (1,5)
set pointsize 1
set logscale x
a=3.9270207371831565
plot \
"simpleq16.dat" using 1:($3<1e-5 ? $2 : 1/0) with lines ls 1 title "simple",\
"mueq16.dat" using 1:($3<1e-5 ? $2 : 1/0) with lines ls 3 title "med",\
"bigeq16.dat" using 1:($3<1e-5 ? $2 : 1/0) with lines ls 5 title "big",\
"2020-08-27+16.dat" using 1:(1-$3) with points ls 2 title "QMC"
"2020-08-27+16.dat" using 1:(1-$3) with points ls 2 title "QMC" ,\
8./(3*sqrt(pi))*sqrt(x*a**3) ls 6 title "Bog"

6
figs/energy.fig/energy1.gnuplot
View File

@ -24,14 +24,18 @@ set style line 2 linetype rgbcolor "#DC143C" linewidth 2
set style line 3 linetype rgbcolor "#32CD32" linewidth 2 dashtype "-"
set style line 4 linetype rgbcolor "#4B0082" linewidth 2
set style line 5 linetype rgbcolor "#DAA520" linewidth 2
set style line 6 linetype rgbcolor "#999999" linewidth 1.5 dashtype (1,5)
set pointsize 1
set logscale x
a=1.2543564105910647
plot \
"simpleq1.dat" using 1:($3<1e-5 ? ($2/$1) : 1/0) with lines ls 1 title "simple" ,\
"mueq1.dat" using 1:($3<1e-5 ? ($2/$1) : 1/0) with lines ls 3 title "med",\
"bigeq1.dat" using 1:($3<1e-5 ? ($2/$1) : 1/0) with lines ls 5 title "big",\
"2020-10-15+energy.dat" using 1:($2/$1) with points ls 2 title "QMC"
"2020-10-15+energy.dat" using 1:($2/$1) with points ls 2 title "QMC" ,\
2*pi*a*(1+128./(15*sqrt(pi))*sqrt(x*a**3)) ls 6 title "LHY"

6
figs/energy.fig/energy16.gnuplot
View File

@ -24,14 +24,18 @@ set style line 2 linetype rgbcolor "#DC143C" linewidth 2
set style line 3 linetype rgbcolor "#32CD32" linewidth 2 dashtype "-"
set style line 4 linetype rgbcolor "#4B0082" linewidth 2
set style line 5 linetype rgbcolor "#DAA520" linewidth 2
set style line 6 linetype rgbcolor "#999999" linewidth 1.5 dashtype (1,5)
set pointsize 1
set logscale x
a=3.9270207371831565
plot \
"simpleq16.dat" using 1:($3<1e-5 ? ($2/$1) : 1/0) with lines ls 1 title "simple",\
"mueq16.dat" using 1:($3<1e-5 ? ($2/$1) : 1/0) with lines ls 3 title "med",\
"bigeq16.dat" using 1:($3<1e-5 ? ($2/$1) : 1/0) with lines ls 5 title "big",\
"2020-08-27+16.dat" using 1:($2/$1) with points ls 2 title "QMC"
"2020-08-27+16.dat" using 1:($2/$1) with points ls 2 title "QMC" ,\
2*pi*a*(1+128./(15*sqrt(pi))*sqrt(x*a**3)) ls 6 title "LHY"

28
figs/energy_relative_error.fig/Makefile
View File

@ -1,6 +1,6 @@
PROJECTNAME=cmp_energy16 cmp_energy1
SIMPLEQ=simpleq
SIMPLEQ=~/Work/Research/2018+bose_gas/cmp/simpleq
DATS= simpleq16.dat mueq16.dat bigeq16.dat simpleq1.dat mueq1.dat bigeq1.dat
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
@ -13,42 +13,28 @@ $(PDFS): $(DATS)
pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
bigeq16.dat:
for rho in 1e-3 5e-3 1e-2 2e-2 1e-1 1e+0; do \
echo -n $$rho " " >> $@-tmp ;\
julia $(SIMPLEQ)/main.jl -p "eq=bigeq;N=12;P=8;J=10;maxiter=100;v_a=16;rho=$$rho;minlrho=-6;nlrho=50" -M medeq energy >> $@-tmp ;\
done
julia $(SIMPLEQ)/main.jl -p "eq=bigeq;N=12;P=8;J=10;maxiter=100;v_a=16;minlrho=-6;nlrho=50;rhos=1e-3,5e-3,1e-2,2e-2,1e-1,1e+0" -M medeq energy > $@-tmp
paste $@-tmp 2020-08-27+16.dat > $@
rm $@-tmp
simpleq16.dat:
for lrho in -3 -2.3010299956639813 -2 -1.6989700043360187 -1 0; do \
julia $(SIMPLEQ)/main.jl -p "tolerance=1e-11;order=100;maxiter=100;v_a=16;minlrho=$$lrho;nlrho=1" -M simpleq energy_rho >> $@-tmp ;\
done
julia $(SIMPLEQ)/main.jl -p "tolerance=1e-11;order=100;maxiter=100;v_a=16;rhos=1e-3,5e-3,1e-2,2e-2,1e-1,1e+0" -M simpleq energy_rho > $@-tmp
paste $@-tmp 2020-08-27+16.dat > $@
rm $@-tmp
mueq16.dat:
for lrho in -3 -2.3010299956639813 -2 -1.6989700043360187 -1 0; do \
julia $(SIMPLEQ)/main.jl -p "tolerance=1e-11;order=100;maxiter=100;v_a=16;minlrho=$$lrho;nlrho=1" -M mueq energy_rho >> $@-tmp ;\
done
julia $(SIMPLEQ)/main.jl -p "tolerance=1e-11;order=100;maxiter=100;v_a=16;rhos=1e-3,5e-3,1e-2,2e-2,1e-1,1e+0" -M mueq energy_rho > $@-tmp
paste $@-tmp 2020-08-27+16.dat > $@
rm $@-tmp
bigeq1.dat:
for rho in 1e-6 1e-4 1e-3 5e-3 1e-2 1.5e-2 2e-2 5e-2 1e-1 1.0 1e1 5e1; do \
echo -n $$rho " " >> $@-tmp ;\
julia $(SIMPLEQ)/main.jl -p "N=12;P=8;J=10;maxiter=100;v_a=1;rho=$$rho;minlrho=-6;nlrho=50;eq=bigeq" -M medeq energy >> $@-tmp ;\
done
julia $(SIMPLEQ)/main.jl -p "N=12;P=8;J=10;maxiter=100;v_a=1;minlrho=-6;nlrho=50;eq=bigeq;rhos=1e-6,1e-4,1e-3,5e-3,1e-2,1.5e-2,2e-2,5e-2,1e-1,1.0,1e1,5e1" -M medeq energy > $@-tmp
paste $@-tmp 2020-10-15+energy.dat > $@
rm $@-tmp
simpleq1.dat:
for lrho in -6 -4 -3 -2.3010299956639813 -2 -1.8239087409443189 -1.6989700043360187 -1.3010299956639813 -1 0 1 1.6989700043360187; do\
julia $(SIMPLEQ)/main.jl -p "tolerance=1e-11;order=100;maxiter=100;v_a=1;minlrho=$$lrho;nlrho=1" -M simpleq energy_rho >> $@-tmp ;\
done
julia $(SIMPLEQ)/main.jl -p "tolerance=1e-11;order=100;maxiter=100;v_a=1;rhos=1e-6,1e-4,1e-3,5e-3,1e-2,1.5e-2,2e-2,5e-2,1e-1,1.0,1e1,5e1" -M simpleq energy_rho > $@-tmp
paste $@-tmp 2020-10-15+energy.dat > $@
rm $@-tmp
mueq1.dat:
for lrho in -6 -4 -3 -2.3010299956639813 -2 -1.8239087409443189 -1.6989700043360187 -1.3010299956639813 -1 0 1 1.6989700043360187; do\
julia $(SIMPLEQ)/main.jl -p "tolerance=1e-11;order=100;maxiter=100;v_a=1;minlrho=$$lrho;nlrho=1" -M mueq energy_rho >> $@-tmp ;\
done
julia $(SIMPLEQ)/main.jl -p "tolerance=1e-11;order=100;maxiter=100;v_a=1;rhos=1e-6,1e-4,1e-3,5e-3,1e-2,1.5e-2,2e-2,5e-2,1e-1,1.0,1e1,5e1" -M mueq energy_rho >> $@-tmp ;\
paste $@-tmp 2020-10-15+energy.dat > $@
rm $@-tmp

21
figs/hardcore.fig/Makefile
View File

@ -1,7 +1,7 @@
PROJECTNAME=hardcore_energy hardcore_condensate
PROJECTNAME=hardcore_energy hardcore_compare hardcore_condensate
SIMPLEQ=simpleq
DATS=simpleq-energy.dat simpleq_soft-energy.dat mueq_soft-energy.dat bigeq_soft-energy.dat simpleq-condensate.dat simpleq_soft-condensate.dat mueq_soft-condensate.dat bigeq_soft-condensate.dat
DATS=simpleq-energy.dat simpleq_soft-energy.dat mueq_soft-energy.dat bigeq_soft-energy.dat simpleq-compare.dat simpleq_soft-compare.dat mueq_soft-compare.dat bigeq_soft-compare.dat simpleq-condensate.dat simpleq_soft-condensate.dat mueq_soft-condensate.dat bigeq_soft-condensate.dat
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
TEXS=$(addsuffix .tikz.tex, $(PROJECTNAME))
@ -21,6 +21,23 @@ mueq_soft-energy.dat:
bigeq_soft-energy.dat:
julia -p 8 $(SIMPLEQ)/main.jl -p "N=12;P=8;eq=bigeq;maxiter=100;maxlrho=0.15;nlrho=64;v_a=512;v_b=1.2494804800401416" -U tent -M medeq energy_rho_init_prevrho > $@
simpleq-compare.dat:
julia -p 8 $(SIMPLEQ)/main.jl -p "N=12;P=8;J=5;rhos=1e-6,5e-6,1e-5,5e-5,1e-4,5e-4,1e-3,5e-3,1e-2,5e-2,1e-1,0.166,0.244" -M simpleq-hardcore energy_rho > $@-tmp
paste $@-tmp GBC99-energy.dat > $@
rm $@-tmp
simpleq_soft-compare.dat:
julia $(SIMPLEQ)/main.jl -p "maxiter=100;v_a=328.77174503097945;v_b=1.2479228505627133;rhos=1e-6,5e-6,1e-5,5e-5,1e-4,5e-4,1e-3,5e-3,1e-2,5e-2,1e-1,0.166,0.244" -U tent -M simpleq energy_rho > $@-tmp
paste $@-tmp GBC99-energy.dat > $@
rm $@-tmp
mueq_soft-compare.dat:
julia $(SIMPLEQ)/main.jl -p "maxiter=100;v_a=328.77174503097945;v_b=1.2479228505627133;rhos=1e-6,5e-6,1e-5,5e-5,1e-4,5e-4,1e-3,5e-3,1e-2,5e-2,1e-1,0.166,0.244" -U tent -M mueq energy_rho > $@-tmp
paste $@-tmp GBC99-energy.dat > $@
rm $@-tmp
bigeq_soft-compare.dat:
julia -p 8 $(SIMPLEQ)/main.jl -p "N=12;P=8;eq=bigeq;maxiter=100;v_a=328.77174503097945;v_b=1.2479228505627133;rhos=1e-6,5e-6,1e-5,5e-5,1e-4,5e-4,1e-3,5e-3,1e-2,5e-2,1e-1,0.166,0.244" -U tent -M medeq energy_rho_init_prevrho > $@-tmp
paste $@-tmp GBC99-energy.dat > $@
rm $@-tmp
simpleq-condensate.dat:
julia -p 8 $(SIMPLEQ)/main.jl -p "N=12;P=8;J=5;maxlrho=0.15;nlrho=24" -M simpleq-hardcore condensate_fraction_rho > $@
simpleq_soft-condensate.dat:

36
figs/hardcore.fig/hardcore_compare.gnuplot Normal file
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@ -0,0 +1,36 @@
set ylabel "energy relative error"
set xlabel "$\\rho$"
set xtics 1e-6, 100, 1
set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0)
unset mxtics
set xrange [1e-9:sqrt(2)]
set ytics 1e-5, 10, 10
set ytics add ("$10^{-5}$" 1e-5, "$10^{-4}$" 1e-4, "$10^{-3}$" 1e-3, "$10^{-2}$" 1e-2, "$10^{-1}$" 1e-1, "$10^{0}$" 1, "$10^1$" 10)
#unset mytics
# default output canvas size: 12.5cm x 8.75cm
set term lua tikz size 8,6 standalone
set key top left box linetype rgbcolor"#999999" width 0.3 height 0.3 spacing 1.3
# set linestyle
set style line 1 linetype rgbcolor "#4169E1" linewidth 2 dashtype "."
set style line 2 linetype rgbcolor "#DC143C" linewidth 2
set style line 3 linetype rgbcolor "#32CD32" linewidth 2 dashtype "-"
set style line 4 linetype rgbcolor "#4B0082" linewidth 2
set style line 5 linetype rgbcolor "#DAA520" linewidth 2
set style line 6 linetype rgbcolor "#999999" linewidth 2
set pointsize 1
set logscale xy
plot \
"simpleq-compare.dat" using 1:($3<1e-2 ? 2*abs($5/2-$2)/$5 : 1/0) with lp ls 4 title "simple hc",\
"simpleq_soft-compare.dat" using 1:($3<1e-2 ? 2*abs($5/2-$2)/$5 : 1/0) with lp ls 1 title "simple",\
"mueq_soft-compare.dat" using 1:($3<1e-2 ? 2*abs($5/2-$2)/$5 : 1/0) with lp ls 3 title "med",\
"bigeq_soft-compare.dat" using 1:($3<1e-2 ? 2*abs($5/2-$2)/$5 : 1/0) with lp ls 5 title "big"

9
figs/hardcore.fig/hardcore_condensate.gnuplot
View File

@ -24,16 +24,19 @@ set style line 2 linetype rgbcolor "#DC143C" linewidth 2
set style line 3 linetype rgbcolor "#32CD32" linewidth 2 dashtype "-"
set style line 4 linetype rgbcolor "#4B0082" linewidth 2
set style line 5 linetype rgbcolor "#DAA520" linewidth 2
set style line 6 linetype rgbcolor "#999999" linewidth 2
set style line 6 linetype rgbcolor "#999999" linewidth 1.5 dashtype (1,5)
set pointsize 1
set logscale x
a=1.
plot \
"simpleq-condensate.dat" using 1:($3<1e-2 ? $2 : 1/0) ls 6 title "simple hc",\
"simpleq-condensate.dat" using 1:($3<1e-2 ? $2 : 1/0) ls 4 title "simple hc",\
"simpleq_soft-condensate.dat" using 1:($3<1e-2 ? $2 : 1/0) with lines ls 1 title "simple" ,\
"mueq_soft-condensate.dat" using 1:($3<1e-2 ? $2 : 1/0) with lines ls 3 title "med",\
"bigeq_soft-condensate.dat" using 1:($3<1e-2 ? $2 : 1/0) with lines ls 5 title "big",\
"GBC99-condensate.dat" using 1:(1-$2) ls 2 title "QMC [15]"
"GBC99-condensate.dat" using 1:(1-$2) ls 2 title "QMC [15]" ,\
8./(3*sqrt(pi))*sqrt(x*a**3) ls 6 title "Bog"

9
figs/hardcore.fig/hardcore_energy.gnuplot
View File

@ -23,16 +23,19 @@ set style line 2 linetype rgbcolor "#DC143C" linewidth 2
set style line 3 linetype rgbcolor "#32CD32" linewidth 2 dashtype "-"
set style line 4 linetype rgbcolor "#4B0082" linewidth 2
set style line 5 linetype rgbcolor "#DAA520" linewidth 2
set style line 6 linetype rgbcolor "#999999" linewidth 2
set style line 6 linetype rgbcolor "#999999" linewidth 1.5 dashtype (1,5)
set pointsize 1
set logscale xy
a=1.
plot \
"simpleq-energy.dat" using 1:($3<1e-2 ? $2/$1 : 1/0) ls 6 title "simple hc",\
"simpleq-energy.dat" using 1:($3<1e-2 ? $2/$1 : 1/0) ls 4 title "simple hc",\
"simpleq_soft-energy.dat" using 1:($3<1e-2 ? $2/$1 : 1/0) with lines ls 1 title "simple",\
"mueq_soft-energy.dat" using 1:($3<1e-2 ? $2/$1 : 1/0) every ::::95 with lines ls 3 title "med",\
"bigeq_soft-energy.dat" using 1:($3<1e-2 ? $2/$1 : 1/0) with lines ls 5 title "big",\
"GBC99-energy.dat" using 1:($2/(2*$1)) ls 2 title "QMC [15]"
"GBC99-energy.dat" using 1:($2/(2*$1)) ls 2 title "QMC [15]" ,\
2*pi*a*(1+128./(15*sqrt(pi))*sqrt(x*a**3)) ls 6 title "LHY"