Ian Jauslin

Ian Jauslin

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-rw-r--r--Jauslin_MC_2021.tex235
-rw-r--r--Makefile51
-rw-r--r--README33
-rw-r--r--figs/bosons-weinersmith.pngbin0 -> 170453 bytes
-rw-r--r--figs/condensate.fig/Makefile34
-rw-r--r--figs/condensate.fig/bigeq.dat100
-rw-r--r--figs/condensate.fig/condensate.gnuplot36
-rw-r--r--figs/condensate.fig/holzmann_2019-12-25.dat11
-rw-r--r--figs/condensate.fig/simpleq.dat100
-rw-r--r--figs/energy.fig/Makefile28
-rw-r--r--figs/energy.fig/erho.dat104
-rw-r--r--figs/energy.fig/erho_effective.gnuplot38
-rw-r--r--figs/energy.fig/erho_fulleq.dat100
-rw-r--r--figs/energy.fig/erho_fulleq.gnuplot37
-rw-r--r--figs/energy.fig/erho_lowhigh.gnuplot37
-rw-r--r--figs/energy.fig/holzmann_2019-12-25.dat11
-rw-r--r--figs/energy16.fig/2020-05-22+16.dat7
-rw-r--r--figs/energy16.fig/Makefile35
-rw-r--r--figs/energy16.fig/energy16.gnuplot34
-rw-r--r--figs/energy16.fig/medeq16.dat100
-rw-r--r--figs/energy16.fig/medeq4.dat100
-rw-r--r--figs/energy16.fig/simpleq16.dat100
-rw-r--r--libs/ian-presentation.cls187
23 files changed, 1518 insertions, 0 deletions
diff --git a/Jauslin_MC_2021.tex b/Jauslin_MC_2021.tex
new file mode 100644
index 0000000..ff6d0b7
--- /dev/null
+++ b/Jauslin_MC_2021.tex
@@ -0,0 +1,235 @@
+\documentclass{ian-presentation}
+
+\usepackage[hidelinks]{hyperref}
+\usepackage{graphicx}
+\usepackage{array}
+\usepackage{xcolor}
+
+
+\definecolor{ipurple}{HTML}{4B0082}
+\definecolor{iyellow}{HTML}{DAA520}
+\definecolor{igreen}{HTML}{32CD32}
+\definecolor{iblue}{HTML}{4169E1}
+\definecolor{ired}{HTML}{DC143C}
+
+\definecolor{highlight}{HTML}{328932}
+\definecolor{highlight}{HTML}{981414}
+
+\begin{document}
+\pagestyle{empty}
+\hbox{}\vfil
+\bf\Large
+\hfil Many interacting quantum particles:\par
+\medskip
+\hfil\large open problems, and a new point of view on an old problem
+\vfil
+\large
+\hfil Ian Jauslin
+\normalsize
+\vfil
+\rm
+\hfil collaborators: {\bf E.A.\-~Carlen, E.H.\-~Lieb, M.\-~Holzmann, M.P.\-~Loss}\par
+\vfil
+arXiv:{\tt\ \parbox[b]{3cm}{
+ \href{https://arxiv.org/abs/1912.04987}{1912.04987}\par
+ \href{https://arxiv.org/abs/2010.13882}{2010.13882}\par
+ \href{https://arxiv.org/abs/2011.10869}{2011.10869}
+}}
+\hfill{\tt \href{http://ian.jauslin.org}{http://ian.jauslin.org}}
+\eject
+
+\setcounter{page}1
+\pagestyle{plain}
+
+\title{Fermions/Bosons}
+\bigskip
+\hfil\includegraphics[height=5.5cm]{bosons-weinersmith.png}
+
+\hfil{\tiny Zach Weinersmith, \href{https://creativecommons.org/licenses/by-nc/3.0/legalcode}{CC-BY-NC 3.0}}
+\vfill
+\eject
+
+\title{Bose-Einstein condensation}
+\begin{itemize}
+\item System of Bosons, e.g. {\color{highlight}Helium} atoms, {\color{highlight}Rubidium} atoms, etc...
+\item At low temperatures, {\color{highlight}superfluidity} (flow with zero viscocity) and {\color{highlight}superconductivity} (currents with zero resistance).
+\item {\color{highlight}Bose-Einstein condensate}: most particles are in the same quantum state.
+\item Predicted theoretically in {\color{highlight}1924-1925}, experimentally observed in {\color{highlight}1995}.
+\item Mathematical understanding: still {\color{highlight}no proof} of the existence of a condensate (at finite density, in the presence of interactions and in the continuum).
+\end{itemize}
+\vfill
+\eject
+
+\title{Repulsive Bose gas}
+\begin{itemize}
+ \item {\color{highlight}$N$-particle} quantum state in a volume $V$:
+ $$
+ \psi(x_1,\cdots,x_N)\in L^2_{\mathrm{symmetric}}((V\mathbb T^3)^N)
+ $$
+
+ \item $|\psi|^2$: probability distribution on the positions of the $N$ particles.
+
+ \item Hamiltonian operator acting on $\psi$:
+ $$
+ H_N\psi:=
+ -\frac12\sum_{i=1}^N\Delta_i\psi
+ +\sum_{1\leqslant i<j\leqslant N}{\color{highlight}v(|x_i-x_j|)}\psi
+ $$
+ {\color{highlight}$v(r)\geqslant 0$}.
+\vfill
+\eject
+
+\title{Energy and condensate fraction}
+\vskip-10pt
+ \item {\color{highlight}Zero-temperature:} Ground state: $\psi_0$, energy $E_0=\inf\mathrm{spec}H_N$:
+ $$
+ H_N\psi_0={\color{highlight}E_0}\psi_0
+ $$
+\vskip-10pt
+ \item In the {\color{highlight}thermodynamic limit}:
+ $$
+ e_0:=\lim_{\displaystyle\mathop{\scriptstyle V,N\to\infty}_{{\color{highlight}\frac NV=\rho}}}\frac{E_0}N
+ .
+ $$
+\vskip-5pt
+ \item Condensate fraction: proportion of particles in the Bose-Einstein condensate: in the {\color{highlight}thermodynamic limit}: ($P_i$: projection onto condensate wavefunction)
+ $$
+ \eta_0:=\lim_{\displaystyle\mathop{\scriptstyle V,N\to\infty}_{{\color{highlight}\frac NV=\rho}}}\frac1N\left<\psi_0\right|\sum_{i=1}^NP_i\left|\psi_0\right>
+ .
+ $$
+\end{itemize}
+\vfill
+\eject
+
+\title{Ground state energy}
+\begin{itemize}
+ \item At low density: {\color{highlight}Bogolyubov theory}: [Bogolyubov, 1947], \href{https://doi.org/10.1103/PhysRev.106.1135}{[Lee, Huang, Yang, 1957]}:
+ $$
+ e_0=2\pi\rho a\left(1+\frac{128}{15\sqrt\pi}\sqrt{\rho a^3}+o(\sqrt\rho)\right)
+ $$
+ \item {\color{highlight} Proved}:
+ \href{https://doi.org/10.1103/PhysRevLett.80.2504}{[Lieb, Yngvason, 1998]},
+ \href{https://doi.org/10.1007/s10955-009-9792-3}{[Yau, Yin, 2009]},
+ (\href{https://arxiv.org/abs/2101.06222}{[Basti, Cenatiempo, Schlein, 2021]}),
+ \href{https://doi.org/10.4007/annals.2020.192.3.5}{[Fournais, Solovej, 2020]}.
+
+ \item At high density: {\color{highlight}Hartree theory}: ({\color{highlight}Proved} in \href{https://doi.org/10.1103/PhysRev.130.2518}{[Lieb, 1963]}).
+ $$
+ {\color{highlight}e_0\sim\frac\rho2\int v}
+ .
+ $$
+\end{itemize}
+\vfill
+\eject
+
+\title{Condensate fraction}
+\begin{itemize}
+ \item At low density: {\color{highlight}Bogolyubov theory}: [Bogolyubov, 1947], \href{https://doi.org/10.1103/PhysRev.106.1135}{[Lee, Huang, Yang, 1957]}:
+ $$
+ 1-\eta_0\sim\frac{8\sqrt{\rho a^3}}{3\sqrt\pi}
+ $$
+
+ \item {\color{highlight}Still open} in the thermodynamic limit. (No proof of Bose-Einstein condensation, in the continuum, at finite density.)
+
+ \item At high density: {\color{highlight}Hartree theory}: ({\color{highlight}open})
+ $$
+ \eta_0\to1
+ $$
+\end{itemize}
+\vfill
+\eject
+
+\title{Effective equations}
+\begin{itemize}
+ \item {\color{highlight}Boltzmann equation}: $N$ classical hard particles with an infinitely small radius (dilute limit)
+ [Lanford, 1976].
+ \item {\color{highlight}Thomas-Fermi theory}: $Z$ electrons orbiting a nucleus in the $Z\to\infty$ limit
+ \href{https://doi.org/10.1103/PhysRevLett.31.681}{[Lieb, Simon, 1973]}.
+ \item{\color{highlight}Hartree-Fock equation}: dynamics of many Fermions in the weakly-interacting limit
+ \href{https://doi.org/10.1142/9789814618144_0011}{[Benedikter, Porta, Schlein, 2015]}.
+ \item{\color{highlight}Hartree-Fock-Bogolyubov equation}: dynamics of many Bosons in the weakly-interacting limit
+ \href{https://arxiv.org/abs/1602.05171}{[Bach, Breteaux, Chen, Fr\"ohlich, Sigal, 2016]}.
+\end{itemize}
+\vfill
+\eject
+
+\title{{\color{iblue}Simple equation}}
+\begin{itemize}
+ \item {\color{iblue}Simple equation}
+ $$
+ -\Delta u(x)=(1-u(x))v(x)- 4eu(x)+2e\rho\ u\ast u(x)
+ $$
+ $$
+ e=\frac\rho2\int dx\ (1-u(x))v(x)
+ $$
+ \item $\rho>0$, $v(x)\geqslant 0$, $v\in L_1(\mathbb R^3)$.
+ \item {\color{highlight}Non-linear} and {\color{highlight}non-local} partial differential equation.
+ \item {\color{highlight}Effective equation} for the ground state of a Bose gas.
+ \item Main idea: think of {\color{highlight}$\psi$ as a probability distribution} instead of $|\psi|^2$.
+\end{itemize}
+\vfill
+\eject
+
+\title{Energy as a function of density for the {\color{iblue}Simple equation}}
+For $v(x)=e^{-|x|}$:
+
+\hfil\includegraphics[height=5.5cm]{erho_lowhigh.pdf}
+\vfill
+\eject
+
+\addtocounter{page}{-1}
+\title{Energy as a function of density for the {\color{iblue}Simple equation}}
+For $v(x)=e^{-|x|}$:
+
+\hfil\includegraphics[height=5.5cm]{erho_effective.pdf}
+\vfill
+\eject
+
+\title{Energy}
+$v(x)=e^{-|x|}$, Blue: {\color{iblue}simple equation}; purple: {\color{ipurple}big equation}; red: {\color{ired}Monte Carlo}
+
+\hfil\includegraphics[height=5.5cm]{erho_fulleq.pdf}
+\vfill
+\eject
+
+\title{{\color{ipurple}Big equation}}
+\begin{itemize}
+\item $x\in\mathbb R^3$,
+ $$
+ -\Delta u(x)
+ =
+ (1-u(x))\left(v(x)-2\rho K(x)+\rho^2 L(x)\right)
+ $$
+ $$
+ K:=
+ u\ast S
+ ,\quad
+ S(y):=(1-u(y))v(y)
+ $$
+ $$
+ L:=
+ u\ast u\ast S
+ -2u\ast(u(u\ast S))
+ .
+ $$
+\end{itemize}
+\vfill
+\eject
+
+\title{Condensate fraction}
+$v(x)=e^{-|x|}$, Blue: {\color{iblue}simple equation}; purple: {\color{ipurple}big equation}; red: {\color{ired}Monte Carlo}
+
+\hfil\includegraphics[height=5.5cm]{condensate.pdf}
+\vfill
+\eject
+
+\title{Conclusions}
+\begin{itemize}
+ \item Two {\color{highlight}effective equations}: the {\color{ipurple}big equation} and the {\color{iblue}simple equation}, which are {\color{highlight}non-linear 1-particle equations}.
+ \item Reproduce the known results for both {\color{highlight}small and large densities}.
+ \item Their derivation is {\color{highlight}different from Bogolyubov theory}, so they may give new insights onto studying the Bose gas in these asymptotic regimes.
+ \item The {\color{ipurple}big equation} is {\color{highlight}quantitatively accurate} at intermediate densities.
+ \item This opens up the possibility of studying the physics of the {\color{highlight}Bose gas at intermediate densities}.
+\end{itemize}
+
+\end{document}
diff --git a/Makefile b/Makefile
new file mode 100644
index 0000000..997ed9e
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,51 @@
+PROJECTNAME=$(basename $(wildcard *.tex))
+LIBS=$(notdir $(wildcard libs/*))
+FIGS=$(notdir $(wildcard figs/*.fig))
+PNGS=$(notdir $(wildcard figs/*.png))
+
+PDFS=$(addsuffix .pdf, $(PROJECTNAME))
+SYNCTEXS=$(addsuffix .synctex.gz, $(PROJECTNAME))
+
+all: $(PROJECTNAME)
+
+$(PROJECTNAME): $(LIBS) $(FIGS) $(PNGS)
+ pdflatex -file-line-error $@.tex
+ pdflatex -synctex=1 $@.tex
+
+$(SYNCTEXS): $(LIBS) $(FIGS)
+ pdflatex -synctex=1 $(patsubst %.synctex.gz, %.tex, $@)
+
+
+$(LIBS):
+ ln -fs libs/$@ ./
+
+
+$(FIGS):
+ make -C figs/$@
+ for pdf in $$(find figs/$@/ -name '*.pdf'); do ln -fs "$$pdf" ./ ; done
+
+$(PNGS):
+ for png in figs/*.png; do ln -fs "$$png" ./ ; done
+
+
+clean-aux: clean-figs-aux
+ rm -f $(addsuffix .aux, $(PROJECTNAME))
+ rm -f $(addsuffix .log, $(PROJECTNAME))
+ rm -f $(addsuffix .out, $(PROJECTNAME))
+
+clean-libs:
+ rm -f $(LIBS)
+
+clean-figs:
+ $(foreach fig,$(addprefix figs/, $(FIGS)), make -C $(fig) clean; )
+ rm -f $(notdir $(wildcard figs/*.fig/*.pdf))
+ rm -f $(PNGS)
+
+clean-figs-aux:
+ $(foreach fig,$(addprefix figs/, $(FIGS)), make -C $(fig) clean-aux; )
+
+
+clean-tex:
+ rm -f $(PDFS) $(SYNCTEXS)
+
+clean: clean-aux clean-tex clean-libs clean-figs
diff --git a/README b/README
new file mode 100644
index 0000000..f8acd04
--- /dev/null
+++ b/README
@@ -0,0 +1,33 @@
+This directory contains the source files to typeset the presentation, and
+generate the figures. This can be accomplished by running
+ make
+
+This document uses a custom class file, located in the 'libs' directory, which
+defines a number of commands.
+
+
+* Dependencies:
+
+ pdflatex
+ TeXlive packages:
+ amsfonts
+ array
+ graphics
+ hyperref
+ latex
+ pgf
+ standalone
+ GNU make
+ gnuplot
+
+* Files:
+
+ Jauslin_MC_2021.tex:
+ main LaTeX file
+
+ libs:
+ custom LaTeX class file
+
+ figs:
+ source code for the figures
+
diff --git a/figs/bosons-weinersmith.png b/figs/bosons-weinersmith.png
new file mode 100644
index 0000000..e0b0ab6
--- /dev/null
+++ b/figs/bosons-weinersmith.png
Binary files differ
diff --git a/figs/condensate.fig/Makefile b/figs/condensate.fig/Makefile
new file mode 100644
index 0000000..c45de65
--- /dev/null
+++ b/figs/condensate.fig/Makefile
@@ -0,0 +1,34 @@
+PROJECTNAME=condensate
+
+PDFS=$(addsuffix .pdf, $(PROJECTNAME))
+DATS= simpleq.dat bigeq.dat
+
+all: $(PDFS)
+
+$(PDFS): $(DATS)
+ gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tikz.tex, $@)
+ pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
+
+simpleq.dat:
+ julia $(SIMPLEQ)/main.jl -p "tolerance=1e-11;order=100;maxiter=100;v_a=1" -M simpleq condensate_fraction > $@
+bigeq.dat:
+ julia -p 8 $(SIMPLEQ)/main.jl -p "eq=bigeq;N=12;P=8;v_a=1" -M medeq condensate_fraction > $@
+
+install: $(PDFS)
+ cp $^ $(INSTALLDIR)/
+
+$(LIBS):
+ ln -fs libs/$@ ./
+
+clean-libs:
+ rm -f $(LIBS)
+
+clean-aux:
+ rm -f $(addsuffix .aux, $(PROJECTNAME))
+ rm -f $(addsuffix .log, $(PROJECTNAME))
+ rm -f $(addsuffix .tex, $(PROJECTNAME))
+
+clean-tex:
+ rm -f $(PDFS)
+
+clean: clean-libs clean-aux clean-tex
diff --git a/figs/condensate.fig/bigeq.dat b/figs/condensate.fig/bigeq.dat
new file mode 100644
index 0000000..e48cbc3
--- /dev/null
+++ b/figs/condensate.fig/bigeq.dat
@@ -0,0 +1,100 @@
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+ 5.754399373371566e-01 5.928114448311252e-02 4.439456789833779e-15
+ 6.918309709189363e-01 5.666617892504009e-02 3.191356061395679e-15
+ 8.317637711026709e-01 5.409948505148902e-02 4.658959396388796e-15
+ 1.000000000000000e+00 5.158863779039475e-02 2.496311679602705e-15
+ 1.202264434617413e+00 4.913983755302447e-02 2.503975647353570e-15
+ 1.445439770745928e+00 4.675806345070745e-02 1.980624000103322e-15
+ 1.737800828749376e+00 4.444721590565470e-02 3.513326611439523e-15
+ 2.089296130854041e+00 4.221024763556332e-02 2.128775949903540e-15
+ 2.511886431509582e+00 4.004928271457441e-02 2.084732824400213e-15
+ 3.019951720402019e+00 3.796572391712868e-02 2.057863428784457e-15
+ 3.630780547701010e+00 3.596034888344765e-02 2.149696722374579e-15
+ 4.365158322401657e+00 3.403339584700401e-02 2.506590750983091e-15
+ 5.248074602497723e+00 3.218463976982702e-02 2.666959749115830e-15
+ 6.309573444801930e+00 3.041345976812730e-02 1.843390243429058e-15
+ 7.585775750291836e+00 2.871889869982439e-02 2.075866723337706e-15
+ 9.120108393559097e+00 2.709971574419922e-02 2.614004879642500e-15
+ 1.096478196143185e+01 2.555443274573189e-02 2.784239762991527e-15
+ 1.318256738556407e+01 2.408137502873176e-02 4.417788851818592e-15
+ 1.584893192461114e+01 2.267870732135474e-02 2.346418536174242e-15
+ 1.905460717963248e+01 2.134446535879641e-02 3.159630166116848e-15
+ 2.290867652767775e+01 2.007658366786368e-02 3.067450163255898e-15
+ 2.754228703338169e+01 1.887291997221849e-02 4.085090221270331e-15
+ 3.311311214825908e+01 1.773127660229970e-02 4.662766446257259e-15
+ 3.981071705534969e+01 1.664941924664940e-02 5.219648685301088e-15
+ 4.786300923226381e+01 1.562509334029200e-02 5.188731853763820e-15
+ 5.754399373371567e+01 1.465603834912039e-02 5.298056449394350e-15
+ 6.918309709189363e+01 1.374000017615125e-02 6.088475789849585e-15
+ 8.317637711026708e+01 1.287474188620420e-02 5.607884807044724e-15
diff --git a/figs/condensate.fig/condensate.gnuplot b/figs/condensate.fig/condensate.gnuplot
new file mode 100644
index 0000000..f1c689d
--- /dev/null
+++ b/figs/condensate.fig/condensate.gnuplot
@@ -0,0 +1,36 @@
+set ylabel "$\\eta$" norotate
+set xlabel "$\\rho$"
+
+set yrange [0.9:1]
+set ytics 0.91, 0.03
+set mytics 3
+
+set xrange [1e-6:100]
+set xtics 1e-6, 100, 100
+set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100)
+unset mxtics
+
+# default output canvas size: 12.5cm x 8.75cm
+set term lua tikz size 8,6 standalone
+
+set key off
+
+# set linestyle
+set style line 1 linetype rgbcolor "#4169E1" linewidth 2
+set style line 2 linetype rgbcolor "#DC143C" linewidth 2
+set style line 3 linetype rgbcolor "#32CD32" linewidth 2
+set style line 4 linetype rgbcolor "#4B0082" linewidth 2
+set style line 5 linetype rgbcolor "#DAA520" linewidth 2
+
+set pointsize 0.6
+
+set label at 0.000005,0.91 "Bogolyubov" textcolor "#32CD32"
+
+set logscale x
+
+a=1.25435641059
+
+plot "simpleq.dat" u 1:(1-$2) w l ls 1, \
+ "bigeq.dat" u 1:(1-$2) w l ls 4 , \
+ 1-8/(3*sqrt(pi))*sqrt(x*a**3) linestyle 3 dashtype "." ,\
+ "holzmann_2019-12-25.dat" u 1:(1-$3) ls 2
diff --git a/figs/condensate.fig/holzmann_2019-12-25.dat b/figs/condensate.fig/holzmann_2019-12-25.dat
new file mode 100644
index 0000000..96689cb
--- /dev/null
+++ b/figs/condensate.fig/holzmann_2019-12-25.dat
@@ -0,0 +1,11 @@
+## data from M. Holzmann, 2019-09-22
+# rho E0 n0
+1e-6 7.902e-6
+1e-4 8.3441e-4 0.0171
+1e-3 9.13384e-3 0.0481
+1e-2 1.061073e-1 0.0871
+1e-1 1.19182e+0 0.0851
+1e-0 1.24302e+1 0.0587
+1e+1 1.25442e+2 0.0319
+5e+1 6.28032e+2 0.021
+
diff --git a/figs/condensate.fig/simpleq.dat b/figs/condensate.fig/simpleq.dat
new file mode 100644
index 0000000..348121c
--- /dev/null
+++ b/figs/condensate.fig/simpleq.dat
@@ -0,0 +1,100 @@
+ 1.000000000000000e-06 2.095081711925015e-03
+ 1.202264434617413e-06 2.295235280091131e-03
+ 1.445439770745928e-06 2.514296186738034e-03
+ 1.737800828749376e-06 2.754005992218143e-03
+ 2.089296130854041e-06 3.016257261240048e-03
+ 2.511886431509582e-06 3.303104592145314e-03
+ 3.019951720402019e-06 3.616775975726918e-03
+ 3.630780547701017e-06 3.959684344305409e-03
+ 4.365158322401657e-06 4.334439155646415e-03
+ 5.248074602497723e-06 4.743857767750661e-03
+ 6.309573444801930e-06 5.190976310677877e-03
+ 7.585775750291836e-06 5.679059686385030e-03
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+ 1.905460717963248e-05 8.865120699464721e-03
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+ 1.318256738556407e+01 1.838707817059403e-04
+ 1.584893192461114e+01 1.530130079086820e-04
+ 1.905460717963248e+01 1.273233330370514e-04
+ 2.290867652767775e+01 1.059394293104648e-04
+ 2.754228703338169e+01 8.814186420712528e-05
+ 3.311311214825908e+01 7.333072418003886e-05
+ 3.981071705534969e+01 6.100596972384632e-05
+ 4.786300923226381e+01 5.075095479639026e-05
+ 5.754399373371567e+01 4.221862079919067e-05
+ 6.918309709189363e+01 3.511994492291246e-05
+ 8.317637711026708e+01 2.921428437169262e-05
diff --git a/figs/energy.fig/Makefile b/figs/energy.fig/Makefile
new file mode 100644
index 0000000..e8d3f12
--- /dev/null
+++ b/figs/energy.fig/Makefile
@@ -0,0 +1,28 @@
+PROJECTNAME=erho_effective erho_fulleq erho_lowhigh
+
+PDFS=$(addsuffix .pdf, $(PROJECTNAME))
+
+all: $(PDFS)
+
+$(PDFS):
+ gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tex, $@)
+ pdflatex -file-line-error $(patsubst %.pdf, %.tex, $@)
+
+install: $(PDFS)
+ cp $^ $(INSTALLDIR)/
+
+$(LIBS):
+ ln -fs libs/$@ ./
+
+clean-libs:
+ rm -f $(LIBS)
+
+clean-aux:
+ rm -f $(addsuffix .aux, $(PROJECTNAME))
+ rm -f $(addsuffix .log, $(PROJECTNAME))
+ rm -f $(addsuffix .tex, $(PROJECTNAME))
+
+clean-tex:
+ rm -f $(PDFS)
+
+clean: clean-libs clean-aux clean-tex
diff --git a/figs/energy.fig/erho.dat b/figs/energy.fig/erho.dat
new file mode 100644
index 0000000..837439f
--- /dev/null
+++ b/figs/energy.fig/erho.dat
@@ -0,0 +1,104 @@
+ # v(x)=exp(-|x|), order=100, tolerance=1e-14
+ #
+ # rho energy
+ #
+ 1.00000000e-06 7.93445832e-06
+ 1.20226443e-06 9.54545091e-06
+ 1.44543977e-06 1.14842358e-05
+ 1.73780083e-06 1.38177301e-05
+ 2.08929613e-06 1.66265809e-05
+ 2.51188643e-06 2.00080034e-05
+ 3.01995172e-06 2.40792133e-05
+ 3.63078055e-06 2.89815779e-05
+ 4.36515832e-06 3.48856405e-05
+ 5.24807460e-06 4.19972045e-05
+ 6.30957344e-06 5.05647046e-05
+ 7.58577575e-06 6.08881446e-05
+ 9.12010839e-06 7.33299394e-05
+ 1.09647820e-05 8.83280780e-05
+ 1.31825674e-05 1.06412115e-04
+ 1.58489319e-05 1.28222614e-04
+ 1.90546072e-05 1.54534805e-04
+ 2.29086765e-05 1.86287394e-04
+ 2.75422870e-05 2.24617677e-04
+ 3.31131121e-05 2.70904370e-04
+ 3.98107171e-05 3.26819905e-04
+ 4.78630092e-05 3.94394317e-04
+ 5.75439937e-05 4.76093386e-04
+ 6.91830971e-05 5.74914264e-04
+ 8.31763771e-05 6.94502595e-04
+ 1.00000000e-04 8.39296065e-04
+ 1.20226443e-04 1.01470042e-03
+ 1.44543977e-04 1.22730542e-03
+ 1.73780083e-04 1.48514988e-03
+ 2.08929613e-04 1.79804690e-03
+ 2.51188643e-04 2.17798310e-03
+ 3.01995172e-04 2.63960836e-03
+ 3.63078055e-04 3.20083623e-03
+ 4.36515832e-04 3.88357954e-03
+ 5.24807460e-04 4.71465030e-03
+ 6.30957344e-04 5.72685888e-03
+ 7.58577575e-04 6.96035420e-03
+ 9.12010839e-04 8.46425370e-03
+ 1.09647820e-03 1.02986208e-02
+ 1.31825674e-03 1.25368572e-02
+ 1.58489319e-03 1.52685874e-02
+ 1.90546072e-03 1.86031268e-02
+ 2.29086765e-03 2.26736380e-02
+ 2.75422870e-03 2.76420977e-02
+ 3.31131121e-03 3.37052167e-02
+ 3.98107171e-03 4.11014850e-02
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+ 5.75439937e-03 6.11081308e-02
+ 6.91830971e-03 7.44879092e-02
+ 8.31763771e-03 9.07655413e-02
+ 1.00000000e-02 1.10550483e-01
+ 1.20226443e-02 1.34575061e-01
+ 1.44543977e-02 1.63718539e-01
+ 1.73780083e-02 1.99036030e-01
+ 2.08929613e-02 2.41793284e-01
+ 2.51188643e-02 2.93508614e-01
+ 3.01995172e-02 3.56003446e-01
+ 3.63078055e-02 4.31463277e-01
+ 4.36515832e-02 5.22511186e-01
+ 5.24807460e-02 6.32296416e-01
+ 6.30957344e-02 7.64601077e-01
+ 7.58577575e-02 9.23968602e-01
+ 9.12010839e-02 1.11585830e+00
+ 1.09647820e-01 1.34683126e+00
+ 1.31825674e-01 1.62477387e+00
+ 1.58489319e-01 1.95916654e+00
+ 1.90546072e-01 2.36140673e+00
+ 2.29086765e-01 2.84519724e+00
+ 2.75422870e-01 3.42701297e+00
+ 3.31131121e-01 4.12666196e+00
+ 3.98107171e-01 4.96795983e+00
+ 4.78630092e-01 5.97954056e+00
+ 5.75439937e-01 7.19583118e+00
+ 6.91830971e-01 8.65822353e+00
+ 8.31763771e-01 1.04164830e+01
+ 1.00000000e+00 1.25304420e+01
+ 1.20226443e+00 1.50720365e+01
+ 1.44543977e+00 1.81277534e+01
+ 1.73780083e+00 2.18015742e+01
+ 2.08929613e+00 2.62185132e+01
+ 2.51188643e+00 3.15288712e+01
+ 3.01995172e+00 3.79133506e+01
+ 3.63078055e+00 4.55892039e+01
+ 4.36515832e+00 5.48176270e+01
+ 5.24807460e+00 6.59126465e+01
+ 6.30957344e+00 7.92518063e+01
+ 7.58577575e+00 9.52890139e+01
+ 9.12010839e+00 1.14569987e+02
+ 1.09647820e+01 1.37750822e+02
+ 1.31825674e+01 1.65620322e+02
+ 1.58489319e+01 1.99126836e+02
+ 1.90546072e+01 2.39410530e+02
+ 2.29086765e+01 2.87842186e+02
+ 2.75422870e+01 3.46069846e+02
+ 3.31131121e+01 4.16074894e+02
+ 3.98107171e+01 5.00239474e+02
+ 4.78630092e+01 6.01427558e+02
+ 5.75439937e+01 7.23082394e+02
+ 6.91830971e+01 8.69343678e+02
+ 8.31763771e+01 1.04518842e+03
diff --git a/figs/energy.fig/erho_effective.gnuplot b/figs/energy.fig/erho_effective.gnuplot
new file mode 100644
index 0000000..f26252e
--- /dev/null
+++ b/figs/energy.fig/erho_effective.gnuplot
@@ -0,0 +1,38 @@
+set ylabel "$\\displaystyle\\frac{e}{\\rho}$" norotate offset -1,0
+set xlabel "$\\rho$"
+
+set xtics 1e-6, 100, 100
+set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100)
+unset mxtics
+
+set ytics 8,1
+set mytics 2
+
+set xrange [0.000001:100]
+set yrange [7.5:13.5]
+
+# default output canvas size: 12.5cm x 8.75cm
+set term lua tikz size 8,6 standalone
+
+set key off
+
+
+# set linestyle
+set style line 1 linetype rgbcolor "#4169E1" linewidth 3
+set style line 2 linetype rgbcolor "#DC143C" linewidth 3
+set style line 3 linetype rgbcolor "#32CD32" linewidth 3
+set style line 4 linetype rgbcolor "#4B0082" linewidth 3
+set style line 5 linetype rgbcolor "#DAA520" linewidth 3
+
+set pointsize 1
+
+set logscale x
+
+a=1.25435641059
+
+set label at 0.0001,2*pi*a*1.03 "LHY" textcolor "#DAA520"
+set label at 0.1,4.1*pi "Hartree" textcolor "#32CD32"
+
+plot "erho.dat" using 1:($2/$1) with lines linestyle 1 ,\
+ 2*pi*a*(1+128/15/sqrt(pi)*sqrt(x*a**3)) linestyle 5 dashtype "." ,\
+ 4*pi linestyle 3 dashtype "."
diff --git a/figs/energy.fig/erho_fulleq.dat b/figs/energy.fig/erho_fulleq.dat
new file mode 100644
index 0000000..351d1b9
--- /dev/null
+++ b/figs/energy.fig/erho_fulleq.dat
@@ -0,0 +1,100 @@
+ 1.000000000000000e-06 7.943042518656766e-06 0
+ 1.202264434617413e-06 9.550219866068997e-06 0
+ 1.445439770745928e-06 1.148608224097378e-05 1
+ 1.737800828749376e-06 1.381647407426905e-05 1
+ 2.089296130854041e-06 1.662160583174429e-05 0
+ 2.511886431509582e-06 2.000065135391551e-05 0
+ 3.019951720402019e-06 2.406839054942614e-05 0
+ 3.630780547701017e-06 2.896662133595565e-05 1
+ 4.365158322401657e-06 3.486570260772683e-05 1
+ 5.248074602497723e-06 4.197087478032896e-05 1
+ 6.309573444801930e-06 5.052956242205629e-05 1
+ 7.585775750291836e-06 6.084048678334965e-05 1
+ 9.120108393559096e-06 7.326450648917462e-05 1
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diff --git a/figs/energy.fig/erho_fulleq.gnuplot b/figs/energy.fig/erho_fulleq.gnuplot
new file mode 100644
index 0000000..2927ead
--- /dev/null
+++ b/figs/energy.fig/erho_fulleq.gnuplot
@@ -0,0 +1,37 @@
+set ylabel "$\\displaystyle\\frac{e}{\\rho}$" norotate offset -1,0
+set xlabel "$\\rho$"
+
+set xtics 1e-6, 100, 100
+set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100)
+unset mxtics
+
+set ytics 8,1
+set mytics 2
+
+set xrange [0.000001:100]
+set yrange [7.5:13.5]
+
+# default output canvas size: 12.5cm x 8.75cm
+set term lua tikz size 8,6 standalone
+
+set key off
+
+
+# set linestyle
+set style line 1 linetype rgbcolor "#4169E1" linewidth 3
+set style line 2 linetype rgbcolor "#DC143C" linewidth 3
+set style line 3 linetype rgbcolor "#32CD32" linewidth 3
+set style line 4 linetype rgbcolor "#4B0082" linewidth 3
+set style line 5 linetype rgbcolor "#DAA520" linewidth 3
+
+set pointsize 1
+
+set logscale x
+
+a=1.25435641059
+
+plot "erho.dat" using 1:($2/$1) with lines linestyle 1 ,\
+ "erho_fulleq.dat" using 1:($2/$1) with lines linestyle 4 ,\
+ 2*pi*a*(1+128/15/sqrt(pi)*sqrt(x*a**3)) linestyle 5 dashtype "." ,\
+ 4*pi linestyle 3 dashtype "." ,\
+ "holzmann_2019-12-25.dat" using 1:($2/$1) with points linestyle 2
diff --git a/figs/energy.fig/erho_lowhigh.gnuplot b/figs/energy.fig/erho_lowhigh.gnuplot
new file mode 100644
index 0000000..9d2a590
--- /dev/null
+++ b/figs/energy.fig/erho_lowhigh.gnuplot
@@ -0,0 +1,37 @@
+set ylabel "$\\displaystyle\\frac{e}{\\rho}$" norotate offset -1,0
+set xlabel "$\\rho$"
+
+set xtics 1e-6, 100, 100
+set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100)
+unset mxtics
+
+set ytics 8,1
+set mytics 2
+
+set xrange [0.000001:100]
+set yrange [7.5:13.5]
+
+# default output canvas size: 12.5cm x 8.75cm
+set term lua tikz size 8,6 standalone
+
+set key off
+
+
+# set linestyle
+set style line 1 linetype rgbcolor "#4169E1" linewidth 3
+set style line 2 linetype rgbcolor "#DC143C" linewidth 3
+set style line 3 linetype rgbcolor "#32CD32" linewidth 3
+set style line 4 linetype rgbcolor "#4B0082" linewidth 3
+set style line 5 linetype rgbcolor "#DAA520" linewidth 3
+
+set pointsize 1
+
+set logscale x
+
+a=1.25435641059
+
+set label at 0.0001,2*pi*a*1.03 "LHY" textcolor "#DAA520"
+set label at 0.1,4.1*pi "Hartree" textcolor "#32CD32"
+
+plot 2*pi*a*(1+128/15/sqrt(pi)*sqrt(x*a**3)) linestyle 5 dashtype "." ,\
+ 4*pi linestyle 3 dashtype "."
diff --git a/figs/energy.fig/holzmann_2019-12-25.dat b/figs/energy.fig/holzmann_2019-12-25.dat
new file mode 100644
index 0000000..96689cb
--- /dev/null
+++ b/figs/energy.fig/holzmann_2019-12-25.dat
@@ -0,0 +1,11 @@
+## data from M. Holzmann, 2019-09-22
+# rho E0 n0
+1e-6 7.902e-6
+1e-4 8.3441e-4 0.0171
+1e-3 9.13384e-3 0.0481
+1e-2 1.061073e-1 0.0871
+1e-1 1.19182e+0 0.0851
+1e-0 1.24302e+1 0.0587
+1e+1 1.25442e+2 0.0319
+5e+1 6.28032e+2 0.021
+
diff --git a/figs/energy16.fig/2020-05-22+16.dat b/figs/energy16.fig/2020-05-22+16.dat
new file mode 100644
index 0000000..c28285d
--- /dev/null
+++ b/figs/energy16.fig/2020-05-22+16.dat
@@ -0,0 +1,7 @@
+# rho E0 n0
+ 1e-3 0.05195 0.61
+ 5e-3 0.449 0.40
+ 1e-2 1.1335 0.34
+ 2e-2 2.748 0.33
+ 1e-1 17.797 0.43
+ 1e+0 197.35 0.70
diff --git a/figs/energy16.fig/Makefile b/figs/energy16.fig/Makefile
new file mode 100644
index 0000000..964a8c5
--- /dev/null
+++ b/figs/energy16.fig/Makefile
@@ -0,0 +1,35 @@
+PROJECTNAME=energy16
+
+SIMPLEQ=~/Work/Research/2018+bose_gas/cmp/simpleq
+
+DATS=simpleq16.dat medeq16.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, $@)
+
+simpleq16.dat:
+ julia $(SIMPLEQ)/main.jl -p "tolerance=1e-11;order=100;maxiter=100;v_a=16" -M simpleq energy_rho > $@
+medeq16.dat:
+ julia -p 8 $(SIMPLEQ)/main.jl -p "aK=1;aL1=1;aL2=1;aL3=0;bK=1;bL1=1;bL2=1;gK=1;gL2=1;gL3=0;N=12;P=8;v_a=16" -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 $(PDFS)
+
+clean: clean-aux clean-tex
diff --git a/figs/energy16.fig/energy16.gnuplot b/figs/energy16.fig/energy16.gnuplot
new file mode 100644
index 0000000..dc996c5
--- /dev/null
+++ b/figs/energy16.fig/energy16.gnuplot
@@ -0,0 +1,34 @@
+set ylabel "$\\displaystyle\\frac{e}{\\rho}$" norotate offset -1,0
+set xlabel "$\\rho$"
+
+set xtics 1e-6, 100, 100
+set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100)
+unset mxtics
+
+#set ytics 0.6, 0.1
+set mytics 2
+
+set xrange [0.000001:100]
+
+# default output canvas size: 12.5cm x 8.75cm
+set term lua tikz size 8,6 standalone
+
+set key off
+
+
+# set linestyle
+set style line 1 linetype rgbcolor "#4169E1" linewidth 2
+set style line 2 linetype rgbcolor "#DC143C" linewidth 2
+set style line 3 linetype rgbcolor "#32CD32" linewidth 2
+set style line 4 linetype rgbcolor "#4B0082" linewidth 2
+set style line 5 linetype rgbcolor "#DAA520" linewidth 2
+
+set pointsize 1
+
+set logscale x
+
+plot \
+ "simpleq16.dat" using 1:($3<1e-5 ? ($2/$1) : 1/0) with lines ls 1 ,\
+ "medeq16.dat" using 1:($3<1e-5 ? ($2/$1) : 1/0) with lines ls 4 ,\
+ "2020-05-22+16.dat" using 1:($2/$1) with points ls 2
+
diff --git a/figs/energy16.fig/medeq16.dat b/figs/energy16.fig/medeq16.dat
new file mode 100644
index 0000000..b670ef5
--- /dev/null
+++ b/figs/energy16.fig/medeq16.dat
@@ -0,0 +1,100 @@
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+ 3.311311214825908e+01 6.657197949756010e+03 5.311424682002792e-14
+ 3.981071705534969e+01 8.003831302911970e+03 8.573716686070972e-15
+ 4.786300923226381e+01 9.622840695326604e+03 5.255692893479381e-14
+ 5.754399373371567e+01 1.156931811166827e+04 5.412915990778012e-16
+ 6.918309709189363e+01 1.390949868589013e+04 5.629397185139020e-14
+ 8.317637711026708e+01 1.672301456399418e+04 8.852629630882290e-12
diff --git a/libs/ian-presentation.cls b/libs/ian-presentation.cls
new file mode 100644
index 0000000..91bd487
--- /dev/null
+++ b/libs/ian-presentation.cls
@@ -0,0 +1,187 @@
+%%
+%% Ian's presentation class
+%%
+
+%% TeX format
+\NeedsTeXFormat{LaTeX2e}[1995/12/01]
+
+%% class name
+\ProvidesClass{ian-presentation}[2017/09/29]
+
+\def\ian@defaultoptions{
+ \pagestyle{plain}
+ \RequirePackage{color}
+ \RequirePackage{amssymb}
+}
+
+%% paper dimensions
+\setlength\paperheight{240pt}
+\setlength\paperwidth{427pt}
+
+%% fonts
+\input{size11.clo}
+\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm}
+\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf}
+\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt}
+\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf}
+\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit}
+
+%% text dimensions
+\textheight=208pt
+\textwidth=370pt
+\hoffset=-1in
+\voffset=-1in
+\oddsidemargin=24pt
+\evensidemargin=24pt
+\topmargin=8pt
+\headheight=0pt
+\headsep=0pt
+\marginparsep=0pt
+\marginparwidth=0pt
+\footskip=16pt
+
+
+%% remove default skips
+\parindent=0pt
+\parskip=0pt
+\baselineskip=0pt
+
+%% something is wrong with \thepage, redefine it
+\gdef\thepage{\the\c@page}
+
+%% correct vertical alignment at the end of a document
+\AtEndDocument{
+ % save total slide count
+ \immediate\write\@auxout{\noexpand\gdef\noexpand\slidecount{\thepage}}
+ \vfill
+ \eject
+}
+
+
+%% footer
+\def\ps@plain{
+ \def\@oddhead{}
+ \def\@evenhead{\@oddhead}
+ \def\@oddfoot{\tiny\hfill\thepage/\safe\slidecount\hfill}
+ \def\@evenfoot{\@oddfoot}
+}
+\def\ps@empty{
+ \def\@oddhead{}
+ \def\@evenhead{\@oddhead}
+ \def\@oddfoot{}
+ \def\@evenfoot{\@oddfoot}
+}
+
+
+%% title of slide
+\def\title#1{
+ \hfil{\bf\large #1}\par
+ \hfil\vrule width0.75\textwidth height0.3pt\par
+ \vskip5pt
+}
+
+
+%% hyperlinks
+% hyperlinkcounter
+\newcounter{lncount}
+% hyperref anchor
+\def\hrefanchor{%
+\stepcounter{lncount}%
+\hypertarget{ln.\thelncount}{}%
+}
+
+%% define a command and write it to aux file
+\def\outdef#1#2{%
+ % define command%
+ \expandafter\xdef\csname #1\endcsname{#2}%
+ % hyperlink number%
+ \expandafter\xdef\csname #1@hl\endcsname{\thelncount}%
+ % write command to aux%
+ \immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1\endcsname{\csname #1\endcsname}}%
+ \immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1@hl\endcsname{\thelncount}}%
+}
+
+%% can call commands even when they are not defined
+\def\safe#1{%
+ \ifdefined#1%
+ #1%
+ \else%
+ {\color{red}\bf?}%
+ \fi%
+}
+
+
+%% itemize
+\newlength\itemizeskip
+% left margin for items
+\setlength\itemizeskip{20pt}
+\newlength\itemizeseparator
+% space between the item symbol and the text
+\setlength\itemizeseparator{5pt}
+% penalty preceding an itemize
+\def\itemizepenalty{0}
+% counter counting the itemize level
+\newcounter{itemizecount}
+
+% item symbol
+\def\itemizept#1{
+ \ifnum#1=1
+ \textbullet
+ \else
+ $\scriptstyle\blacktriangleright$
+ \fi
+}
+
+\newlength\current@itemizeskip
+\setlength\current@itemizeskip{0pt}
+\def\itemize{
+ \par\penalty\itemizepenalty\medskip\penalty\itemizepenalty
+ \addtocounter{itemizecount}{1}
+ \addtolength\current@itemizeskip{\itemizeskip}
+ \leftskip\current@itemizeskip
+}
+\def\enditemize{
+ \addtocounter{itemizecount}{-1}
+ \addtolength\current@itemizeskip{-\itemizeskip}
+ \par\leftskip\current@itemizeskip
+ \medskip
+}
+\newlength\itempt@total
+\def\item{
+ \settowidth\itempt@total{\itemizept\theitemizecount}
+ \addtolength\itempt@total{\itemizeseparator}
+ \par
+ \medskip
+ \hskip-\itempt@total\itemizept\theitemizecount\hskip\itemizeseparator
+}
+
+%% enumerate
+\newcounter{enumerate@count}
+\def\enumerate{
+ \setcounter{enumerate@count}0
+ \let\olditem\item
+ \let\olditemizept\itemizept
+ \def\item{
+ % counter
+ \stepcounter{enumerate@count}
+ % set header
+ \def\itemizept{\theenumerate@count.}
+ % hyperref anchor
+ \hrefanchor
+ % define tag (for \label)
+ \xdef\tag{\theenumerate@count}
+ \olditem
+ }
+ \itemize
+}
+\def\endenumerate{
+ \enditemize
+ \let\item\olditem
+ \let\itemizept\olditemizept
+}
+
+
+%% end
+\ian@defaultoptions
+
+\endinput
generated by cgit v1.2.3-70-g09d2 (git 2.51.1) at 2025-11-04 01:28:53 +0000