As presented in Tubingen on 2022-01-03HEAD v1.0 master

author: Ian Jauslin <ian@jauslin.org> 2022-02-20 17:50:35 -0500
committer: Ian Jauslin <ian@jauslin.org> 2022-02-20 17:50:35 -0500
commit: 601999d5c035bb51784ba03e478429e981bbbdfa (patch)
tree: 59489154099c4b1951d34ca3fe34672e077c98cc
49 files changed, 2729 insertions, 0 deletions
diff --git a/Jauslin_Tubingen_2022.tex b/Jauslin_Tubingen_2022.tex
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+\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 An effective equation to study Bose gases\par
+\smallskip
+\hfil at all densities\par
+\vfil
+\large
+\hfil Ian Jauslin
+\normalsize
+\vfil
+\hfil\rm joint with {\bf Eric A. Carlen}, {\bf Markus Holzmann}, {\bf Elliott H. Lieb}\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{Bose-Einstein condensation}
+\begin{itemize}
+\item System of many Bosons, e.g. {\color{highlight}Helium} atoms, {\color{highlight}Rubidium} atoms, etc...
+\item {\color{highlight}Bose-Einstein condensate}: most particles are in the same quantum state.
+\item Related to the phenomena of {\color{highlight}superfluidity} (flow with zero viscocity) and {\color{highlight}superconductivity} (currents with zero resistance).
+\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 Potential: {\color{highlight}$v(r)\geqslant 0$} and {\color{highlight}$v\in L_1(\mathbb R^3)$}, Hamiltonian:
+  $$
+    H_N:=
+    -\frac12\sum_{i=1}^N\Delta_i
+    +\sum_{1\leqslant i<j\leqslant N}v(|x_i-x_j|)
+  $$
+  \vskip-5pt
+  \item Ground state: $\psi_0$, energy $E_0$.
+  \item Observables in the {\color{highlight}thermodynamic limit}: ground state energy per particle and condensate fraction: $P_i$: projection onto condensate state
+  $$
+    e_0:=\lim_{\displaystyle\mathop{\scriptstyle V,N\to\infty}_{{\color{highlight}\frac NV=\rho}}}\frac{E_0}N
+    ,\quad
+    \eta_0:=\lim_{\displaystyle\mathop{\scriptstyle V,N\to\infty}_{{\color{highlight}\frac NV=\rho}}}\frac1N\sum_{i=1}^N\left<\psi_0\right|P_i\left|\psi_0\right>
+    .
+  $$
+\end{itemize}
+\vfill
+\eject
+
+\title{Low density}
+\begin{itemize}
+  \item Bogolyubov theory: {\color{highlight}approximation scheme} that reduces the problem to an effective {\color{highlight}1-particle problem}.
+  \item Predictions \href{https://doi.org/10.1103/PhysRev.106.1135}{[Lee, Huang, Yang, 1957]}:
+  \begin{itemize}
+    \item Energy:
+    $$
+      {\color{highlight}e_0=2\pi\rho a\left(1+\frac{128}{15\sqrt\pi}\sqrt{\rho a^3}+o(\sqrt\rho)\right)}
+    $$
+    \vskip-10pt
+    \item Condensate fraction:
+    $$
+      {\color{highlight}1-\eta_0\sim\frac{8\sqrt{\rho a^3}}{3\sqrt\pi}}
+    $$
+  \end{itemize}
+\end{itemize}
+\vfill
+\eject
+
+\title{Low density}
+\begin{itemize}
+  \item Energy asymptotics: {\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://doi.org/10.4007/annals.2020.192.3.5}{[Fournais, Solovej, 2020]}.
+
+  \item Condensate fraction: {\color{highlight}still open} in the theormodynamic limit, but there are proofs of condensation in the Gross-Pitaevskii regime (ultra-dilute):
+  \href{https://doi.org/10.1103/PhysRevLett.88.170409}{[Lieb, Seiringer, 2002]},
+  \href{https://doi.org/10.1007/s00220-017-3016-5}{[Boccato, Brennecke, Cenatiempo, Schlein, 2018]}.
+
+\end{itemize}
+\vfill
+\eject
+
+\title{High density}
+\begin{itemize}
+  \item [Bogolyubov, 1947]: if $\hat v\geqslant 0$.
+  $$
+    {\color{highlight}e_0\sim\frac\rho2\int v}
+  $$
+  {\color{highlight}Hartree} (mean field) energy.
+  \item {\color{highlight}Proved} in \href{https://doi.org/10.1103/PhysRev.130.2518}{[Lieb, 1963]}.
+  \item Condensate fraction
+  $$
+    \eta\to1
+  $$
+  {\color{highlight}open}.
+\end{itemize}
+\vfill
+\eject
+
+\title{Energy as a function of density}
+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 $v(x)=e^{-|x|}$:
+
+\hfil\includegraphics[height=5.5cm]{erho_effective.pdf}
+\vfill
+\eject
+
+\title{Derivation of the equation}
+\begin{itemize}
+  \item \href{https://doi.org/10.1103/PhysRev.130.2518}{[Lieb, 1963]}.
+  \item Integrate $H_N\psi_0=E_0\psi_0$:
+  $$
+    \int dx_1\cdots dx_N\ 
+    \left(
+      -\frac12\sum_{i=1}^N\Delta_i\psi_0
+      +\sum_{1\leqslant i<j\leqslant N} v(x_i-x_j)\psi_0
+    \right)
+    =E_0\int dx_1\cdots dx_N\ \psi_0
+  $$
+  \item Therefore,
+  $$
+    \frac{N(N-1)}2\int dx_1dx_2\ v(x_1-x_2)\frac{\int dx_3\cdots dx_N\ \psi_0}{\int dx_1\cdots dx_N\ \psi_0}
+    =E_0
+  $$
+\end{itemize}
+\vfill
+\eject
+
+\title{Derivation of the equation}
+\begin{itemize}
+  \item Thus,
+  $$
+    \frac{E_0}N=\frac{N-1}{2V}\int dx\ v(x)g_2(0,x)
+  $$
+  \item {\color{highlight}$\psi_0\geqslant 0$}, so it can be thought of as a probability distribution.
+  \item $g_n$: {\color{highlight}correlation functions} of $V^{-N}\psi_0$
+  $$
+    g_n(x_1,\cdots,x_n):=\frac{V^n\int dx_{n+1}\cdots dx_N\ \psi_0(x_1,\cdots,x_N)}{\int dx_1\cdots dx_N\ \psi_0(x_1,\cdots,x_N)}
+  $$
+\end{itemize}
+\vfill
+\eject
+
+\title{Hierarchy}
+\vskip-10pt
+\begin{itemize}
+  \item Equation for $g_2$: integrate $H_N\psi_0=E_0\psi_0$ with respect to $x_3,\cdots,x_N$:
+  $$
+    \begin{array}{>\displaystyle l}
+      -\frac12(\Delta_x+\Delta_y) g_2(x,y)
+      +\frac{N-2}V\int dz\ (v(x-z)+v(y-z))g_3(x,y,z)
+      \\[0.5cm]\hfill
+      +v(x-y)g_2(x,y)
+      +\frac{(N-2)(N-3)}{2V^2}\int dzdt\ v(z-t)g_4(x,y,z,t)
+      =E_0g_2(x,y)
+    \end{array}
+  $$
+  \item Factorization {\color{highlight}assumption}:
+  $$
+    g_3(x_1,x_2,x_3)=g_2(x_1,x_2)g_2(x_1,x_3)g_2(x_2,x_3)
+  $$
+  $$
+    g_4(x_1,x_2,x_3,x_4)=\prod_{i<j}(g_2(x_i,x_j)+O(V^{-1}))
+  $$
+\end{itemize}
+\vfill
+\eject
+
+\title{{\color{ipurple}Big equation}}
+\begin{itemize}
+\item In the thermodynamic limit, if ${\color{highlight}u(x):=1-g_2(0,x)}$,
+  $$
+    -\Delta u(x)
+    =
+    (1-u(x))\left(v(x)-2\rho K(x)+\rho^2 L(x)\right)
+  $$
+  $$
+    K:=
+    u\ast S
+    ,\quad
+    S(y):=(1-u(y))v(y)
+  $$
+  $$
+    L:=
+    u\ast u\ast S
+    -2u\ast(u(u\ast S))
+    +\frac12
+    \int dydz\ u(y)u(z-x)u(z)u(y-x)S(z-y)
+    .
+  $$
+
+  \item {\color{ipurple}``Big'' equation}:
+  $$
+    L\approx
+    u\ast u\ast S
+    -2u\ast (u(u\ast S))
+  $$
+\end{itemize}
+\vfill
+\eject
+  
+\title{{\color{iblue}Simple equation}}
+\vskip-10pt
+\begin{itemize}
+  \item Further approximate $S(x)\approx\frac{2e}\rho\delta(x)$ and $u\ll 1$.
+  \item Simple equation
+  $$
+    {\color{iblue}-\Delta u(x)=(1-u(x))v(x)- 4eu(x)+2e\rho\ u\ast u(x)}
+  $$
+  $$
+    {\color{iblue}e=\frac\rho2\int dx\ (1-u(x))v(x)}
+  $$
+  \item {\bf Theorem 1}:
+  If $v(x)\geqslant 0$ and $v\in L_1\cap L_2(\mathbb R^3)$, then the {\color{iblue}simple equation} has an {\color{highlight}integrable solution} (proved constructively), with $0\leqslant u\leqslant 1$.
+\end{itemize}
+\vfill
+\eject
+
+\title{Energy for the {\color{iblue}simple equation}}
+\vskip-10pt
+\begin{itemize}
+  \item {\bf Theorem 2}:
+  $$
+    \frac{e}{\rho}\mathop{\longrightarrow}_{\rho\to\infty}\frac12\int dx\ v(x)
+  $$
+  (note that there is no condition that $\hat v\geqslant 0$).
+  This coincides with the {\color{highlight}Hartree energy}.
+  \item {\bf Theorem 3}:
+  $$
+    e=2\pi\rho a\left(1+\frac{128}{15\sqrt\pi}\sqrt{\rho a^3}+o(\sqrt\rho)\right)
+  $$
+  This coincides with the {\color{highlight}Lee-Huang-Yang prediction}.
+\end{itemize}
+\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{Energy}
+$v(x)=e^{-|x|}$, Blue: {\color{iblue}simple equation}; red: {\color{ired}Jastrow}; purple: {\color{ipurple}big equation}
+
+\hfil\includegraphics[height=5.5cm]{cmp_energy1.pdf}
+\vfill
+\eject
+
+\title{Condensate fraction}
+\begin{itemize}
+  \item Add a parameter $\mu$ to the Hamiltonian:
+  $$
+    H_N(\mu):=
+    -\frac12\sum_{i=1}^N\Delta_i
+    +\sum_{1\leqslant i<j\leqslant N}v(x_i-x_j)
+    {\color{highlight}-\mu\sum_{i=1}^NP_i}
+  $$
+  \item Projection onto condensate wavefunction: $P_i$.
+  \item Condensate fraction:
+  $$
+    {\color{highlight}\eta_0}:=\frac1N\left<\psi_0\right|\sum_{i=1}^NP_i\left|\psi_0\right>
+    =-\frac1N\partial_\mu \left<\psi_0\right|H_N(\mu)\left|\psi_0\right>|_{\mu_0}
+    \equiv
+    {\color{highlight}-\partial_\mu e_0(\mu)|_{\mu=0}}
+  $$
+\end{itemize}
+\vfill
+\eject
+
+\title{Condensate fraction}
+\begin{itemize}
+  \item {\bf Theorem 4}:
+  For the {\color{iblue}simple equation}, as $\rho\to0$
+  $$
+    1-\eta\sim\frac{8\sqrt{\rho a^3}}{3\sqrt\pi}
+  $$
+  which coincides with {\color{highlight}Bogolyubov's prediction}.
+\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{Two point correlation function}
+$v(x)=16e^{-|x|}$, Blue: {\color{iblue}simple equation}; purple: {\color{ipurple}big equation}; red: {\color{ired}Monte Carlo}
+
+\hfil\includegraphics[height=5.5cm]{correlation.pdf}
+\vfill
+\eject
+
+\title{Summary and outlook}
+\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}
+\vfill
+\eject
+
+\title{Open problems}
+\vfill
+\begin{itemize}
+  \item {\color{highlight}Uniqueness} of the solution of the {\color{iblue}simple equation} (done for small and large $\rho$).
+  \vfill
+
+  \item LHY as an {\color{highlight}upper bound} at low density using the {\color{iblue}simple equation} to construct an Ansatz.
+  \vfill
+
+  \item {\color{highlight}Existence} (and uniqueness) of the solution of the {\color{ipurple}big equation}.
+
+\end{itemize}
+\vfill
+\eject
+
+\title{The uniqueness problem}
+  $$
+    -\Delta u(x)=(1-u(x))v(x)- 4eu(x)+2e\rho\ u\ast u(x)
+    ,\quad
+    e=\frac\rho2\int dx\ (1-u(x))v(x)
+  $$
+\begin{itemize}
+  \item Change the point of view: {\color{highlight}fix $e>0$}, and compute $\rho$ and $u$.
+
+  \item {\color{highlight}Iteration}: $u_0=0$,
+  $$
+    (-\Delta+4e+v)u_n=v+2e\rho_{n-1}u_{n-1}\ast u_{n-1}
+    ,\quad
+    \rho_n:=\frac{2e}{\int dx\ (1-u_n(x))v(x)}
+    .
+  $$
+\end{itemize}
+\vfill
+\eject
+
+\title{The uniqueness problem}
+\begin{itemize}
+  \item {\bf Lemma}: $u_n(x)$ is an {\color{highlight}increasing} sequence, and is {\color{highlight}bounded} $u_n(x)\leqslant 1$.
+  It converges to a function $u$, which is the {\color{highlight}unique} integrable solution of the equation {\color{highlight}with $e$ fixed}.
+
+  \item {\bf Lemma}: $e\mapsto\rho(e)$ is {\color{highlight}continuous}, and $\rho(0)=0$ and $\rho(\infty)=\infty$, which allows us to  compute solutions for the problem at fixed $\rho$.
+
+  \item We thus have a {\color{highlight}restricted} notion of uniqueness.
+  The full uniqueness would follow from a proof that $e\mapsto\rho(r)$ is {\color{highlight}monotone increasing} (which must be true for the physics to make sense).
+\end{itemize}
+\vfill
+\eject
+
+\title{Upper bound at low density}
+\begin{itemize}
+  \item \href{https://doi.org/10.1007/s10955-009-9792-3}{[Yau, Yin, 2009]}: proof for {\color{highlight}weak, smooth}, rapidly decaying potentials.
+  \item \href{https://arxiv.org/abs/2101.06222}{[Basti, Cenatiempo, Schlein, 2021]}: extended for {\color{highlight}$L_3$} (and compactly supported) potentials (excludes hard-core interactions).
+  \item {\color{iblue}Simple Equation}: our analysis holds for the hard-core, so if one could find a good {\color{highlight}Ansatz} from it, one might get an upper bound for the energy in this case.
+  \item Idea for Ansatz? (Jastrow, Dyson-Jastrow?).
+\end{itemize}
+\vfill
+\eject
+
+\title{Upper bound at low density: Jastrow function}
+\begin{itemize}
+  \item Idea:
+  $$
+    \psi=\prod_{i<j}e^{-u(x_i-x_j)}
+  $$
+
+  \item Why this: $\rho\ll1$, and {\color{highlight}if $\rho\|u\|_1\ll1$},
+  $$
+    g_2\sim1-u
+    .
+  $$
+
+  \item Again, {\color{highlight}if $\rho\|u\|_1\ll1$}, we would be able to compute the energy of $\psi$ using a cluster expansion!
+
+  \item However, {\color{highlight}$\|u\|_1=\frac1\rho$}!
+\end{itemize}
+\vfill
+\eject
+
+\title{Existence for the {\color{ipurple}Big Equation}}
+\begin{itemize}
+  \item Numerical method: {\color{highlight}Newton algorithm}.
+
+  \item For the existence of a solution, it would suffice to prove that the Newton algorithm has a {\color{highlight}Basin of attraction}. (Kantorovich-like theorem?)
+
+  \item Such a result, applied to the {\color{iblue}Simple Equation}, would imply the {\color{highlight}uniqueness} of a solution (provided we have convergence in an appropriate norm).
+\end{itemize}
+
+\end{document}
diff --git a/Makefile b/Makefile
new file mode 100644
index 0000000..94f61ff
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,47 @@
+PROJECTNAME=$(basename $(wildcard *.tex))
+LIBS=$(notdir $(wildcard libs/*))
+FIGS=$(notdir $(wildcard figs/*.fig))
+
+PDFS=$(addsuffix .pdf, $(PROJECTNAME))
+SYNCTEXS=$(addsuffix .synctex.gz, $(PROJECTNAME))
+
+all: $(PROJECTNAME)
+
+$(PROJECTNAME): $(LIBS) $(FIGS)
+	pdflatex -file-line-error $@.tex
+	pdflatex -synctex=1 $@.tex
+
+$(SYNCTEXS): $(LIBS) $(FIGS)
+	pdflatex -synctex=1 $(patsubst %.synctex.gz, %.tex, $@)
+
+$(LIBS):
+	ln -fs libs/$@ ./
+
+
+figs: $(FIGS)
+
+$(FIGS):
+	make -C figs/$@
+	for pdf in $$(find figs/$@/ -name '*.pdf'); do ln -fs "$$pdf" ./ ; 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))
+
+clean-figs-aux:
+	$(foreach fig,$(addprefix figs/, $(FIGS)), make -C $(fig) clean-aux; )
+
+
+clean-tex:
+	rm -f $(PDFS) $(SYNCTEXS)
+
+clean: clean-aux clean-tex clean-libs clean-figs
diff --git a/README b/README
new file mode 100644
index 0000000..f628548
--- /dev/null
+++ b/README
@@ -0,0 +1,32 @@
+This directory contains the source files to typeset the presentation, and
+generate the figures. This can be accomplished by running
+  make
+
+This document uses a custom class file, located in the 'libs' directory, which
+defines a number of commands.
+
+
+* Dependencies:
+
+  pdflatex
+  TeXlive packages:
+    amsfonts
+    array
+    graphics
+    hyperref
+    latex
+    pgf
+    standalone
+  GNU make
+
+* Files:
+
+  Jauslin_Tubingen_2022.tex:
+    main LaTeX file
+
+  libs:
+    custom LaTeX class file
+
+  figs:
+    source code for the figures
+
diff --git a/figs/condensate.fig/Makefile b/figs/condensate.fig/Makefile
new file mode 100644
index 0000000..c45de65
--- /dev/null
+++ b/figs/condensate.fig/Makefile
@@ -0,0 +1,34 @@
+PROJECTNAME=condensate
+
+PDFS=$(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 $(PDFS)
+
+clean: clean-libs clean-aux clean-tex
diff --git a/figs/condensate.fig/bigeq.dat b/figs/condensate.fig/bigeq.dat
new file mode 100644
index 0000000..e48cbc3
--- /dev/null
+++ b/figs/condensate.fig/bigeq.dat
@@ -0,0 +1,100 @@
+ 1.000000000000000e-06  1.942109602248065e-03  1.702970665674168e-12
+ 1.202264434617413e-06  2.144142093189251e-03  1.178808810520995e-13
+ 1.445439770745928e-06  2.370859341242408e-03  1.192336354552407e-12
+ 1.737800828749376e-06  2.623985546948715e-03  4.076932518598860e-12
+ 2.089296130854041e-06  2.904135074720890e-03  3.065737407737518e-12
+ 2.511886431509582e-06  3.210803051150611e-03  6.684762465649123e-13
+ 3.019951720402019e-06  3.543752141002869e-03  4.093999456324028e-14
+ 3.630780547701017e-06  3.904216206875963e-03  4.822691376657683e-14
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diff --git a/figs/condensate.fig/condensate.gnuplot b/figs/condensate.fig/condensate.gnuplot
new file mode 100644
index 0000000..f1c689d
--- /dev/null
+++ b/figs/condensate.fig/condensate.gnuplot
@@ -0,0 +1,36 @@
+set ylabel "$\\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/condensate.pdf b/figs/condensate.fig/condensate.pdf
new file mode 100644
index 0000000..9e965a4
--- /dev/null
+++ b/figs/condensate.fig/condensate.pdf
diff --git a/figs/condensate.fig/condensate.tikz.tex b/figs/condensate.fig/condensate.tikz.tex
new file mode 100644
index 0000000..4f7da70
--- /dev/null
+++ b/figs/condensate.fig/condensate.tikz.tex
@@ -0,0 +1,142 @@
+\documentclass[10pt]{article}
+\usepackage[T1]{fontenc}
+\usepackage{textcomp}
+
+\usepackage[utf8x]{inputenc}
+\SetUnicodeOption{mathletters}
+
+\usepackage{gnuplot-lua-tikz}
+\pagestyle{empty}
+\usepackage[active,tightpage]{preview}
+\PreviewEnvironment{tikzpicture}
+\setlength\PreviewBorder{\gpbboxborder}
+\begin{document}
+
+\begin{tikzpicture}[gnuplot]
+%% generated with GNUPLOT 5.4p2 (Lua 5.4; terminal rev. Jun 2020, script rev. 114)
+%% Sun Jan  2 22:45:53 2022
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+  --(6.478,4.089)--(6.535,4.176)--(6.592,4.260)--(6.649,4.339)--(6.706,4.416)--(6.763,4.488)%
+  --(6.820,4.558)--(6.877,4.624)--(6.934,4.687)--(6.991,4.746)--(7.048,4.803)--(7.105,4.857)%
+  --(7.162,4.907)--(7.219,4.956)--(7.276,5.001)--(7.333,5.044)--(7.390,5.085);
+\gpcolor{rgb color={0.196,0.804,0.196}}
+\gpsetdashtype{dash pattern=on 2.00*\gpdashlength off 5.00*\gpdashlength }
+\draw[gp path] (1.748,5.592)--(1.806,5.582)--(1.863,5.571)--(1.921,5.560)--(1.978,5.547)%
+  --(2.036,5.533)--(2.093,5.517)--(2.151,5.500)--(2.209,5.482)--(2.266,5.461)--(2.324,5.439)%
+  --(2.381,5.414)--(2.439,5.387)--(2.496,5.358)--(2.554,5.325)--(2.611,5.289)--(2.669,5.250)%
+  --(2.727,5.207)--(2.784,5.160)--(2.842,5.108)--(2.899,5.052)--(2.957,4.989)--(3.014,4.921)%
+  --(3.072,4.846)--(3.130,4.763)--(3.187,4.673)--(3.245,4.574)--(3.302,4.465)--(3.360,4.345)%
+  --(3.417,4.214)--(3.475,4.070)--(3.533,3.912)--(3.590,3.738)--(3.648,3.548)--(3.705,3.339)%
+  --(3.763,3.110)--(3.820,2.858)--(3.878,2.582)--(3.935,2.279)--(3.993,1.946)--(4.051,1.581)%
+  --(4.108,1.180)--(4.133,0.985);
+\gpcolor{rgb color={0.863,0.078,0.235}}
+\gpsetpointsize{2.40}
+\gp3point{gp mark 2}{}{(3.173,4.886)}
+\gp3point{gp mark 2}{}{(3.885,3.427)}
+\gp3point{gp mark 2}{}{(4.598,1.592)}
+\gp3point{gp mark 2}{}{(5.310,1.686)}
+\gp3point{gp mark 2}{}{(6.022,2.929)}
+\gp3point{gp mark 2}{}{(6.735,4.190)}
+\gp3point{gp mark 2}{}{(7.233,4.703)}
+\gpcolor{color=gp lt color border}
+\gpsetdashtype{gp dt solid}
+\gpsetlinewidth{1.00}
+\draw[gp path] (1.748,5.691)--(1.748,0.985)--(7.447,0.985)--(7.447,5.691)--cycle;
+%% coordinates of the plot area
+\gpdefrectangularnode{gp plot 1}{\pgfpoint{1.748cm}{0.985cm}}{\pgfpoint{7.447cm}{5.691cm}}
+\end{tikzpicture}
+%% gnuplot variables
+\end{document}
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
+ 9.120108393559096e-06  6.211610171947045e-03
+ 1.096478196143185e-05  6.792374027485015e-03
+ 1.318256738556407e-05  7.425345312781278e-03
+ 1.584893192461114e-05  8.114765932045185e-03
+ 1.905460717963248e-05  8.865120699464721e-03
+ 2.290867652767775e-05  9.681125931789915e-03
+ 2.754228703338163e-05  1.056770975064344e-02
+ 3.311311214825908e-05  1.152998189333092e-02
+ 3.981071705534969e-05  1.257319039145271e-02
+ 4.786300923226380e-05  1.370266197723624e-02
+ 5.754399373371566e-05  1.492372253381352e-02
+ 6.918309709189363e-05  1.624159332185176e-02
+ 8.317637711026709e-05  1.766125812610249e-02
+ 1.000000000000000e-04  1.918729591875359e-02
+ 1.202264434617413e-04  2.082367319967555e-02
+ 1.445439770745928e-04  2.257348995912804e-02
+ 1.737800828749376e-04  2.443867336254203e-02
+ 2.089296130854039e-04  2.641961398528058e-02
+ 2.511886431509580e-04  2.851474099050601e-02
+ 3.019951720402016e-04  3.072003537104471e-02
+ 3.630780547701014e-04  3.302848464372067e-02
+ 4.365158322401661e-04  3.542948859291789e-02
+ 5.248074602497728e-04  3.790823417663501e-02
+ 6.309573444801930e-04  4.044506877087432e-02
+ 7.585775750291835e-04  4.301491450154334e-02
+ 9.120108393559096e-04  4.558678199565728e-02
+ 1.096478196143185e-03  4.812345827946150e-02
+ 1.318256738556408e-03  5.058145864328128e-02
+ 1.584893192461114e-03  5.291134289200051e-02
+ 1.905460717963246e-03  5.505849827399160e-02
+ 2.290867652767772e-03  5.696447960043553e-02
+ 2.754228703338166e-03  5.856896678930269e-02
+ 3.311311214825911e-03  5.981234782238041e-02
+ 3.981071705534973e-03  6.063886048364867e-02
+ 4.786300923226385e-03  6.100013371714988e-02
+ 5.754399373371567e-03  6.085886970213172e-02
+ 6.918309709189363e-03  6.019231791545348e-02
+ 8.317637711026709e-03  5.899513433487237e-02
+ 1.000000000000000e-02  5.728121486315967e-02
+ 1.202264434617413e-02  5.508415858187780e-02
+ 1.445439770745928e-02  5.245615721904299e-02
+ 1.737800828749376e-02  4.946530746709376e-02
+ 2.089296130854041e-02  4.619156855992348e-02
+ 2.511886431509582e-02  4.272179185226004e-02
+ 3.019951720402019e-02  3.914438480508303e-02
+ 3.630780547701010e-02  3.554420649152192e-02
+ 4.365158322401656e-02  3.199821953636445e-02
+ 5.248074602497723e-02  2.857226663349834e-02
+ 6.309573444801930e-02  2.531914059520501e-02
+ 7.585775750291836e-02  2.227792229852985e-02
+ 9.120108393559097e-02  1.947440831436047e-02
+ 1.096478196143185e-01  1.692235880228233e-02
+ 1.318256738556407e-01  1.462526717442258e-02
+ 1.584893192461114e-01  1.257837345877809e-02
+ 1.905460717963248e-01  1.077069465848733e-02
+ 2.290867652767775e-01  9.186909564013418e-03
+ 2.754228703338169e-01  7.808998508205012e-03
+ 3.311311214825908e-01  6.617591964706389e-03
+ 3.981071705534969e-01  5.593022042416338e-03
+ 4.786300923226380e-01  4.716097668760250e-03
+ 5.754399373371566e-01  3.968639441621027e-03
+ 6.918309709189363e-01  3.333816454742892e-03
+ 8.317637711026709e-01  2.796327604398189e-03
+ 1.000000000000000e+00  2.342466331442259e-03
+ 1.202264434617413e+00  1.960102269258443e-03
+ 1.445439770745928e+00  1.638607138480099e-03
+ 1.737800828749376e+00  1.368746272215081e-03
+ 2.089296130854041e+00  1.142551829784601e-03
+ 2.511886431509582e+00  9.531892670181336e-04
+ 3.019951720402019e+00  7.948250154423670e-04
+ 3.630780547701010e+00  6.625005224425910e-04
+ 4.365158322401657e+00  5.520157121243856e-04
+ 5.248074602497723e+00  4.598234179345307e-04
+ 6.309573444801930e+00  3.829352915009887e-04
+ 7.585775750291836e+00  3.188389988971121e-04
+ 9.120108393559097e+00  2.654260840747906e-04
+ 1.096478196143185e+01  2.209296357978901e-04
+ 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/condensate16.fig/.energy16.gnuplot.swp b/figs/condensate16.fig/.energy16.gnuplot.swp
new file mode 100644
index 0000000..d23db08
--- /dev/null
+++ b/figs/condensate16.fig/.energy16.gnuplot.swp
diff --git a/figs/condensate16.fig/2020-05-22+16.dat b/figs/condensate16.fig/2020-05-22+16.dat
new file mode 100644
index 0000000..c28285d
--- /dev/null
+++ b/figs/condensate16.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/condensate16.fig/Makefile b/figs/condensate16.fig/Makefile
new file mode 100644
index 0000000..d44f73c
--- /dev/null
+++ b/figs/condensate16.fig/Makefile
@@ -0,0 +1,35 @@
+PROJECTNAME=condensate16
+
+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 condensate_fraction > $@
+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 condensate_fraction > $@
+
+
+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 $(PDFS)
+
+clean: clean-aux clean-tex
diff --git a/figs/condensate16.fig/condensate16.gnuplot b/figs/condensate16.fig/condensate16.gnuplot
new file mode 100644
index 0000000..e94eb1a
--- /dev/null
+++ b/figs/condensate16.fig/condensate16.gnuplot
@@ -0,0 +1,34 @@
+set ylabel "$\\eta$" norotate offset -1,0
+set xlabel "$\\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 ? 1-$2 : 1/0) with lines ls 1 ,\
+ "medeq16.dat" using 1:($3<1e-5 ? 1-$2 : 1/0) with lines ls 4 ,\
+ "2020-05-22+16.dat" using 1:3 with points ls 2
+
diff --git a/figs/condensate16.fig/condensate16.pdf b/figs/condensate16.fig/condensate16.pdf
new file mode 100644
index 0000000..0cc97fd
--- /dev/null
+++ b/figs/condensate16.fig/condensate16.pdf
diff --git a/figs/condensate16.fig/medeq16.dat b/figs/condensate16.fig/medeq16.dat
new file mode 100644
index 0000000..16ef72d
--- /dev/null
+++ b/figs/condensate16.fig/medeq16.dat
@@ -0,0 +1,100 @@
+ 1.000000000000000e-06  1.166000749536307e-02  1.397500557749096e-14
+ 1.202264434617413e-06  1.294150659557208e-02  1.638378932477403e-14
+ 1.445439770745928e-06  1.433395863576837e-02  2.068669778175053e-14
+ 1.737800828749376e-06  1.585523520080719e-02  9.413457244472722e-15
+ 2.089296130854041e-06  1.752468227078358e-02  2.147730951610164e-14
+ 2.511886431509582e-06  1.936219857512355e-02  5.079185685242370e-14
+ 3.019951720402019e-06  2.138821025238190e-02  4.890613903920614e-14
+ 3.630780547701017e-06  2.362406333962305e-02  3.239855276438957e-14
+ 4.365158322401657e-06  2.609258293662487e-02  6.114316674680731e-14
+ 5.248074602497723e-06  2.881866901219256e-02  2.406593746021106e-14
+ 6.309573444801930e-06  3.182986273284136e-02  5.235506117228457e-14
+ 7.585775750291836e-06  3.515686411604940e-02  2.215175470514193e-14
+ 9.120108393559096e-06  3.883401898804675e-02  1.629554526288622e-14
+ 1.096478196143185e-05  4.289981143876489e-02  4.459384031826223e-15
+ 1.318256738556407e-05  4.739739018972533e-02  7.959533672028488e-14
+ 1.584893192461114e-05  5.237512938256743e-02  1.856627535995191e-14
+ 1.905460717963248e-05  5.788719492270885e-02  1.690345207320381e-14
+ 2.290867652767775e-05  6.399407839575801e-02  8.321647126329251e-15
+ 2.754228703338163e-05  7.076308123314866e-02  1.217647346338456e-14
+ 3.311311214825908e-05  7.826876839555350e-02  8.937613010647126e-15
+ 3.981071705534969e-05  8.659343186556372e-02  1.053125999750607e-14
+ 4.786300923226380e-05  9.582758472268986e-02  2.683673474487137e-14
+ 5.754399373371566e-05  1.060704517836634e-01  1.137789331779729e-14
+ 6.918309709189363e-05  1.174303688455619e-01  2.458170758492918e-14
+ 8.317637711026709e-05  1.300249907645473e-01  3.251467169362365e-14
+ 1.000000000000000e-04  1.439812489667652e-01  1.604790218801148e-14
+ 1.202264434617413e-04  1.594350485585813e-01  1.208705427621754e-14
+ 1.445439770745928e-04  1.765306819395882e-01  9.949882875987985e-15
+ 1.737800828749376e-04  1.954198298344809e-01  9.175378143390922e-15
+ 2.089296130854039e-04  2.162598861818270e-01  2.214874949422118e-14
+ 2.511886431509580e-04  2.392112901954234e-01  8.309109937206045e-14
+ 3.019951720402016e-04  2.644336112806493e-01  2.396263674278965e-13
+ 3.630780547701014e-04  2.920802203955168e-01  7.677444642221211e-13
+ 4.365158322401661e-04  3.222913892466672e-01  2.316125381119014e-12
+ 5.248074602497728e-04  3.551856019023070e-01  6.550410386633497e-12
+ 6.309573444801930e-04  3.908488535122212e-01  1.868355419086652e-15
+ 7.585775750291835e-04  4.293218114670888e-01  2.423897582964416e-15
+ 9.120108393559096e-04  4.705848954147140e-01  6.448772157311636e-15
+ 1.096478196143185e-03  5.145415573312192e-01  5.163654832442502e-15
+ 1.318256738556408e-03  5.610003206868235e-01  9.938237834818324e-15
+ 1.584893192461114e-03  6.096564869738526e-01  1.561488943107384e-14
+ 1.905460717963246e-03  6.600748309932439e-01  1.480152300205420e-14
+ 2.290867652767772e-03  7.116750527032143e-01  2.186407540038661e-14
+ 2.754228703338166e-03  7.637221822124044e-01  8.674104990124533e-15
+ 3.311311214825911e-03  8.153244713068495e-01  3.829444151273552e-14
+ 3.981071705534973e-03  8.654414602027135e-01  1.538039001478893e-14
+ 4.786300923226385e-03  9.129047921304377e-01  6.821521006308993e-15
+ 5.754399373371567e-03  9.564538682725248e-01  2.800593843254869e-15
+ 6.918309709189363e-03  9.947874470918988e-01  4.113794640712594e-15
+ 8.317637711026709e-03  1.026630567329738e+00  3.133249774936964e-15
+ 1.000000000000000e-02  1.050813611431618e+00  4.457911153045777e-15
+ 1.202264434617413e-02  1.066357266225810e+00  6.422681440463997e-15
+ 1.445439770745928e-02  1.072554343989952e+00  4.370320881832804e-15
+ 1.737800828749376e-02  1.069037933552943e+00  3.253121018609543e-15
+ 2.089296130854041e-02  1.055825877502355e+00  3.370516638785516e-15
+ 2.511886431509582e-02  1.033334096440169e+00  5.365630506272522e-15
+ 3.019951720402019e-02  1.002355180715882e+00  3.715496417945286e-15
+ 3.630780547701010e-02  9.640034053554465e-01  3.496056342568733e-15
+ 4.365158322401656e-02  9.196325847132431e-01  1.506892881848512e-15
+ 5.248074602497723e-02  8.707370299052170e-01  1.746468145174605e-15
+ 6.309573444801930e-02  8.188475009356775e-01  1.661095648248939e-15
+ 7.585775750291836e-02  7.654340485028318e-01  2.123676640240517e-15
+ 9.120108393559097e-02  7.118255460316097e-01  4.350828619157266e-12
+ 1.096478196143185e-01  6.591523262981006e-01  1.196771616697282e-12
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diff --git a/figs/condensate16.fig/simpleq16.dat b/figs/condensate16.fig/simpleq16.dat
new file mode 100644
index 0000000..c19b5fd
--- /dev/null
+++ b/figs/condensate16.fig/simpleq16.dat
@@ -0,0 +1,100 @@
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diff --git a/figs/correlation.fig/2020-08-27+correlation.dat b/figs/correlation.fig/2020-08-27+correlation.dat
new file mode 100644
index 0000000..c436b89
--- /dev/null
+++ b/figs/correlation.fig/2020-08-27+correlation.dat
@@ -0,0 +1,102 @@
+# Potential: 16 e^{-|x|}, rho=0.02
+#          |x|    2-pt correlation
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diff --git a/figs/correlation.fig/Makefile b/figs/correlation.fig/Makefile
new file mode 100644
index 0000000..fd4b6c3
--- /dev/null
+++ b/figs/correlation.fig/Makefile
@@ -0,0 +1,36 @@
+PROJECTNAME=correlation
+
+SIMPLEQ=~/Work/Research/2018+bose_gas/cmp/simpleq
+
+DATS=bigeq.dat mueq.dat simpleq.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, $@)
+
+simpleq.dat:
+	julia $(SIMPLEQ)/main.jl -p "rho=2e-2;minlrho=-6;nlrho=60;eq=simpleq;N=12;P=8;xmax=10" -M medeq 2pt-simpleq > $@
+mueq.dat:
+	julia $(SIMPLEQ)/main.jl -p "rho=2e-2;minlrho=-6;nlrho=60;eq=mueq;N=12;P=8;xmax=10" -M medeq 2pt > $@
+bigeq.dat:
+	julia $(SIMPLEQ)/main.jl -p "rho=2e-2;minlrho=-6;nlrho=60;v_a=16;eq=bigeq;N=12;P=8;xmax=10" -M medeq 2pt > $@
+
+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 $(PDFS)
+
+clean: clean-aux clean-tex
diff --git a/figs/correlation.fig/bigeq.dat b/figs/correlation.fig/bigeq.dat
new file mode 100644
index 0000000..23a7360
--- /dev/null
+++ b/figs/correlation.fig/bigeq.dat
@@ -0,0 +1,100 @@
+ 1.000000000000000e-01  2.815645668703404e-07
+ 2.000000000000000e-01  3.771201995017570e-07
+ 3.000000000000000e-01  5.573083439994964e-07
+ 4.000000000000000e-01  8.556251627958034e-07
+ 5.000000000000000e-01  1.320674217324758e-06
+ 6.000000000000000e-01  2.018694725059689e-06
+ 7.000000000000000e-01  3.035072077005863e-06
+ 8.000000000000000e-01  4.474473100824739e-06
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+ 1.000000000000000e+00  9.145824377893419e-06
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+ 9.000000000000000e+00  4.011614782779821e-04
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+ 9.199999999999999e+00  4.012185293630343e-04
+ 9.300000000000001e+00  4.012064074730058e-04
+ 9.400000000000000e+00  4.011720950022673e-04
+ 9.500000000000000e+00  4.011186205709775e-04
+ 9.600000000000000e+00  4.010502350510486e-04
+ 9.699999999999999e+00  4.009708050953865e-04
+ 9.800000000000001e+00  4.008825998897835e-04
+ 9.900000000000000e+00  4.007873038383584e-04
+ 1.000000000000000e+01  4.006865033429884e-04
diff --git a/figs/correlation.fig/correlation.gnuplot b/figs/correlation.fig/correlation.gnuplot
new file mode 100644
index 0000000..9be226f
--- /dev/null
+++ b/figs/correlation.fig/correlation.gnuplot
@@ -0,0 +1,26 @@
+set ylabel "$\\frac{C_2}{\\rho^2}$" norotate offset -1,0
+set xlabel "$|\\mathbf x|$"
+
+# default output canvas size: 12.5cm x 8.75cm
+set term lua tikz size 8,6 standalone
+
+unset key
+
+
+# set linestyle
+set style line 1 linetype rgbcolor "#4169E1" linewidth 2
+set style line 2 linetype rgbcolor "#DC143C" linewidth 1
+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 style line 6 linetype rgbcolor "#555500" linewidth 2
+
+set pointsize 0.5
+
+rho=2e-2
+
+plot \
+ "simpleq.dat" using 1:($2/rho**2) with lines ls 1,\
+ "bigeq.dat" using 1:($2/rho**2) with lines ls 4,\
+ "2020-08-27+correlation.dat" using 1:2 ls 2
+
diff --git a/figs/correlation.fig/correlation.pdf b/figs/correlation.fig/correlation.pdf
new file mode 100644
index 0000000..9014dbf
--- /dev/null
+++ b/figs/correlation.fig/correlation.pdf
diff --git a/figs/correlation.fig/mueq.dat b/figs/correlation.fig/mueq.dat
new file mode 100644
index 0000000..a9436ee
--- /dev/null
+++ b/figs/correlation.fig/mueq.dat
@@ -0,0 +1,100 @@
+ 1.000000000000000e-01  2.409497558083658e-05
+ 2.000000000000000e-01  2.563753036922520e-05
+ 3.000000000000000e-01  2.803118585850437e-05
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+ 8.800000000000001e+00  3.998981560232808e-04
+ 8.900000000000000e+00  4.000120750153000e-04
+ 9.000000000000000e+00  4.001156540235223e-04
+ 9.100000000000000e+00  4.001996752915817e-04
+ 9.199999999999999e+00  4.002501809460462e-04
+ 9.300000000000001e+00  4.002669595454145e-04
+ 9.400000000000000e+00  4.002605281513629e-04
+ 9.500000000000000e+00  4.002385076791408e-04
+ 9.600000000000000e+00  4.002191096985464e-04
+ 9.699999999999999e+00  4.002159414484124e-04
+ 9.800000000000001e+00  4.002265566088204e-04
+ 9.900000000000000e+00  4.002407173561036e-04
+ 1.000000000000000e+01  4.002468273509336e-04
diff --git a/figs/correlation.fig/simpleq.dat b/figs/correlation.fig/simpleq.dat
new file mode 100644
index 0000000..8c759ad
--- /dev/null
+++ b/figs/correlation.fig/simpleq.dat
@@ -0,0 +1,100 @@
+ 1.000000000000000e-01  1.605737780249551e-04
+ 2.000000000000000e-01  1.646572439544047e-04
+ 3.000000000000000e-01  1.704080757058912e-04
+ 4.000000000000000e-01  1.773557851093461e-04
+ 5.000000000000000e-01  1.851044224101348e-04
+ 6.000000000000000e-01  1.934631179487515e-04
+ 7.000000000000000e-01  2.022815783256444e-04
+ 8.000000000000000e-01  2.113166008266444e-04
+ 9.000000000000000e-01  2.205514062470601e-04
+ 1.000000000000000e+00  2.299100922022419e-04
+ 1.100000000000000e+00  2.392010687597398e-04
+ 1.200000000000000e+00  2.483927431722189e-04
+ 1.300000000000000e+00  2.574627216447642e-04
+ 1.400000000000000e+00  2.663716782880825e-04
+ 1.500000000000000e+00  2.750255307210101e-04
+ 1.600000000000000e+00  2.833194447156991e-04
+ 1.700000000000000e+00  2.913275920636644e-04
+ 1.800000000000000e+00  2.990690118719876e-04
+ 1.900000000000000e+00  3.064419508037350e-04
+ 2.000000000000000e+00  3.134041571052762e-04
+ 2.100000000000000e+00  3.199627655953121e-04
+ 2.200000000000000e+00  3.261914657071729e-04
+ 2.300000000000000e+00  3.320914753877319e-04
+ 2.400000000000000e+00  3.375867483959618e-04
+ 2.500000000000000e+00  3.427111066585070e-04
+ 2.600000000000000e+00  3.474867111992544e-04
+ 2.700000000000000e+00  3.519144752983667e-04
+ 2.800000000000000e+00  3.560412420485770e-04
+ 2.900000000000000e+00  3.598804117875528e-04
+ 3.000000000000000e+00  3.634395288473944e-04
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+ 3.200000000000000e+00  3.696276336197819e-04
+ 3.300000000000000e+00  3.723593036530465e-04
+ 3.400000000000000e+00  3.749209046753350e-04
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+ 3.600000000000000e+00  3.793778269156589e-04
+ 3.700000000000000e+00  3.812660868878752e-04
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+ 8.600000000000000e+00  3.997159549569427e-04
+ 8.699999999999999e+00  3.997607579547200e-04
+ 8.800000000000001e+00  3.998197942978559e-04
+ 8.900000000000000e+00  3.998946829458393e-04
+ 9.000000000000000e+00  3.999714677968415e-04
+ 9.100000000000000e+00  4.000305881360316e-04
+ 9.199999999999999e+00  4.000410500051843e-04
+ 9.300000000000001e+00  4.000014391187070e-04
+ 9.400000000000000e+00  3.999330105526194e-04
+ 9.500000000000000e+00  3.998492973740165e-04
+ 9.600000000000000e+00  3.997874738537067e-04
+ 9.699999999999999e+00  3.997749691406509e-04
+ 9.800000000000001e+00  3.998043912261032e-04
+ 9.900000000000000e+00  3.998519077270098e-04
+ 1.000000000000000e+01  3.998904866755104e-04
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
+ 4.78630092e-03  5.01195435e-02
+ 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_effective.pdf b/figs/energy.fig/erho_effective.pdf
new file mode 100644
index 0000000..351ba36
--- /dev/null
+++ b/figs/energy.fig/erho_effective.pdf
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
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+ 8.317637711026709e-01  1.032245608693097e+01 1
+ 1.000000000000000e+00  1.243026753303222e+01 1
+ 1.202264434617413e+00  1.496562561057760e+01 1
+ 1.445439770745928e+00  1.801502869576436e+01 1
+ 1.737800828749376e+00  2.168246883802093e+01 1
+ 2.089296130854041e+00  2.609297014699965e+01 1
+ 2.511886431509582e+00  3.139684282320142e+01 1
+ 3.019951720402019e+00  3.777479758723231e+01 1
+ 3.630780547701010e+00  4.544409456028400e+01 1
+ 4.365158322401657e+00  5.466593586138625e+01 1
+ 5.248074602497723e+00  6.575435350738108e+01 1
+ 6.309573444801930e+00  7.908689506783082e+01 1
+ 7.585775750291836e+00  9.511747067219883e+01 1
+ 9.120108393559097e+00  1.143917984731058e+02 1
+ 1.096478196143185e+01  1.375659740282897e+02 1
+ 1.318256738556407e+01  1.654287952107530e+02 1
+ 1.584893192461114e+01  1.989286012247062e+02 1
+ 1.905460717963248e+01  2.392055363411829e+02 0
+ 2.290867652767775e+01  2.876303621855438e+02 0
+ 2.754228703338169e+01  3.458511552270688e+02 0
+ 3.311311214825908e+01  4.158492765508882e+02 0
+ 3.981071705534969e+01  5.000067330413117e+02 0
+ 4.786300923226381e+01  6.011878314695363e+02 0
+ 5.754399373371567e+01  7.228352310513908e+02 0
+ 6.918309709189363e+01  8.690894472935229e+02 0
+ 8.317637711026708e+01  1.044926046890143e+03 0
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/$1) with points linestyle 2
diff --git a/figs/energy.fig/erho_fulleq.pdf b/figs/energy.fig/erho_fulleq.pdf
new file mode 100644
index 0000000..3094403
--- /dev/null
+++ b/figs/energy.fig/erho_fulleq.pdf
diff --git a/figs/energy.fig/erho_lowhigh.gnuplot b/figs/energy.fig/erho_lowhigh.gnuplot
new file mode 100644
index 0000000..9d2a590
--- /dev/null
+++ b/figs/energy.fig/erho_lowhigh.gnuplot
@@ -0,0 +1,37 @@
+set ylabel "$\\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/erho_lowhigh.pdf b/figs/energy.fig/erho_lowhigh.pdf
new file mode 100644
index 0000000..4872d49
--- /dev/null
+++ b/figs/energy.fig/erho_lowhigh.pdf
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/energy16.pdf b/figs/energy16.fig/energy16.pdf
new file mode 100644
index 0000000..0472d94
--- /dev/null
+++ b/figs/energy16.fig/energy16.pdf
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 @@
+ 1.000000000000000e-06  2.554068644475559e-05  1.397500557749096e-14
+ 1.202264434617413e-06  3.080347047701689e-05  1.638378932477403e-14
+ 1.445439770745928e-06  3.716098929256974e-05  2.068669778175053e-14
+ 1.737800828749376e-06  4.484410409494435e-05  9.413457244472722e-15
+ 2.089296130854041e-06  5.413333030032436e-05  2.147730951610164e-14
+ 2.511886431509582e-06  6.536981275090576e-05  5.079185685242370e-14
+ 3.019951720402019e-06  7.896881202049198e-05  4.890613903920614e-14
+ 3.630780547701017e-06  9.543630295201912e-05  3.239855276438957e-14
+ 4.365158322401657e-06  1.153894399986016e-04  6.114316674680731e-14
+ 5.248074602497723e-06  1.395818383298505e-04  2.406593746021106e-14
+ 6.309573444801930e-06  1.689348660488532e-04  5.235506117228457e-14
+ 7.585775750291836e-06  2.045764562134621e-04  2.215175470514193e-14
+ 9.120108393559096e-06  2.478893480268333e-04  1.629554526288622e-14
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+ 3.019951720402016e-04  1.174573571624843e-02  2.396263674278965e-13
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+ 1.000000000000000e-02  1.111191929557474e+00  4.457911153045777e-15
+ 1.202264434617413e-02  1.413827980332061e+00  6.422681440463997e-15
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+ 1.737800828749376e-02  2.268395559532093e+00  3.253121018609543e-15
+ 2.089296130854041e-02  2.858958045662395e+00  3.370516638785516e-15
+ 2.511886431509582e-02  3.590510376831549e+00  5.365630506272522e-15
+ 3.019951720402019e-02  4.493013035241590e+00  3.715496417945286e-15
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+ 4.365158322401656e-02  6.960668080208332e+00  1.506892881848512e-15
+ 5.248074602497723e-02  8.619356424678557e+00  1.746468145174605e-15
+ 6.309573444801930e-02  1.063914751302661e+01  1.661095648248939e-15
+ 7.585775750291836e-02  1.309296777581257e+01  2.123676640240517e-15
+ 9.120108393559097e-02  1.606826398387775e+01  4.350828619157266e-12
+ 1.096478196143185e-01  1.966999980308274e+01  1.196771616697282e-12
+ 1.318256738556407e-01  2.402425994094341e+01  3.018342123439392e-13
+ 1.584893192461114e-01  2.928257887420183e+01  6.985575344309217e-14
+ 1.905460717963248e-01  3.562713643064021e+01  2.023128031947868e-14
+ 2.290867652767775e-01  4.327699319810110e+01  7.636489971812963e-14
+ 2.754228703338169e-01  5.249557556550972e+01  3.450372875056261e-14
+ 3.311311214825908e-01  6.359966407666808e+01  1.050825065430309e-14
+ 3.981071705534969e-01  7.697019095971760e+01  1.016139346429647e-14
+ 4.786300923226380e-01  9.306521489952080e+01  6.058578163892193e-15
+ 5.754399373371566e-01  1.124355155175409e+02  3.382728454855092e-15
+ 6.918309709189363e-01  1.357433392373146e+02  2.709608246018857e-15
+ 8.317637711026709e-01  1.637849353682065e+02  1.878556843412201e-15
+ 1.000000000000000e+00  1.975176500593190e+02  1.223063234010325e-15
+ 1.202264434617413e+00  2.380925007021913e+02  1.993050434866885e-15
+ 1.445439770745928e+00  2.868933397000474e+02  3.043149243838522e-15
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+ 2.089296130854041e+00  4.161646092494719e+02  2.611515016643540e-15
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+ 5.248074602497723e+00  1.050824705077102e+03  3.818189041855540e-15
+ 6.309573444801930e+00  1.264163827184745e+03  3.557698468765215e-15
+ 7.585775750291836e+00  1.520672510488972e+03  3.200776178020959e-15
+ 9.120108393559097e+00  1.829082315295077e+03  2.768978034961086e-15
+ 1.096478196143185e+01  2.199890869853228e+03  2.784644153002823e-15
+ 1.318256738556407e+01  2.645719082839147e+03  2.561848808069188e-15
+ 1.584893192461114e+01  3.181740607495819e+03  3.342103900653102e-15
+ 1.905460717963248e+01  3.826198171331817e+03  3.061126283356729e-15
+ 2.290867652767775e+01  4.601024341151761e+03  3.012741771786859e-15
+ 2.754228703338169e+01  5.532587846940884e+03  3.540875919778527e-15
+ 3.311311214825908e+01  6.652590860664027e+03  3.384458193003484e-15
+ 3.981071705534969e+01  7.999147762757379e+03  3.313778691885289e-15
+ 4.786300923226381e+01  9.618082104785730e+03  4.116261947533335e-15
+ 5.754399373371567e+01  1.156448590156131e+04  3.799276533234762e-15
+ 6.918309709189363e+01  1.390459431262479e+04  4.136504038005983e-15
+ 8.317637711026708e+01  1.671803950512843e+04  4.852059592739983e-15
diff --git a/figs/energy16.fig/medeq4.dat b/figs/energy16.fig/medeq4.dat
new file mode 100644
index 0000000..ffaa5eb
--- /dev/null
+++ b/figs/energy16.fig/medeq4.dat
@@ -0,0 +1,100 @@
+ 1.000000000000000e-06  1.627424240030753e-05  9.007835427072701e-12
+ 1.202264434617413e-06  1.959943745344100e-05  1.671351637616213e-12
+ 1.445439770745928e-06  2.360770720466136e-05  4.387069667322242e-12
+ 1.737800828749376e-06  2.844048299127554e-05  3.371679780930921e-14
+ 2.089296130854041e-06  3.426881796805706e-05  3.499980814968632e-14
+ 2.511886431509582e-06  4.129969708194542e-05  7.218204810983588e-15
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diff --git a/figs/energy16.fig/simpleq16.dat b/figs/energy16.fig/simpleq16.dat
new file mode 100644
index 0000000..2bc4ebc
--- /dev/null
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diff --git a/figs/energy_relative_error.fig/2020-10-15+energy.dat b/figs/energy_relative_error.fig/2020-10-15+energy.dat
new file mode 100644
index 0000000..8a6566c
--- /dev/null
+++ b/figs/energy_relative_error.fig/2020-10-15+energy.dat
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+1.5e-2   1.6337e-1   1.6338e-1   0.090      0.091   1.6342e-1     1.6343e-1        0.088             0.089
+2e-2     2.2162e-1   2.2163e-1   0.093      0.094   2.2169e-1     2.2170e-1        0.090             0.091
+5e-2     5.8044e-1   5.8045e-1   0.091      0.092   5.8046e-1     5.8047e-1        0.091             0.092
+1e-1     1.1918e+0   1.1919e+0   0.088      0.089   1.1919e+0     1.1920e+0        0.085             0.086
+1e-0     1.2430e+1   1.2431e+1   0.058      0.059    1.245e+1      1.246e+1         0.05              0.06
+1e+1     1.2544e+2   1.2545e+2   0.031      0.032
+5e+1     6.2803e+2   6.2804e+2    0.02       0.03
+
diff --git a/figs/energy_relative_error.fig/Makefile b/figs/energy_relative_error.fig/Makefile
new file mode 100644
index 0000000..93e03f5
--- /dev/null
+++ b/figs/energy_relative_error.fig/Makefile
@@ -0,0 +1,51 @@
+PROJECTNAME=cmp_energy1
+
+SIMPLEQ=~/Work/Research/2018+bose_gas/cmp/simpleq
+
+DATS= simpleq1.dat mueq1.dat bigeq1.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, $@)
+
+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
+	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=$$lrho;nlrho=1" -M simpleq energy_rho >> $@-tmp ;\
+	done
+	paste $@-tmp 2020-10-15+energy.dat > $@
+	rm $@-tmp
+mueq1.dat:
+	for lrho in -6 -4 -3 -2.3010299956639813 -2 -1.8239087409443189 -1.6989700043360187 -1.3010299956639813 -1 0 1 1.6989700043360187; do\
+	  julia $(SIMPLEQ)/main.jl -p "tolerance=1e-11;order=100;maxiter=100;v_a=1;minlrho=$$lrho;nlrho=1" -M mueq energy_rho >> $@-tmp ;\
+	done
+	paste $@-tmp 2020-10-15+energy.dat > $@
+	rm $@-tmp
+
+
+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)
+	rm -f Abar.dat
+
+clean-tex:
+	rm -f $(PDFS)
+
+clean: clean-aux clean-tex
diff --git a/figs/energy_relative_error.fig/bigeq1.dat b/figs/energy_relative_error.fig/bigeq1.dat
new file mode 100644
index 0000000..ccab7cc
--- /dev/null
+++ b/figs/energy_relative_error.fig/bigeq1.dat
@@ -0,0 +1,13 @@
+1e-6    7.933345669932108e-06  1.702110068633820e-12	1e-6       7.90e-6     7.91e-6
+1e-4    8.349333596092273e-04  1.112527655484278e-13	1e-4      8.344e-4    8.345e-4   0.017      0.018    8.355e-4      8.356e-4        0.015             0.016
+1e-3    9.146316224214820e-03  2.077370190827862e-12	1e-3     9.1338e-3   9.1339e-3   0.048      0.049    9.142e-3      9.143e-3        0.045             0.046
+5e-3    5.063551121414726e-02  8.398015568932763e-12	5e-3     5.0613e-2   5.0614e-2   0.080      0.081   5.0648e-2     5.0649e-2        0.070             0.071
+1e-2    1.061166635113156e-01  5.017547334745932e-15	1e-2    1.06107e-1  1.06108e-1   0.087      0.088   1.0627e-1     1.0628e-1        0.073             0.074
+1.5e-2    1.633545333357252e-01  2.212732350724188e-15	1.5e-2   1.6337e-1   1.6338e-1   0.090      0.091   1.6342e-1     1.6343e-1        0.088             0.089
+2e-2    2.216006926766234e-01  4.554921896809050e-15	2e-2     2.2162e-1   2.2163e-1   0.093      0.094   2.2169e-1     2.2170e-1        0.090             0.091
+5e-2    5.805467427278628e-01  3.333614946727334e-15	5e-2     5.8044e-1   5.8045e-1   0.091      0.092   5.8046e-1     5.8047e-1        0.091             0.092
+1e-1    1.191928562890024e+00  2.450444415773880e-15	1e-1     1.1918e+0   1.1919e+0   0.088      0.089   1.1919e+0     1.1920e+0        0.085             0.086
+1.0    1.243051761633436e+01  3.791416729017179e-12	1e-0     1.2430e+1   1.2431e+1   0.058      0.059    1.245e+1      1.246e+1         0.05              0.06
+1e1    1.254476421597336e+02  2.677873467933947e-13	1e+1     1.2544e+2   1.2545e+2   0.031      0.032
+5e1 nan nan	5e+1     6.2803e+2   6.2804e+2    0.02       0.03
+	
diff --git a/figs/energy_relative_error.fig/cmp_energy1.gnuplot b/figs/energy_relative_error.fig/cmp_energy1.gnuplot
new file mode 100644
index 0000000..c2b1afd
--- /dev/null
+++ b/figs/energy_relative_error.fig/cmp_energy1.gnuplot
@@ -0,0 +1,37 @@
+set title "$v(\\mathbf x)=e^{-|\\mathbf x|}$"
+set ylabel "energy relative error" offset +3
+set xlabel "$\\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 xrange [1e-6:1e2]
+
+set ytics 1e-5, 10, 1e-1
+set ytics add ("$10^{-5}$" 1e-5, "$10^{-4}$" 1e-4, "$10^{-3}$" 1e-3, "$10^{-2}$" 1e-2, "$10^{-1}$" 1e-1)
+set yrange [1e-5:1e-1]
+
+# default output canvas size: 12.5cm x 8.75cm
+set term lua tikz size 8,6 standalone
+
+unset key
+
+
+# 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
+
+max(x,y)=(x>y ? x : y)
+
+set logscale xy
+
+plot \
+ "simpleq1.dat" using 1:($3<1e-5 ? max(abs($2-$5)/$5,abs($2-$6)/$6) : 1/0) every ::1 with lp ls 1 ,\
+ "bigeq1.dat" using 1:($3<1e-5 ? max(abs($2-$5)/$5,abs($2-$6)/$6) : 1/0) every ::1 with lp ls 4 ,\
+ "2020-10-15+energy.dat" using 1:(max(max(abs($6-$2)/$2,abs($6-$3)/$3),max(abs($7-$2)/$2,abs($7-$3)/$3))) every ::1 with lp ls 2
+
diff --git a/figs/energy_relative_error.fig/cmp_energy1.pdf b/figs/energy_relative_error.fig/cmp_energy1.pdf
new file mode 100644
index 0000000..601b146
--- /dev/null
+++ b/figs/energy_relative_error.fig/cmp_energy1.pdf
diff --git a/figs/energy_relative_error.fig/mueq1.dat b/figs/energy_relative_error.fig/mueq1.dat
new file mode 100644
index 0000000..6680ed3
--- /dev/null
+++ b/figs/energy_relative_error.fig/mueq1.dat
@@ -0,0 +1,13 @@
+ 1.000000000000000e-06  7.934286257047026e-06  3.235575358862730e-14	1e-6       7.90e-6     7.91e-6
+ 1.000000000000000e-04  8.377752370367244e-04  3.201262322514326e-14	1e-4      8.344e-4    8.345e-4   0.017      0.018    8.355e-4      8.356e-4        0.015             0.016
+ 1.000000000000000e-03  9.227516472314044e-03  5.926882960328585e-12	1e-3     9.1338e-3   9.1339e-3   0.048      0.049    9.142e-3      9.143e-3        0.045             0.046
+ 4.999999999999999e-03  5.110614907540598e-02  1.069784208067329e-14	5e-3     5.0613e-2   5.0614e-2   0.080      0.081   5.0648e-2     5.0649e-2        0.070             0.071
+ 1.000000000000000e-02  1.069255387977072e-01  1.572627931557844e-14	1e-2    1.06107e-1  1.06108e-1   0.087      0.088   1.0627e-1     1.0628e-1        0.073             0.074
+ 1.500000000000000e-02  1.643925118385577e-01  2.494863657028789e-14	1.5e-2   1.6337e-1   1.6338e-1   0.090      0.091   1.6342e-1     1.6343e-1        0.088             0.089
+ 2.000000000000000e-02  2.228019992986293e-01  1.448625206361080e-14	2e-2     2.2162e-1   2.2163e-1   0.093      0.094   2.2169e-1     2.2170e-1        0.090             0.091
+ 5.000000000000000e-02  5.821600306289594e-01  2.429130993459621e-14	5e-2     5.8044e-1   5.8045e-1   0.091      0.092   5.8046e-1     5.8047e-1        0.091             0.092
+ 1.000000000000000e-01  1.193625606724180e+00  9.289627651289616e-14	1e-1     1.1918e+0   1.1919e+0   0.088      0.089   1.1919e+0     1.1920e+0        0.085             0.086
+ 1.000000000000000e+00  1.243092200540192e+01  3.956891809887943e-12	1e-0     1.2430e+1   1.2431e+1   0.058      0.059    1.245e+1      1.246e+1         0.05              0.06
+ 1.000000000000000e+01  1.254464788052155e+02  1.136222076562384e-14	1e+1     1.2544e+2   1.2545e+2   0.031      0.032
+ 4.999999999999999e+01  6.280479158155819e+02  4.085062088184932e-15	5e+1     6.2803e+2   6.2804e+2    0.02       0.03
+	
diff --git a/figs/energy_relative_error.fig/simpleq1.dat b/figs/energy_relative_error.fig/simpleq1.dat
new file mode 100644
index 0000000..0a9946c
--- /dev/null
+++ b/figs/energy_relative_error.fig/simpleq1.dat
@@ -0,0 +1,13 @@
+ 1.000000000000000e-06  7.934458317554763e-06  1.386474846476237e-14	1e-6       7.90e-6     7.91e-6
+ 1.000000000000000e-04  8.392960650211980e-04  4.992772141681879e-14	1e-4      8.344e-4    8.345e-4   0.017      0.018    8.355e-4      8.356e-4        0.015             0.016
+ 1.000000000000000e-03  9.335885024335848e-03  9.476600935679491e-12	1e-3     9.1338e-3   9.1339e-3   0.048      0.049    9.142e-3      9.143e-3        0.045             0.046
+ 4.999999999999999e-03  5.253256909806337e-02  2.904203225041083e-14	5e-3     5.0613e-2   5.0614e-2   0.080      0.081   5.0648e-2     5.0649e-2        0.070             0.071
+ 1.000000000000000e-02  1.105504827786785e-01  3.695967730970493e-14	1e-2    1.06107e-1  1.06108e-1   0.087      0.088   1.0627e-1     1.0628e-1        0.073             0.074
+ 1.500000000000000e-02  1.702888708763101e-01  2.044316796426063e-14	1.5e-2   1.6337e-1   1.6338e-1   0.090      0.091   1.6342e-1     1.6343e-1        0.088             0.089
+ 2.000000000000000e-02  2.309054339970606e-01  1.984104771646051e-14	2e-2     2.2162e-1   2.2163e-1   0.093      0.094   2.2169e-1     2.2170e-1        0.090             0.091
+ 5.000000000000000e-02  6.014214358150070e-01  1.045253287889987e-14	5e-2     5.8044e-1   5.8045e-1   0.091      0.092   5.8046e-1     5.8047e-1        0.091             0.092
+ 1.000000000000000e-01  1.226000446492040e+00  3.630493925691041e-15	1e-1     1.1918e+0   1.1919e+0   0.088      0.089   1.1919e+0     1.1920e+0        0.085             0.086
+ 1.000000000000000e+00  1.253044200066420e+01  1.230015282154983e-13	1e-0     1.2430e+1   1.2431e+1   0.058      0.059    1.245e+1      1.246e+1         0.05              0.06
+ 1.000000000000000e+01  1.256270224354739e+02  6.086298884133178e-15	1e+1     1.2544e+2   1.2545e+2   0.031      0.032
+ 4.999999999999999e+01  6.282817756461592e+02  1.506690451671515e-15	5e+1     6.2803e+2   6.2804e+2    0.02       0.03
+	
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
author	Ian Jauslin <ian@jauslin.org>	2022-02-20 17:50:35 -0500
committer	Ian Jauslin <ian@jauslin.org>	2022-02-20 17:50:35 -0500
commit	601999d5c035bb51784ba03e478429e981bbbdfa (patch)
tree	59489154099c4b1951d34ca3fe34672e077c98cc