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| author | Ian Jauslin <ian.jauslin@rutgers.edu> | 2023-03-09 11:48:20 -0500 |
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| committer | Ian Jauslin <ian.jauslin@rutgers.edu> | 2023-03-09 11:48:20 -0500 |
| commit | 6086bbc8826d558bedab6933913c6793850470fb (patch) | |
| tree | 632f32f7e1e50f58a6a57a0dd22f1fdfccf54730 | |
37 files changed, 2996 insertions, 0 deletions
diff --git a/Jauslin_Rutgers_2023.tex b/Jauslin_Rutgers_2023.tex new file mode 100644 index 0000000..508a8b7 --- /dev/null +++ b/Jauslin_Rutgers_2023.tex @@ -0,0 +1,457 @@ +\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}{981414} + +\begin{document} +\pagestyle{empty} +\hbox{}\vfil +\bf\Large +\hfil Interacting Bosons at intermediate densities\par +\vfil +\large +\hfil Ian Jauslin +\normalsize +\vfil +\hfil\rm joint with {\bf Eric A. Carlen}, {\bf Elliott H. Lieb}\par +\vfil +arXiv:{\tt\ \parbox[b]{6cm}{ + \href{https://arxiv.org/abs/1912.04987}{1912.04987}\ + \href{https://arxiv.org/abs/2010.13882}{2010.13882}\par + \href{https://arxiv.org/abs/2011.10869}{2011.10869}\ + \href{https://arxiv.org/abs/2202.07637}{2202.07637}\par + \href{https://arxiv.org/abs/2302.13446}{2302.13446}\ + \href{https://arxiv.org/abs/2302.13449}{2302.13449} +}} +\hfill{\tt \href{http://ian.jauslin.org}{http://ian.jauslin.org}} +\eject + +\setcounter{page}1 +\pagestyle{plain} + +\title{Bosons} +\begin{itemize} +\item Quantum particles are either {\color{highlight}Fermions} or {\color{highlight}Bosons} (in 3D). + +\item Fermions: electrons, protons, neutrinos, etc... + +\item Bosons: photons, Helium atoms, Higgs particle, etc... + +\item At low temperatures: inherently {\color{highlight}quantum} behavior: e.g. {\color{highlight}Bose-Einstein condensation}, superfluidity, quantized vortices, etc... + +\item Difficult to handle mathematically: usual approach {\color{highlight}effective theories}. + +\item The connection between the original model and the effective theory is, in most cases, poorly understood. +\end{itemize} +\vfill +\eject + +\title{Repulsive Bose gas} +\begin{itemize} + \item Potential: {\color{highlight}$v(r)\geqslant 0$}, {\color{highlight}$\hat v\geqslant 0$} and {\color{highlight}$v\in L_1(\mathbb R^3)$}, on a torus of volume $V$: + $$ + H_N:= + -\frac12\sum_{i=1}^N\Delta_i + +\sum_{1\leqslant i<j\leqslant N}v(|x_i-x_j|) + $$ + \vskip-5pt + \item Ground state ({\color{highlight}zero temperature}): $\psi_0$, energy $E_0$. + + \item Observables in the {\color{highlight}thermodynamic limit}: for instance, ground state energy per particle + $$ + e_0:=\lim_{\displaystyle\mathop{\scriptstyle V,N\to\infty}_{{\color{highlight}\frac NV=\rho}}}\frac{E_0}N + . + $$ + + \item Main difficulty: dealing with the interactions. +\end{itemize} +\vfill +\eject + +\title{Known results} +\begin{itemize} + \item {\color{highlight}Low density}: \href{https://doi.org/10.1103/PhysRev.106.1135}{Lee-Huang-Yang} formula + $$ + e_0=2\pi\rho a\left(1+\frac{128}{15\sqrt\pi}\sqrt{\rho a^3}+o(\sqrt{\rho a^3})\right) + $$ + 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]}, + \href{https://doi.org/10.1017/fms.2021.66}{[Basti, Cenatiempo, Schlein, 2021]}. + + \item {\color{highlight}High density}: Hartree energy: + $$ + e_0\sim\frac\rho2\int v + $$ + proved: \href{https://doi.org/10.1103/PhysRev.130.2518}{[Lieb, 1963]}. +\end{itemize} +\vfill +\eject + +\title{The Simplified approach: proof of concept} +For $v(x)=e^{-|x|}$: {\color{ipurple}Simplified approach}, {\color{iyellow}LHY}, {\color{igreen}Hartree}, {\color{ired}Monte Carlo} + +\hfil\includegraphics[height=5.5cm]{energy.pdf} +\vfill +\eject + +\title{The Simplified approach} +\begin{itemize} + \item \href{https://doi.org/10.1103/PhysRev.130.2518}{[Lieb, 1963]}, + \href{https://arxiv.org/abs/2302.13446}{[Jauslin, 2023]}. + + \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, + $$ + \frac{N(N-1)}2\int dx_1dx_2\ v(x_1-x_2)\frac{\int dx_3\cdots dx_N\ \psi_0}{\int dy_1\cdots dy_N\ \psi_0} + =E_0 + $$ +\end{itemize} +\vfill +\eject + +\title{The Simplified approach} +\begin{itemize} + \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 $V^{-N}\psi_0$ + $$ + g_n(x_1,\cdots,x_n):=\frac{V^n\int dx_{n+1}\cdots dx_N\ \psi_0(x_1,\cdots,x_N)}{\int dy_1\cdots dy_N\ \psi_0(y_1,\cdots,y_N)} + $$ + \item Thus, + $$ + \frac{E_0}N=\frac{N-1}{2V}\int dx\ v(x)g_2(0,x) + $$ +\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 {\color{highlight}Infinite hierarchy} of equations. +\end{itemize} +\vfill +\eject + +\title{Factorization assumption} +\begin{itemize} + \item Factorization {\color{highlight}assumption} (clustering property): for $n=3,4$, + $$ + g_n(x_1,\cdots,x_n)=\prod_{1\leqslant i<j\leqslant n}(1-u_n(x_i-x_j)) + ,\quad + u_n\in L_1(\mathbb R^3) + $$ + + \item Consistency condition: + $$ + \int \frac{dx_3}V\ g_3(x_1,x_2,x_3)=g_2(x_1,x_2) + ,\quad + \int \frac{dx_3}V\frac{dx_4}V\ g_4(x_1,x_2,x_3,x_4)=g_2(x_1,x_2) + $$ + + \item Remark: in general, + $$ + \int \frac{dx_4}V\ g_4(x_1,x_2,x_3,x_4)\neq g_3(x_1,x_2,x_3) + $$ +\end{itemize} +\vfill +\eject + +\title{Factorization assumption} +\begin{itemize} + \item {\bf Lemma} + \href{https://doi.org/10.1103/PhysRev.130.2518}{[Lieb, 1963]}, + \href{https://arxiv.org/abs/2302.13446}{[Jauslin, 2023]}: + Under the Factorization assumption and the consistency condition, + $$ + u_3(x-y)=u(x-y)+\frac1V(1-u(x-y))\int dz\ u(x-z)u(z-y)+O(V^{-2}) + $$ + $$ + u_4(x-y)=u(x-y)+\frac2V(1-u(x-y))\int dz\ u(x-z)u(z-y)+O(V^{-2}) + $$ + + \item With $u(x):=1-g_2(0,x)$. +\end{itemize} +\vfill +\eject + +\title{{\color{ipurple}Big equation}} +\begin{itemize} +\item In the thermodynamic limit, + $$ + -\Delta u(x) + = + (1-u(x))\left(v(x)-2\rho K(x)+\rho^2 L(x)\right) + $$ + $$ + K:= + u\ast S + ,\quad + S(y):=(1-u(y))v(y) + $$ + $$ + L:= + u\ast u\ast S + -2u\ast(u(u\ast S)) + +\frac12 + \int dydz\ u(y)u(z-x)u(z)u(y-x)S(z-y) + . + $$ + + \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 {\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 {\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}: + $$ + \frac{e}{\rho}\mathop{\longrightarrow}_{\rho\to\infty}\frac12\int dx\ v(x) + . + $$ + 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} +$v(x)=e^{-|x|}$, {\color{ipurple}Big equation}, {\color{ired}Monte Carlo} + +\hfil\includegraphics[height=5.5cm]{energy.pdf} +\vfill +\eject + +\title{Radial distribution function} +\begin{itemize} + \item + {\color{highlight}Two-point correlation}: + $$ + C_2(y-z)=\sum_{i,j}\left<\psi_0\right|\delta(y-x_i)\delta(z-x_j)\left|\psi_0\right> + . + $$ + \item + {\color{highlight}Radial distribution}: spherical average and normalization: + $$ + G(r):=\frac1{\rho^2}\int\frac{dy}{4\pi r^2}\ \delta(|y|-r)C_2(y) + . + $$ + + \item + Compute $C_2$ using + $$ + C_2(x)=2\rho\frac{\delta e_0}{\delta v(x)} + . + $$ +\end{itemize} +\vfill +\eject + +\title{Radial distribution function} +$v(x)=16e^{-|x|}$, $\rho=0.02$ {\color{ipurple}Big equation}, {\color{ired}Monte Carlo} + +\hfil\includegraphics[height=5.5cm]{2pt.pdf} +\vfill +\eject + +\title{Radial distribution function} +$v(x)=8e^{-|x|}$, $\rho=10^{-5}$-$10^{-1}$ + +\hfil\includegraphics[height=5.5cm]{2pt_rho.pdf} +\vfill +\eject + +\title{Radial distribution function} +$v(x)=8e^{-|x|}$, maximal value as a function of $\rho$: + +\hfil\includegraphics[height=5.5cm]{2pt_max.pdf} +\vfill +\eject + +\title{Liquid behavior} +\begin{itemize} + \item Maximum above $1$: there is a length scale at which it is {\color{highlight} more probable} to find pairs of particles. + \item {\color{highlight}No} long range order. + \item {\color{highlight}Short-range order}: {\color{highlight}Liquid}-like behavior. +\end{itemize} +\vfill +\eject + +\title{Structure factor} +\begin{itemize} + \item + {\color{highlight}Structure factor}: Fourier transform of $G$: + $$ + S(|k|):=1+\rho\int dx\ e^{ikx}(G(|x|)-1) + . + $$ + + \item + Directly observable in X-ray scattering experiments. + + \item + Sharp peaks: order. + + \item + Large deviation from $1$: uniformity. +\end{itemize} +\vfill +\eject + +\title{Structure factor} +$v(x)=8e^{-|x|}$, $\rho=10^{-5}$-$0.3$ + +\hfil\includegraphics[height=5.5cm]{2pt_fourier_full.pdf} +\vfill +\eject + +\title{Structure factor} +$v(x)=8e^{-|x|}$, $\rho=10^{-5}$-$0.3$ + +\hfil\includegraphics[height=5.5cm]{2pt_fourier_peak.pdf} +\vfill +\eject + +\title{Structure factor} +$v(x)=8e^{-|x|}$, maximal value as a function of $\rho$: + +\hfil\includegraphics[height=5.5cm]{2pt_fourier_max.pdf} +\vfill +\eject + +\title{Liquid behavior} +\begin{itemize} + \item Sharpening of the peak: more order. + \item Not Bragg peaks: {\color{highlight}No} long range order. + \item Larger deviation from 1: more uniform (not even close to hyperuniform). + \item {\color{highlight}Short-range order}: {\color{highlight}Liquid}-like behavior. +\end{itemize} +\vfill +\eject + +\title{Critical densities} +\begin{itemize} + \item + We have found two critical densities: $\rho_*\approx 0.9\times10^{-3}$ and $\rho_{**}\approx0.2$. + + \item The radial distribution function has a maximum only for $\rho>\rho_*$. + + \item The structure factor has a maximum only for $\rho<\rho_{**}$. +\end{itemize} +\vfill +\eject + +\title{Condensate fraction} +\begin{itemize} + \item + Proportion of particles in the condensate state: + $$ + \eta:=\frac1N\sum_i\left<\psi_0\right|P_i\left|\psi_0\right> + $$ + where $P_i$ is the projector onto the constant state $V^{-\frac12}$. + + \item + $\eta>0$ in thermodynamic limit: {\color{highlight}Bose-Einstein condensation} (still not proved to occur). +\end{itemize} +\vfill +\eject + +\title{Condensate fraction} +$v(x)=8e^{-|x|}$: + +\hfil\includegraphics[height=5.5cm]{condensate.pdf} +\vfill +\eject + +\title{Summary and outlook} +\begin{itemize} + \item Using the {\color{highlight}Simplified approach}, we were able to probe the repulsive Bose gas {\color{highlight}beyond the dilute regime}. + + \item Evidence for {\color{highlight}non-trivial behavior} at intermediate densities $\rho_*<\rho<\rho_{**}$: {\color{highlight}short-range order}. + + \item Is there a phase transition? + + \item The intermediate density regime has not been studied much, due to the lack of tools to do so. + As we have seen, there is non-trivial behavior there. + This warrants further investigation, both theoretical and experimental. +\end{itemize} +\vfill +\eject + +\title{Open problems on the Simplified approach} +\begin{itemize} + \item + Connect the Simplified approach to the many-Boson system: numerics suggests the prediction of the Simplified approach is an {\color{highlight}upper bound}, for all densities. + + \item + Understand the factorization assumption. + It certainly does not hold exactly. + Does it hold approximately, in some sense? + + \item + There are still many questions about the Bose gas with hard core interactions. + The Simplified approach is easily defined in the hard core case. + Can it shed some light? +\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 @@ -0,0 +1,36 @@ +This directory contains the source files to typeset the presentation, and +generate the figures. This can be accomplished by running + make + +The figures were obtained using simplesolv v0.4: + http://ian.jauslin.org/software/simplesolv + +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 + xcolor + GNU make + +* Files: + + Jauslin_Rutgers_2023.tex: + main LaTeX file + + libs: + custom LaTeX class file + + figs: + source code for the figures + diff --git a/figs/2pt.fig/2020-08-27+correlation.dat b/figs/2pt.fig/2020-08-27+correlation.dat new file mode 100644 index 0000000..c436b89 --- /dev/null +++ b/figs/2pt.fig/2020-08-27+correlation.dat @@ -0,0 +1,102 @@ +# Potential: 16 e^{-|x|}, rho=0.02 +# |x| 2-pt correlation + 0.04641589 0.00532330 0.00040199 0.00532330 0.00040199 0.00000000 0.00000000 0.00000000 0.00000000 + 0.13924767 0.00537264 0.00024875 0.00537264 0.00024875 0.00000000 0.00000000 0.00000000 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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 \ + "2pt.dat" using 1:($2/rho**2) with lines ls 4,\ + "2020-08-27+correlation.dat" using 1:2 ls 2 + diff --git a/figs/2pt.fig/Makefile b/figs/2pt.fig/Makefile new file mode 100644 index 0000000..abe0ad2 --- /dev/null +++ b/figs/2pt.fig/Makefile @@ -0,0 +1,35 @@ +PROJECT=$(basename $(wildcard *.gnuplot)) + +SIMPLESOLV=simplesolv~/Work/Research/2018+bose_gas/cmp/simplesolv/source/src + +all: $(addsuffix .pdf, $(PROJECT)) + +define gnuplot2pdf + gnuplot $(1).gnuplot > $(1).tikz.tex + pdflatex -jobname $(1) -file-line-error $(1).tikz.tex +endef + +define bigeq_run + julia $(SIMPLESOLV)/main.jl -p "eq=bigeq;N=12;P=8;J=10;maxiter=100;v_a=16;minlrho_init=-6;nlrho_init=100;rho=2e-2;xmax=10" -M anyeq 2pt > 2pt.dat +endef + +2pt.dat: + $(call bigeq_run) + +DATS=2pt.dat + +2pt.pdf: 2pt.dat + $(call gnuplot2pdf,$(basename $@)) + + +clean-aux: + rm -f $(addsuffix .tikz.tex, $(PROJECT)) + rm -f *.aux *.log + +clean-dat: + rm -f $(DATS) + +clean-pdf: + rm -f $(addsuffix .pdf, $(PROJECT)) + +clean: clean-aux clean-pdf diff --git a/figs/2pt_fourier.fig/2pt_fourier_0.3.dat b/figs/2pt_fourier.fig/2pt_fourier_0.3.dat new file mode 100644 index 0000000..148b17f --- /dev/null +++ b/figs/2pt_fourier.fig/2pt_fourier_0.3.dat @@ -0,0 +1,100 @@ + 8.000000000000000e-02 -1.069194620875982e-03 + 1.600000000000000e-01 -1.067888214371927e-03 + 2.400000000000000e-01 -1.065677844902660e-03 + 3.200000000000000e-01 -1.062514454983640e-03 + 4.000000000000000e-01 -1.058330218372295e-03 + 4.800000000000000e-01 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7.360000000000000e+00 9.408865936103095e-18 + 7.440000000000000e+00 1.018839994078537e-17 + 7.520000000000000e+00 7.619996292048443e-18 + 7.600000000000000e+00 5.816978372988440e-18 + 7.680000000000000e+00 5.148231789904560e-18 + 7.760000000000000e+00 5.383942633396342e-18 + 7.840000000000000e+00 5.428621622765750e-18 + 7.920000000000000e+00 1.582058916889151e-18 + 8.000000000000000e+00 -8.357646780010464e-18 diff --git a/figs/2pt_fourier.fig/2pt_fourier_full.gnuplot b/figs/2pt_fourier.fig/2pt_fourier_full.gnuplot new file mode 100644 index 0000000..7dcb44a --- /dev/null +++ b/figs/2pt_fourier.fig/2pt_fourier_full.gnuplot @@ -0,0 +1,45 @@ +set ylabel norotate "$\\mathcal S(\\kappa)$" +set xlabel "$\\kappa$" + +#set xtics 1e-6, 1000, 1e6 +#set xtics add ("$10^{-6}$" 0.000001, "$10^{-3}$" 0.001, "$10^{0}$" 1, "$10^{3}$" 1000, "$10^6$" 1000000) +#unset mxtics +set xrange [:8] + +#set ytics 0, 1e-5, 2e-5 +#set ytics add ("$10^{-5}$" 1e-5) +#set mytics +#set yrange [0.99998:1.0001] + +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 8,6 standalone + +set key bottom right box linetype rgbcolor"#999999" width 2.5 height 0.3 spacing 1.3 + +rgb(r,g,b) = 65536 * int(r) + 256 * int(g) + int(b) +circle_2_rgb(x) = (x < 1./6 ? rgb(255,x*6*255,0) : \ + (x < 2./6 ? rgb((2./6-x)*6*255,255,0) : \ + (x < 3./6 ? rgb(0,255,(x-2./6)*6*255) : \ + (x < 4./6 ? rgb(0,(4./6-x)*6*255,255) : \ + (x < 5./6 ? rgb((x-4./6)*6*255,0,255) : \ + rgb(255,0,(1-x)*6*255) \ + ))))) + + +set style line 1 linetype rgbcolor circle_2_rgb(0.0) linewidth 2 +set style line 2 linetype rgbcolor circle_2_rgb(0.17) linewidth 2 +set style line 3 linetype rgbcolor circle_2_rgb(0.33) linewidth 2 +set style line 4 linetype rgbcolor circle_2_rgb(0.5) linewidth 2 +set style line 5 linetype rgbcolor circle_2_rgb(0.67) linewidth 2 +set style line 6 linetype rgbcolor circle_2_rgb(0.83) linewidth 2 + + +plot \ + "2pt_fourier_5.dat" using 1:(1+$2/1e-5) with lines ls 1 title "$\\rho=10^{-5}$" ,\ + "2pt_fourier_4.dat" using 1:(1+$2/1e-4) with lines ls 2 title "$\\rho=10^{-4}$" ,\ + "2pt_fourier_3.dat" using 1:(1+$2/1e-3) with lines ls 3 title "$\\rho=10^{-3}$" ,\ + "2pt_fourier_2.dat" using 1:(1+$2/1e-2) with lines ls 4 title "$\\rho=10^{-2}$" ,\ + "2pt_fourier_1.dat" using 1:(1+$2/1e-1) with lines ls 5 title "$\\rho=10^{-1}$" ,\ + "2pt_fourier_0.3.dat" using 1:(1+$2/0.3) with lines ls 6 title "$\\rho=0.3$" + + diff --git a/figs/2pt_fourier.fig/2pt_fourier_peak.gnuplot b/figs/2pt_fourier.fig/2pt_fourier_peak.gnuplot new file mode 100644 index 0000000..1382c9c --- /dev/null +++ b/figs/2pt_fourier.fig/2pt_fourier_peak.gnuplot @@ -0,0 +1,45 @@ +set ylabel norotate "$\\mathcal S(\\kappa)$" +set xlabel "$\\kappa$" + +#set xtics 1e-6, 1000, 1e6 +#set xtics add ("$10^{-6}$" 0.000001, "$10^{-3}$" 0.001, "$10^{0}$" 1, "$10^{3}$" 1000, "$10^6$" 1000000) +#unset mxtics +set xrange [:8] + +#set ytics 0, 1e-5, 2e-5 +#set ytics add ("$10^{-5}$" 1e-5) +#set mytics +set yrange [0.99998:1.0001] + +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 8,6 standalone + +set key top right box linetype rgbcolor"#999999" width 2.5 height 0.3 spacing 1.3 + +rgb(r,g,b) = 65536 * int(r) + 256 * int(g) + int(b) +circle_2_rgb(x) = (x < 1./6 ? rgb(255,x*6*255,0) : \ + (x < 2./6 ? rgb((2./6-x)*6*255,255,0) : \ + (x < 3./6 ? rgb(0,255,(x-2./6)*6*255) : \ + (x < 4./6 ? rgb(0,(4./6-x)*6*255,255) : \ + (x < 5./6 ? rgb((x-4./6)*6*255,0,255) : \ + rgb(255,0,(1-x)*6*255) \ + ))))) + + +set style line 1 linetype rgbcolor circle_2_rgb(0.0) linewidth 2 +set style line 2 linetype rgbcolor circle_2_rgb(0.17) linewidth 2 +set style line 3 linetype rgbcolor circle_2_rgb(0.33) linewidth 2 +set style line 4 linetype rgbcolor circle_2_rgb(0.5) linewidth 2 +set style line 5 linetype rgbcolor circle_2_rgb(0.67) linewidth 2 +set style line 6 linetype rgbcolor circle_2_rgb(0.83) linewidth 2 + + +plot \ + "2pt_fourier_5.dat" using 1:(1+$2/1e-5) with lines ls 1 title "$\\rho=10^{-5}$" ,\ + "2pt_fourier_4.dat" using 1:(1+$2/1e-4) with lines ls 2 title "$\\rho=10^{-4}$" ,\ + "2pt_fourier_3.dat" using 1:(1+$2/1e-3) with lines ls 3 title "$\\rho=10^{-3}$" ,\ + "2pt_fourier_2.dat" using 1:(1+$2/1e-2) with lines ls 4 title "$\\rho=10^{-2}$" ,\ + "2pt_fourier_1.dat" using 1:(1+$2/1e-1) with lines ls 5 title "$\\rho=10^{-1}$" ,\ + "2pt_fourier_0.3.dat" using 1:(1+$2/0.3) with lines ls 6 title "$\\rho=0.3$" + + diff --git a/figs/2pt_fourier.fig/Makefile b/figs/2pt_fourier.fig/Makefile new file mode 100644 index 0000000..e5ca83d --- /dev/null +++ b/figs/2pt_fourier.fig/Makefile @@ -0,0 +1,53 @@ +PROJECT=$(basename $(wildcard *.gnuplot)) + +SIMPLESOLV=simplesolv~/Work/Research/2018+bose_gas/cmp/simplesolv/source/src + +all: $(addsuffix .pdf, $(PROJECT)) + +define gnuplot2pdf + gnuplot $(1).gnuplot > $(1).tikz.tex + pdflatex -jobname $(1) -file-line-error $(1).tikz.tex +endef + +define bigeq_run + julia -p 16 $(SIMPLESOLV)/main.jl -p "eq=bigeq;N=12;P=8;J=10;maxiter=100;v_a=8;rho=1e-$(1);minlrho_init=-6;nlrho_init=100;window_L=100;kmin=0;kmax=8;nk=100" -M anyeq 2pt_fourier > 2pt_fourier_$(1).dat +endef +define bigeq_run_fine + julia -p 16 $(SIMPLESOLV)/main.jl -p "eq=bigeq;N=12;P=8;J=10;maxiter=100;v_a=8;rho=1e-$(1);minlrho_init=-6;nlrho_init=100;window_L=100;kmin=0;kmax=8;nk=150" -M anyeq 2pt_fourier > 2pt_fourier_$(1).dat +endef +define bigeq_run_plus + julia -p 16 $(SIMPLESOLV)/main.jl -p "eq=bigeq;N=18;P=12;J=15;maxiter=100;v_a=8;rho=1e-$(1);minlrho_init=-6;nlrho_init=100;window_L=50;kmin=0;kmax=8;nk=100" -M anyeq 2pt_fourier > 2pt_fourier_$(1).dat +endef + +2pt_fourier_5.dat: + $(call bigeq_run,5) +2pt_fourier_4.dat: + $(call bigeq_run,4) +2pt_fourier_3.dat: + $(call bigeq_run,3) +2pt_fourier_2.dat: + $(call bigeq_run_fine,2) +2pt_fourier_1.dat: + $(call bigeq_run_plus,1) +2pt_fourier_0.3.dat: + julia -p 16 $(SIMPLESOLV)/main.jl -p "eq=bigeq;N=18;P=12;J=15;maxiter=100;v_a=8;rho=0.3;minlrho_init=-6;nlrho_init=100;window_L=25;kmin=0;kmax=8;nk=100" -M anyeq 2pt_fourier > 2pt_fourier_0.3.dat + +DATS=2pt_fourier_5.dat 2pt_fourier_4.dat 2pt_fourier_3.dat 2pt_fourier_2.dat 2pt_fourier_1.dat 2pt_fourier_0.3.dat + +2pt_fourier_peak.pdf: $(DATS) + $(call gnuplot2pdf,$(basename $@)) +2pt_fourier_full.pdf: $(DATS) + $(call gnuplot2pdf,$(basename $@)) + + +clean-aux: + rm -f $(addsuffix .tikz.tex, $(PROJECT)) + rm -f *.aux *.log + +clean-dat: + rm -f $(DATS) + +clean-pdf: + rm -f $(addsuffix .pdf, $(PROJECT)) + +clean: clean-aux clean-pdf diff --git a/figs/2pt_fourier_max.fig/2pt_fourier_max.dat b/figs/2pt_fourier_max.fig/2pt_fourier_max.dat new file mode 100644 index 0000000..1f635ce --- /dev/null +++ b/figs/2pt_fourier_max.fig/2pt_fourier_max.dat @@ -0,0 +1,64 @@ + 1.000000000000000e-05 9.345814412397834e-01 8.552150897032670e-13 + 1.177476859744159e-05 9.346664121067549e-01 1.202135749463409e-12 + 1.386451755232967e-05 9.347707343163895e-01 1.691440674471414e-12 + 1.632514858938491e-05 9.348990198469196e-01 2.382386207082547e-12 + 1.922248469588574e-05 9.350570204371854e-01 3.359292303397934e-12 + 2.263403091619170e-05 9.352519151585713e-01 4.742339255615403e-12 + 2.665104764654962e-05 9.354926698796786e-01 6.703107484819423e-12 + 3.138099189175128e-05 9.357904855291631e-01 9.486984590044240e-12 + 3.695039178835623e-05 9.361593545288540e-01 1.344553010199956e-11 + 4.350823128927006e-05 9.366167475170035e-01 1.908329671284983e-11 + 5.122993555151229e-05 9.371844539822675e-01 2.712565615880497e-11 + 6.032206363809036e-05 9.378895996626473e-01 3.861715148932982e-11 + 7.102783406586597e-05 9.387658591053332e-01 5.506419158683554e-11 + 8.363363101030509e-05 9.398548706385174e-01 7.864206171680841e-11 + 9.847666521101578e-05 9.412078402022969e-01 1.124949675067762e-10 + 1.159539945107438e-04 9.428872868003285e-01 1.611700774661894e-10 + 1.365331453313020e-04 9.449688332938058e-01 2.312433761632351e-10 + 1.607646192156945e-04 9.475428839956032e-01 3.322177644407015e-10 + 1.892966189920617e-04 9.507159629563738e-01 4.778032877984084e-10 + 2.228923884909594e-04 9.546114332252015e-01 6.877261557190169e-10 + 2.624506296612100e-04 9.593693055081258e-01 9.902567270374855e-10 + 3.090295432513592e-04 9.651449063175064e-01 1.425694374417351e-09 + 3.638751361557823e-04 9.721063279266348e-01 2.051093841395011e-09 + 4.284545526596889e-04 9.804308118714142e-01 2.946554554451515e-09 + 5.044953212088191e-04 9.903004673782504e-01 4.223408397651924e-09 + 5.940315665725812e-04 1.001897911604214e+00 6.034615287011951e-09 + 6.994584235967866e-04 1.015402464935713e+00 8.587587607130816e-09 + 8.235961081383442e-04 1.030987417813764e+00 1.215948830640918e-08 + 9.697653591082486e-04 1.048818648812522e+00 1.711475484821645e-08 + 1.141876269731449e-03 1.069054603188533e+00 2.392416506589299e-08 + 1.344532884299761e-03 1.091847421943818e+00 3.318416187524993e-08 + 1.583156358428039e-03 1.117344890815988e+00 4.563439072334752e-08 + 1.864129977405847e-03 1.145692855860799e+00 6.217050807946128e-08 + 2.194969911950787e-03 1.177037801671126e+00 8.384837125104746e-08 + 2.584526279156727e-03 1.211529381168928e+00 1.118748629464322e-07 + 3.043219887107719e-03 1.249322789409432e+00 1.475800562872608e-07 + 3.583320996182576e-03 1.290580888657717e+00 1.923654728380341e-07 + 4.219277554040372e-03 1.335475882250091e+00 2.476241099209779e-07 + 4.968101684720475e-03 1.384190602239726e+00 3.146299028920229e-07 + 5.849824770614332e-03 1.436920277779574e+00 3.943976640740961e-07 + 6.888033300956561e-03 1.493874516611379e+00 4.875196670765305e-07 + 8.110499821023527e-03 1.555276513243977e+00 5.939900926164071e-07 + 9.549925860214359e-03 1.621361584913291e+00 7.130306870751327e-07 + 1.124481671267474e-02 1.692388171755712e+00 8.429399726165237e-07 + 1.324051147123890e-02 1.768632854261179e+00 9.810002396404356e-07 + 1.559039586856090e-02 1.850367899140888e+00 1.123421023005990e-06 + 1.835733036948140e-02 1.937928997570602e+00 1.265373028294286e-06 + 2.161533171674304e-02 2.031651119110462e+00 1.401147518050647e-06 + 2.545155291215895e-02 2.131939113048738e+00 1.524341932452881e-06 + 2.996861459862124e-02 2.239068052585921e+00 1.628031290653131e-06 + 3.528735020846751e-02 2.353931883140321e+00 1.705267895310798e-06 + 4.155003831215873e-02 2.476473586798379e+00 1.749433558398301e-06 + 4.892420863405017e-02 2.608108911035392e+00 1.753923871494640e-06 + 5.760712354788948e-02 2.749217073584620e+00 1.713932075467129e-06 + 6.783105493406272e-02 2.901057281252259e+00 1.624920203679081e-06 + 7.986949755689382e-02 3.068959046043353e+00 1.486982339138430e-06 + 9.404448517263514e-02 3.260310183958069e+00 1.295796996233772e-06 + 1.107352050773305e-01 3.458519146546352e+00 1.059995284580743e-06 + 1.303881415375808e-01 3.664453732410328e+00 7.719169503830476e-07 + 1.535290194455476e-01 3.909581268324730e+00 4.464140314802704e-07 + 1.807768676963434e-01 4.203498863449478e+00 1.232187307927003e-07 + 2.128605784894758e-01 4.258761292369216e+00 -3.918953798048501e-07 + 2.506384055231131e-01 4.447638616870782e+00 -6.847213979772985e-07 + 2.951209226666384e-01 4.454425085066641e+00 -1.846897477962818e-06 diff --git a/figs/2pt_fourier_max.fig/2pt_fourier_max.gnuplot b/figs/2pt_fourier_max.fig/2pt_fourier_max.gnuplot new file mode 100644 index 0000000..1d6efdb --- /dev/null +++ b/figs/2pt_fourier_max.fig/2pt_fourier_max.gnuplot @@ -0,0 +1,38 @@ +set ylabel norotate "$\\mathcal S(\\kappa_*)$" +set xlabel "$\\rho$" + +set xtics 1e-5, 1, 10 +set xtics add ("$10^{-5}$" 0.00001, "$10^{-4}$" 0.0001, "$10^{-3}$" 0.001, "$10^{-2}$" 0.01, "$10^{-1}$" 0.1, "$1$" 1) +unset mxtics +set xrange [0.00001:1] + +#set ytics 0, 1e-5, 2e-5 +#set ytics add ("$10^{-5}$" 1e-5) +#set mytics +#set yrange [0.999:] + +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 8,6 standalone + +set key off + +set style line 1 linetype rgbcolor "#4169E1" linewidth 2 dashtype "." +set style line 2 linetype rgbcolor "#DC143C" linewidth 2 +set style line 3 linetype rgbcolor "#32CD32" linewidth 2 +set style line 4 linetype rgbcolor "#4B0082" linewidth 2 +set style line 5 linetype rgbcolor "#DAA520" linewidth 2 +set style line 6 linetype rgbcolor "#999999" linewidth 2 dashtype (2,2) +set style line 11 linetype rgbcolor "#4169E1" linewidth 1 dashtype (1,2) +set style line 12 linetype rgbcolor "#DC143C" linewidth 1 dashtype (1,2) + +set logscale x + +#set arrow from 1.9e-3,1.00008 to 1.9e-3,0.99999 nohead ls 11 +#set arrow from 0.9e-3,1.00008 to 0.9e-3,0.99999 nohead ls 12 + +plot \ + 1 ls 6 notitle,\ + (x>=0.19 ? 1 : sqrt(-1)) with lines ls 4 notitle,\ + "2pt_fourier_max.dat" using 1:($3>0 ? 1+$3/$1 : 1) with lines ls 4 + + diff --git a/figs/2pt_fourier_max.fig/Makefile b/figs/2pt_fourier_max.fig/Makefile new file mode 100644 index 0000000..305450f --- /dev/null +++ b/figs/2pt_fourier_max.fig/Makefile @@ -0,0 +1,35 @@ +PROJECT=$(basename $(wildcard *.gnuplot)) + +SIMPLESOLV=simplesolv~/Work/Research/2018+bose_gas/cmp/simplesolv/source/src + +all: $(addsuffix .pdf, $(PROJECT)) + +define gnuplot2pdf + gnuplot $(1).gnuplot > $(1).tikz.tex + pdflatex -jobname $(1) -file-line-error $(1).tikz.tex +endef + +define bigeq_run + julia -p 16 $(SIMPLESOLV)/main.jl -p "eq=bigeq;N=18;P=12;J=15;maxiter=100;v_a=8;minlrho=-5;maxlrho=-0.53;nlrho=64;window_L=100;dk=1e-4;maxstep=0.1" -M anyeq 2pt_fourier_max_rho > 2pt_fourier_max.dat +endef + +2pt_fourier_max.dat: + $(call bigeq_run) + +DATS=2pt_fourier_max.dat + +2pt_fourier_max.pdf: 2pt_fourier_max.dat + $(call gnuplot2pdf,$(basename $@)) + + +clean-aux: + rm -f $(addsuffix .tikz.tex, $(PROJECT)) + rm -f *.aux *.log + +clean-dat: + rm -f $(DATS) + +clean-pdf: + rm -f $(addsuffix .pdf, $(PROJECT)) + +clean: clean-aux clean-pdf diff --git a/figs/2pt_max.fig/2pt_max.dat b/figs/2pt_max.fig/2pt_max.dat new file mode 100644 index 0000000..f83c547 --- /dev/null +++ b/figs/2pt_max.fig/2pt_max.dat @@ -0,0 +1,59 @@ + 7.220809018385464e-04 2.018973565973845e+01 5.211229116520497e-07 + 8.111308307896872e-04 1.739509445768228e+01 6.576636156499842e-07 + 9.111627561154887e-04 1.523059825227606e+01 8.302333247422031e-07 + 1.023531021899027e-03 1.387331723806022e+01 1.048415025334355e-06 + 1.149756995397736e-03 1.285566507206079e+01 1.324303448465614e-06 + 1.291549665014884e-03 1.194801886571412e+01 1.673210489577455e-06 + 1.450828778495940e-03 1.126962289641431e+01 2.114491962368022e-06 + 1.629750834620644e-03 1.063415003004839e+01 2.672749854539034e-06 + 1.830738280295368e-03 1.011689961825143e+01 3.378959975269341e-06 + 2.056512308348652e-03 9.614622003268412e+00 4.272305392686213e-06 + 2.310129700083158e-03 9.178257425458384e+00 5.402697266619999e-06 + 2.595024211399737e-03 8.783487899154855e+00 6.832287818065473e-06 + 2.915053062825176e-03 8.400087365492075e+00 8.640690704253858e-06 + 3.678379771828634e-03 7.745111761585086e+00 1.382076631238977e-05 + 4.641588833612782e-03 7.144706722479198e+00 2.210027389724007e-05 + 6.579332246575682e-03 6.393774597139051e+00 4.465012231410845e-05 + 8.302175681319744e-03 5.944916899632466e+00 7.130485532670318e-05 + 9.326033468832200e-03 5.744396472510482e+00 9.007848588332599e-05 + 1.047615752789665e-02 5.547651829606133e+00 1.137675501456023e-04 + 1.176811952434998e-02 5.357427743741679e+00 1.436572369795343e-04 + 1.321941148466029e-02 5.175142321646281e+00 1.813691885996321e-04 + 1.484968262254465e-02 5.006476097704476e+00 2.289320042467527e-04 + 1.668100537200059e-02 4.843500230606333e+00 2.889035712280707e-04 + 1.873817422860383e-02 4.689243621580819e+00 3.645130850275416e-04 + 2.104904144512020e-02 4.542147958998562e+00 4.598076132141278e-04 + 2.364489412645407e-02 4.396049752656342e+00 5.799249403751192e-04 + 3.764935806792467e-02 3.890625424864157e+00 1.465464005334726e-03 + 4.750810162102798e-02 3.663479217958253e+00 2.328143035109476e-03 + 5.336699231206307e-02 3.563304920231506e+00 2.934278174022928e-03 + 5.994842503189409e-02 3.468775419753054e+00 3.697933125644822e-03 + 6.734150657750822e-02 3.376199168574197e+00 4.660073971471896e-03 + 1.072267222010323e-01 3.035126008562789e+00 1.175532933763886e-02 + 1.204503540258782e-01 2.963209828607758e+00 1.481497246608100e-02 + 1.353047774579806e-01 2.889870627807464e+00 1.867153234794507e-02 + 1.519911082952933e-01 2.819431535034761e+00 2.353311763560754e-02 + 1.707352647470690e-01 2.750361767006201e+00 2.966222975889765e-02 + 1.917910261672489e-01 2.683581390366167e+00 3.738998865289806e-02 + 2.154434690031884e-01 2.620113300842895e+00 4.713412029366486e-02 + 2.718588242732940e-01 2.506680445892512e+00 7.491234297411424e-02 + 3.430469286314919e-01 2.397861132187415e+00 1.190842774019350e-01 + 3.853528593710527e-01 2.348709126442317e+00 1.501531313324748e-01 + 5.462277217684343e-01 2.213998487416692e+00 3.010537094548759e-01 + 6.135907273413169e-01 2.159190780322460e+00 3.796531910629315e-01 + 6.892612104349695e-01 2.104318598346585e+00 4.788093262468083e-01 + 7.742636826811270e-01 2.054957669792689e+00 6.039029328900501e-01 + 8.697490026177834e-01 2.014717733267600e+00 7.617095007448773e-01 + 1.097498765493057e+00 1.944232229835132e+00 1.211873664289093e+00 + 1.555676143930472e+00 1.849679137183402e+00 2.432230525785016e+00 + 2.205130739903046e+00 1.755851623363939e+00 4.881957590314813e+00 + 2.477076355991709e+00 1.715067006985843e+00 6.158508335889029e+00 + 2.782559402207126e+00 1.654928891762455e+00 7.769211167278110e+00 + 3.511191734215128e+00 1.567813951102577e+00 1.236681523118124e+01 + 3.944206059437656e+00 1.542436734218897e+00 1.560301160065102e+01 + 4.430621457583878e+00 1.520671270243120e+00 1.968602995118866e+01 + 4.977023564332113e+00 1.500406364404500e+00 2.483738995641643e+01 + 5.590810182512223e+00 1.481300360506878e+00 3.133660892477183e+01 + 6.280291441834247e+00 1.463684701974351e+00 3.953632925420883e+01 + 8.902150854450392e+00 1.412546112155323e+00 7.940057353781076e+01 + 1.000000000000000e+01 1.392593488777013e+00 1.001767762256856e+02 diff --git a/figs/2pt_max.fig/2pt_max.gnuplot b/figs/2pt_max.fig/2pt_max.gnuplot new file mode 100644 index 0000000..b37c8a1 --- /dev/null +++ b/figs/2pt_max.fig/2pt_max.gnuplot @@ -0,0 +1,34 @@ +set ylabel norotate "$G(r_*)$" +set xlabel "$\\rho$" + +set xtics 1e-4, 100, 10 +set xtics add ("$10^{-4}$" 0.0001, "$10^{-3}$" 0.001, "$10^{-2}$" 0.01, "$10^{-1}$" 0.1, "$1$" 1, "$10$" 10) +unset mxtics +set xrange [0.0001:10] + +#set ytics 0, 1e-5, 2e-5 +#set ytics add ("$10^{-5}$" 1e-5) +#set mytics +set yrange [0.999:] + +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 8,6 standalone + +set key off + +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 style line 6 linetype rgbcolor "#000000" linewidth 1 + +se logscale x + + +plot \ + 1 ls 6 notitle,\ + (x<=7.23e-4 ? 1 : sqrt(-1)) with lines ls 4 notitle,\ + "2pt_max.dat" using 1:($3/$1**2>=1 ? $3/$1**2 : 1) with lines ls 4 + + diff --git a/figs/2pt_max.fig/Makefile b/figs/2pt_max.fig/Makefile new file mode 100644 index 0000000..b419fee --- /dev/null +++ b/figs/2pt_max.fig/Makefile @@ -0,0 +1,35 @@ +PROJECT=$(basename $(wildcard *.gnuplot)) + +SIMPLESOLV=simplesolv~/Work/Research/2018+bose_gas/cmp/simplesolv/source/src + +all: $(addsuffix .pdf, $(PROJECT)) + +define gnuplot2pdf + gnuplot $(1).gnuplot > $(1).tikz.tex + pdflatex -jobname $(1) -file-line-error $(1).tikz.tex +endef + +define bigeq_run + julia -p 16 $(SIMPLESOLV)/main.jl -p "eq=bigeq;N=12;P=8;J=10;maxiter=100;v_a=8;minlrho=-4;maxlrho=1;nlrho=100;window_L=1000;dx=1e-4;maxstep=0.1" -M anyeq 2pt_max_rho > 2pt_max.dat +endef + +2pt_max.dat: + $(call bigeq_run) + +DATS=2pt_max.dat + +2pt_max.pdf: 2pt_max.dat + $(call gnuplot2pdf,$(basename $@)) + + +clean-aux: + rm -f $(addsuffix .tikz.tex, $(PROJECT)) + rm -f *.aux *.log + +clean-dat: + rm -f $(DATS) + +clean-pdf: + rm -f $(addsuffix .pdf, $(PROJECT)) + +clean: clean-aux clean-pdf diff --git a/figs/2pt_rho.fig/2pt_1.dat b/figs/2pt_rho.fig/2pt_1.dat new file mode 100644 index 0000000..5a7050e --- /dev/null +++ b/figs/2pt_rho.fig/2pt_1.dat @@ -0,0 +1,100 @@ + 6.500000000000000e-02 2.124106903868166e-03 + 1.300000000000000e-01 2.167462874073794e-03 + 1.950000000000000e-01 2.237296985127973e-03 + 2.600000000000000e-01 2.331605451031708e-03 + 3.250000000000000e-01 2.448941547781181e-03 + 3.900000000000000e-01 2.588140107411339e-03 + 4.550000000000000e-01 2.748057991645383e-03 + 5.200000000000000e-01 2.927777097002868e-03 + 5.850000000000000e-01 3.126536998535562e-03 + 6.500000000000000e-01 3.343345300613759e-03 + 7.150000000000000e-01 3.576823032139147e-03 + 7.800000000000000e-01 3.825564291357081e-03 + 8.450000000000000e-01 4.088347880430513e-03 + 9.100000000000000e-01 4.363771211293593e-03 + 9.750000000000000e-01 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a/figs/2pt_rho.fig/2pt_2.dat b/figs/2pt_rho.fig/2pt_2.dat new file mode 100644 index 0000000..1edf2f7 --- /dev/null +++ b/figs/2pt_rho.fig/2pt_2.dat @@ -0,0 +1,100 @@ + 1.400000000000000e-01 1.488043827565062e-06 + 2.800000000000000e-01 1.682490793450653e-06 + 4.200000000000000e-01 2.012392878526759e-06 + 5.600000000000001e-01 2.497842610503254e-06 + 7.000000000000000e-01 3.169462751290156e-06 + 8.400000000000000e-01 4.063501152271771e-06 + 9.800000000000000e-01 5.221881209449808e-06 + 1.120000000000000e+00 6.685588932583900e-06 + 1.260000000000000e+00 8.494580586418807e-06 + 1.400000000000000e+00 1.068397234740815e-05 + 1.540000000000000e+00 1.327826576527692e-05 + 1.680000000000000e+00 1.629096680706187e-05 + 1.820000000000000e+00 1.972445619317546e-05 + 1.960000000000000e+00 2.356202944493775e-05 + 2.100000000000000e+00 2.777290282324146e-05 + 2.240000000000000e+00 3.231459777435289e-05 + 2.380000000000000e+00 3.712916581792513e-05 + 2.520000000000000e+00 4.214818471315268e-05 + 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1.311300000000000e+02 9.990344410781654e-11 + 1.325250000000000e+02 9.990797176682055e-11 + 1.339200000000000e+02 9.991350192105834e-11 + 1.353150000000000e+02 9.991572316062209e-11 + 1.367100000000000e+02 9.991628956042748e-11 + 1.381050000000000e+02 9.992368802420682e-11 + 1.395000000000000e+02 9.992789534028236e-11 diff --git a/figs/2pt_rho.fig/2pt_rho.gnuplot b/figs/2pt_rho.fig/2pt_rho.gnuplot new file mode 100644 index 0000000..08b35f1 --- /dev/null +++ b/figs/2pt_rho.fig/2pt_rho.gnuplot @@ -0,0 +1,48 @@ +set ylabel norotate "$G(r)$" +set xlabel "$r\\rho^{1/3}$" + +#set xtics 1e-6, 1000, 1e6 +#set xtics add ("$10^{-6}$" 0.000001, "$10^{-3}$" 0.001, "$10^{0}$" 1, "$10^{3}$" 1000, "$10^6$" 1000000) +#unset mxtics +set xrange [:3] + +#set ytics 0, 1e-5, 2e-5 +#set ytics add ("$10^{-5}$" 1e-5) +#set mytics +set yrange [0.8:] + +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 8,6 standalone + +set key bottom right box linetype rgbcolor"#999999" width 3 height 0.3 spacing 1.3 + + +rgb(r,g,b) = 65536 * int(r) + 256 * int(g) + int(b) +circle_2_rgb(x) = (x < 1./6 ? rgb(255,x*6*255,0) : \ + (x < 2./6 ? rgb((2./6-x)*6*255,255,0) : \ + (x < 3./6 ? rgb(0,255,(x-2./6)*6*255) : \ + (x < 4./6 ? rgb(0,(4./6-x)*6*255,255) : \ + (x < 5./6 ? rgb((x-4./6)*6*255,0,255) : \ + rgb(255,0,(1-x)*6*255) \ + ))))) + + +set style line 1 linetype rgbcolor circle_2_rgb(0.0) linewidth 2 +set style line 2 linetype rgbcolor circle_2_rgb(0.2) linewidth 2 +set style line 3 linetype rgbcolor circle_2_rgb(0.4) linewidth 2 +set style line 4 linetype rgbcolor circle_2_rgb(0.6) linewidth 2 +set style line 5 linetype rgbcolor circle_2_rgb(0.8) linewidth 2 +set style line 6 linetype rgbcolor (0,0,0) linewidth 1 + +set pointsize 1 + + +plot \ + 1 ls 6 notitle,\ + "2pt_5.dat" using ($1*1e-5**(1./3)):($2/1e-5**2) with lines ls 1 title "$\\rho=10^{-5}$" ,\ + "2pt_4.dat" using ($1*1e-4**(1./3)):($2/1e-4**2) with lines ls 2 title "$\\rho=10^{-4}$" ,\ + "2pt_3.dat" using ($1*1e-3**(1./3)):($2/1e-3**2) with lines ls 3 title "$\\rho=10^{-3}$" ,\ + "2pt_2.dat" using ($1*1e-2**(1./3)):($2/1e-2**2) with lines ls 4 title "$\\rho=10^{-2}$" ,\ + "2pt_1.dat" using ($1*1e-1**(1./3)):($2/1e-1**2) with lines ls 5 title "$\\rho=10^{-1}$" + + diff --git a/figs/2pt_rho.fig/Makefile b/figs/2pt_rho.fig/Makefile new file mode 100644 index 0000000..bdd3eca --- /dev/null +++ b/figs/2pt_rho.fig/Makefile @@ -0,0 +1,46 @@ +PROJECT=$(basename $(wildcard *.gnuplot)) + +SIMPLESOLV=simplesolv~/Work/Research/2018+bose_gas/cmp/simplesolv/source/src + +all: $(addsuffix .pdf, $(PROJECT)) + +define gnuplot2pdf + gnuplot $(1).gnuplot > $(1).tikz.tex + pdflatex -jobname $(1) -file-line-error $(1).tikz.tex +endef + +define bigeq_run + julia $(SIMPLESOLV)/main.jl -p "eq=bigeq;N=12;P=8;J=10;maxiter=100;v_a=8;rho=1e-$(1);minlrho_init=-6;nlrho_init=100;window_L=100;xmin=0;xmax=$(2);nx=100" -M anyeq 2pt > 2pt_$(1).dat +endef +define bigeq_run_plus + julia $(SIMPLESOLV)/main.jl -p "eq=bigeq;N=18;P=12;J=15;maxiter=100;v_a=8;rho=1e-$(1);minlrho_init=-6;nlrho_init=100;window_L=100;xmin=0;xmax=$(2);nx=100" -M anyeq 2pt > 2pt_$(1).dat +endef + +2pt_5.dat: + $(call bigeq_run_plus,5,139.5) +2pt_4.dat: + $(call bigeq_run,4,64.5) +2pt_3.dat: + $(call bigeq_run,3,30) +2pt_2.dat: + $(call bigeq_run,2,14) +2pt_1.dat: + $(call bigeq_run,1,6.5) + +DATS=2pt_5.dat 2pt_4.dat 2pt_3.dat 2pt_2.dat 2pt_1.dat + +2pt_rho.pdf: $(DATS) + $(call gnuplot2pdf,$(basename $@)) + + +clean-aux: + rm -f $(addsuffix .tikz.tex, $(PROJECT)) + rm -f *.aux *.log + +clean-dat: + rm -f $(DATS) + +clean-pdf: + rm -f $(addsuffix .pdf, $(PROJECT)) + +clean: clean-aux clean-pdf diff --git a/figs/condensate.fig/Makefile b/figs/condensate.fig/Makefile new file mode 100644 index 0000000..9983ef7 --- /dev/null +++ b/figs/condensate.fig/Makefile @@ -0,0 +1,35 @@ +PROJECT=$(basename $(wildcard *.gnuplot)) + +SIMPLESOLV=simplesolv~/Work/Research/2018+bose_gas/cmp/simplesolv/source/src + +all: $(addsuffix .pdf, $(PROJECT)) + +define gnuplot2pdf + gnuplot $(1).gnuplot > $(1).tikz.tex + pdflatex -jobname $(1) -file-line-error $(1).tikz.tex +endef + +define bigeq_run + julia -p 16 $(SIMPLESOLV)/main.jl -p "eq=bigeq;N=12;P=8;J=10;maxiter=100;v_a=8;minlrho=-6;nlrho=100;maxlrho=2" -M anyeq condensate_fraction_rho > condensate.dat +endef + +condensate.dat: + $(call bigeq_run) + +DATS=condensate.dat + +condensate.pdf: $(DATS) + $(call gnuplot2pdf,$(basename $@)) + + +clean-aux: + rm -f $(addsuffix .tikz.tex, $(PROJECT)) + rm -f *.aux *.log + +clean-dat: + rm -f $(DATS) + +clean-pdf: + rm -f $(addsuffix .pdf, $(PROJECT)) + +clean: clean-aux clean-pdf diff --git a/figs/condensate.fig/condensate.dat b/figs/condensate.fig/condensate.dat new file mode 100644 index 0000000..7beede0 --- /dev/null +++ b/figs/condensate.fig/condensate.dat @@ -0,0 +1,100 @@ + 1.000000000000000e-06 8.524653565633833e-03 7.195282669866215e-15 + 1.204503540258781e-06 9.482931278294420e-03 1.219933599614962e-14 + 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1.592498142496109e-01 2.193439580869223e-15 + 1.384886371393875e+00 1.486963029452997e-01 1.648286202055480e-15 + 1.668100537200059e+00 1.388880394362550e-01 3.124563475483895e-15 + 2.009233002565050e+00 1.297669712794426e-01 2.212240236489514e-15 + 2.420128264794383e+00 1.212792919665664e-01 1.822578297170560e-15 + 2.915053062825182e+00 1.133754387934347e-01 1.293726888514874e-15 + 3.511191734215135e+00 1.060099602551520e-01 1.638195775953276e-15 + 4.229242874389508e+00 9.914130199191040e-02 1.752453175614045e-15 + 5.094138014816386e+00 9.273154661320844e-02 2.383213588406398e-15 + 6.135907273413176e+00 8.674613226064723e-02 4.673666845465575e-15 + 7.390722033525790e+00 8.115356686357338e-02 3.843207367033268e-15 + 8.902150854450392e+00 7.592514919615562e-02 2.889463903956984e-15 + 1.072267222010325e+01 7.103470363590553e-02 2.577031650678448e-15 + 1.291549665014885e+01 6.645833257136877e-02 3.567371947044331e-15 + 1.555676143930475e+01 6.217418839914374e-02 2.678037011024236e-15 + 1.873817422860387e+01 5.816226574695751e-02 3.465354011432907e-15 + 2.257019719633922e+01 5.440421374532894e-02 2.975998245290574e-15 + 2.718588242732946e+01 5.088316761973691e-02 3.428201805340647e-15 + 3.274549162877732e+01 4.758359840543907e-02 3.879983823861438e-15 + 3.944206059437664e+01 4.449117916775601e-02 3.988638949817691e-15 + 4.750810162102803e+01 4.159266589368779e-02 4.204239894057915e-15 + 5.722367659350220e+01 3.887579136661706e-02 4.017134010366431e-15 + 6.892612104349709e+01 3.632917078016813e-02 4.381717563239069e-15 + 8.302175681319753e+01 3.394221826626880e-02 9.103579900515236e-12 + 1.000000000000000e+02 3.170507358779736e-02 6.838220457800429e-12 diff --git a/figs/condensate.fig/condensate.gnuplot b/figs/condensate.fig/condensate.gnuplot new file mode 100644 index 0000000..c2fbcc9 --- /dev/null +++ b/figs/condensate.fig/condensate.gnuplot @@ -0,0 +1,38 @@ +set ylabel norotate "$\\eta$" +set xlabel "$\\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, 1e-5, 2e-5 +#set ytics add ("$10^{-5}$" 1e-5) +#set mytics +set yrange [0:1] + +# default output canvas size: 12.5cm x 8.75cm +set term lua tikz size 8,6 standalone + +set key off + + +set style line 1 linetype rgbcolor "#4169E1" linewidth 2 dashtype "." +set style line 2 linetype rgbcolor "#DC143C" linewidth 2 +set style line 3 linetype rgbcolor "#32CD32" linewidth 2 +set style line 4 linetype rgbcolor "#4B0082" linewidth 2 +set style line 5 linetype rgbcolor "#DAA520" linewidth 2 +set style line 6 linetype rgbcolor "#999999" linewidth 2 dashtype (2,2) +set style line 11 linetype rgbcolor "#4169E1" linewidth 1 dashtype (1,2) +set style line 12 linetype rgbcolor "#DC143C" linewidth 1 dashtype (1,2) + +set logscale x + +set arrow from 0.9e-3,1 to 0.9e-3,0 nohead ls 12 +set arrow from 0.2,1 to 0.2,0 nohead ls 12 + +set label "$\\rho_*$" at 0.9e-3,-0.05 center textcolor rgbcolor "#DC143C" +set label "$\\rho_{**}$" at 0.2,-0.05 center textcolor rgbcolor "#DC143C" + +plot \ + "condensate.dat" using 1:(1-$2) with lines ls 4 + diff --git a/figs/energy.fig/Makefile b/figs/energy.fig/Makefile new file mode 100644 index 0000000..6278330 --- /dev/null +++ b/figs/energy.fig/Makefile @@ -0,0 +1,35 @@ +PROJECT=$(basename $(wildcard *.gnuplot)) + +SIMPLESOLV=simplesolv~/Work/Research/2018+bose_gas/cmp/simplesolv/source/src + +all: $(addsuffix .pdf, $(PROJECT)) + +define gnuplot2pdf + gnuplot $(1).gnuplot > $(1).tikz.tex + pdflatex -jobname $(1) -file-line-error $(1).tikz.tex +endef + +define bigeq_run + julia -p 16 $(SIMPLESOLV)/main.jl -p "eq=bigeq;N=12;P=8;J=10;maxiter=100;v_a=1;minlrho=-6;maxlrho=2;nlrho=100" -M anyeq energy_rho > energy.dat +endef + +energy.dat: + $(call bigeq_run) + +DATS=energy.dat + +energy.pdf: energy.dat + $(call gnuplot2pdf,$(basename $@)) + + +clean-aux: + rm -f $(addsuffix .tikz.tex, $(PROJECT)) + rm -f *.aux *.log + +clean-dat: + rm -f $(DATS) + +clean-pdf: + rm -f $(addsuffix .pdf, $(PROJECT)) + +clean: clean-aux clean-pdf diff --git a/figs/energy.fig/energy.dat b/figs/energy.fig/energy.dat new file mode 100644 index 0000000..3dcfb71 --- /dev/null +++ b/figs/energy.fig/energy.dat @@ -0,0 +1,100 @@ + 1.000000000000000e-06 7.933345669932108e-06 1.703886592783066e-12 + 1.204503540258781e-06 9.561695772478549e-06 3.497161949718074e-13 + 1.450828778495940e-06 1.152494614052415e-05 1.108062277037754e-13 + 1.747528400007683e-06 1.389218915189634e-05 6.516057688008037e-13 + 2.104904144512022e-06 1.674683575161553e-05 2.538326122985294e-13 + 2.535364493970111e-06 2.018960215367572e-05 1.886089276338240e-14 + 3.053855508833412e-06 2.434212593011697e-05 3.224578200780056e-14 + 3.678379771828634e-06 2.935134616878758e-05 2.059872930370073e-14 + 4.430621457583877e-06 3.539481155461295e-05 2.957473052054922e-13 + 5.336699231206313e-06 4.268711577772934e-05 8.111079833349440e-13 + 6.428073117284319e-06 5.148770312835425e-05 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6.135907273413176e+00 7.690694209247896e+01 5.199587559531442e-13 + 7.390722033525790e+00 9.266893489306236e+01 4.063077569699647e-13 + 8.902150854450392e+00 1.116556685689670e+02 3.150233501240136e-13 + 1.072267222010325e+01 1.345266139156320e+02 2.426172105183155e-13 + 1.291549665014885e+01 1.620761041088648e+02 1.855816678657911e-13 + 1.555676143930475e+01 1.952609146057077e+02 1.407559657444627e-13 + 1.873817422860387e+01 2.352334832362353e+02 1.059913343555381e-13 + 2.257019719633922e+01 2.833819239247995e+02 7.975489876162496e-14 + 2.718588242732946e+01 3.413782233614627e+02 5.927370872708888e-14 + 3.274549162877732e+01 4.112362940653811e+02 4.383124064542629e-14 + 3.944206059437664e+01 4.953818995066683e+02 3.264094881514513e-14 + 4.750810162102803e+01 5.967368791641958e+02 2.438481071043009e-14 + 5.722367659350220e+01 7.188205979063789e+02 1.781857723825451e-14 + 6.892612104349709e+01 8.658721421294766e+02 1.398488788949389e-14 + 8.302175681319753e+01 1.042997505438325e+03 1.067384424838066e-14 + 1.000000000000000e+02 1.256346874319010e+03 8.542571473538560e-15 diff --git a/figs/energy.fig/energy.gnuplot b/figs/energy.fig/energy.gnuplot new file mode 100644 index 0000000..377a2e9 --- /dev/null +++ b/figs/energy.fig/energy.gnuplot @@ -0,0 +1,36 @@ +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 "energy.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/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/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 |