diff options
| -rw-r--r-- | Jauslin_TAMU_2020.tex | 365 | ||||
| -rw-r--r-- | Makefile | 50 | ||||
| -rw-r--r-- | README | 32 | ||||
| -rw-r--r-- | figs/plots.fig/Makefile | 28 | ||||
| -rw-r--r-- | figs/plots.fig/condensate.gnuplot | 36 | ||||
| -rw-r--r-- | figs/plots.fig/condensate_fulleq.dat | 100 | ||||
| -rw-r--r-- | figs/plots.fig/condensate_simpleq.dat | 100 | ||||
| -rw-r--r-- | figs/plots.fig/erho.dat | 104 | ||||
| -rw-r--r-- | figs/plots.fig/erho_effective.gnuplot | 38 | ||||
| -rw-r--r-- | figs/plots.fig/erho_fulleq.dat | 100 | ||||
| -rw-r--r-- | figs/plots.fig/erho_fulleq.gnuplot | 37 | ||||
| -rw-r--r-- | figs/plots.fig/holzmann_2019-12-25.dat | 11 | ||||
| -rw-r--r-- | libs/ian-presentation.cls | 187 |
13 files changed, 1188 insertions, 0 deletions
diff --git a/Jauslin_TAMU_2020.tex b/Jauslin_TAMU_2020.tex new file mode 100644 index 0000000..244fa2d --- /dev/null +++ b/Jauslin_TAMU_2020.tex @@ -0,0 +1,365 @@ +\documentclass{ian-presentation} + +\usepackage[hidelinks]{hyperref} +\usepackage{graphicx} +\usepackage{array} + +\begin{document} +\pagestyle{empty} +\hbox{}\vfil +\bf\Large +\hfil A simple equation to study interacting Bose gasses\par +\vfil +\large +\hfil Ian Jauslin +\normalsize +\vfil +\hfil\rm joint with {\bf Eric A. Carlen}, {\bf Elliott H. Lieb}\par +\vfil +arXiv:{\tt \href{https://arxiv.org/abs/1912.04987}{1912.04987}} +\hfill{\tt \href{http://ian.jauslin.org}{http://ian.jauslin.org}} +\eject + +\setcounter{page}1 +\pagestyle{plain} + +\title{Lieb's simple equation (1963)} +\vskip-10pt +\begin{itemize} + \item \href{https://doi.org/10.1103/PhysRev.130.2518}{[Lieb, 1963]}: $x\in\mathbb R^d$ + $$ + (-\Delta+v(x)+4e)u(x)=v(x)+2e\rho\ u\ast u(x) + $$ + $$ + e=\frac\rho2\int dx\ (1-u(x))v(x) + $$ + \item with + $$ + \rho>0 + ,\quad + v(x)\geqslant 0 + ,\quad + v\in L_1\cap L_{\frac d2+\epsilon}(\mathbb R^d) + $$ + \item and + $$ + u\in L_1(\mathbb R^d) + ,\quad + u\ast u(x):=\int dy\ u(x-y)u(y) + $$ +\end{itemize} +\vfill +\eject + +\title{Interacting Bose gas} +\vskip-10pt +\begin{itemize} + \item State: symmetric wave functions in a finite box of volume $V$ with periodic boundary conditions: + $$ + \psi(x_1,\cdots,x_N) + ,\quad + x_i\in \Lambda_d:=V^{\frac1d}\mathbb T^d + $$ + \item Probability distribution: $|\psi(x_1,\cdots,x_N)|^2$ + \item $N$-particle Hamiltonian: + $$ + H_N:= + -\frac12\sum_{i=1}^N\Delta_i + +\sum_{1\leqslant i<j\leqslant N}v(x_i-x_j) + $$ + with $v(x-y)\geqslant 0$ and $v\in L_1\cap L_{\frac d2+\epsilon}(\mathbb R^d)$. +\end{itemize} +\vfill +\eject + +\title{Interacting Bose gas} +\vskip-10pt +\begin{itemize} + \item Ground state: + $$ + H_N\psi_0=E_0\psi_0 + ,\quad + E_0=\min\mathrm{spec}(H_N) + $$ + \item Compute the ground state-energy per particle in the thermodynamic limit: + $$ + e_0:=\lim_{\displaystyle\mathop{\scriptstyle V,N\to\infty}_{\frac NV=\rho}}\frac{E_0}N + $$ +\end{itemize} +\vfill +\eject + +\title{Asymptotics for the Bose gas} +\vskip-10pt +\begin{itemize} + \item {\bf Theorem} \href{https://doi.org/10.1103/PhysRev.130.2518}{[Lieb, 1963]}: if $\hat v(k):=\int dx\ e^{ikx}v(x)\geqslant 0$, then + $$ + \frac{e_0}{\rho}\mathop{\longrightarrow}_{\rho\to\infty}\frac12\int dx\ v(x) + $$ + \item {\bf Theorem} \href{https://doi.org/10.1103/PhysRevLett.80.2504}{[Lieb, Yngvason, 1998]}: in 3 dimensions ($a$: scattering length) + $$ + \frac{e_0}{\rho}\mathop{\longrightarrow}_{\rho\to0}2\pi a + $$ + \href{https://doi.org/10.1103/PhysRev.106.1135}{[Lee, Huang, Yang, 1957]}, \href{https://doi.org/10.1007/s10955-009-9792-3}{[Yau, Yin, 2009]}, \href{https://arxiv.org/abs/1904.06164}{[Fournais, Solovej, 2019]}: + $$ + e_0=2\pi\rho a\left(1+\frac{128}{15\sqrt\pi}\sqrt{\rho a^3}+o(\sqrt\rho)\right) + $$ +\end{itemize} +\vfill +\eject + +\title{Simple equation for $v(x)=e^{-|x|}$ in 3 dimensions} +\hfil\includegraphics[height=6cm]{erho_effective.pdf} +\vfill +\eject + +\title{Main Theorem} +\vskip-5pt +\begin{itemize} + \item If $v(x)\geqslant 0$ and $v\in L_1\cap L_{\frac d2+\epsilon}(\mathbb R^d)$, then Lieb's simple equation + $$ + (-\Delta+4e+v)u=v+2e\rho u\ast u + ,\quad + e=\frac\rho2\int dx\ (1-u(x))v(x) + $$ + has an integrable solution (proved constructively), with $0\leqslant u\leqslant 1$. + + \item For $d=3$, + $$ + e=2\pi\rho a\left(1+\frac{128}{15\sqrt\pi}\sqrt{\rho a^3}+o(\sqrt\rho)\right) + ,\quad + \frac{e}\rho\mathop{\longrightarrow}_{\rho\to\infty}\frac12\int dx\ v(x) + . + $$ + + \item For $d=3$, if $v(x)\equiv v(|x|)$ is radially symmetric and decays exponentially, + $$ + u(|x|)\mathop\sim_{|x|\to\infty}\frac\alpha{|x|^4} + . + $$ +\end{itemize} +\vfill +\eject + +\title{Existence of a solution (sketch)} +\begin{itemize} + \item Simple equation: fixed $\rho>0$, + $$ + (-\Delta+4e+v)u=v+2e\rho u\ast u + ,\quad + e=\frac\rho2\int dx\ (1-u(x))v(x) + $$ + + \item Change the point of view: fix $e>0$, and compute $\rho$ and $u$. + + \item 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{Existence of a solution (sketch)} +\begin{itemize} + $$ + u_n=(-\Delta+4e+v)^{-1}\left(v+2e\rho_{n-1}u_{n-1}\ast u_{n-1}\right) + ,\quad + \rho_n:=\frac{2e}{\int dx\ (1-u_n(x))v(x)} + . + $$ + \item $u_n(x)$ is an increasing sequence: since $v\geqslant 0$, + \begin{itemize} + \item $(-\Delta+4e+v)^{-1}$ is positivity preserving. + \item $\rho_n$ is an increasing function of $u_n$. + \end{itemize} +\end{itemize} +\vfill +\eject + +\title{Existence of a solution (sketch)} +\begin{itemize} + $$ + -\Delta u_n=(1-u_n)v-4eu_n+2e\rho_{n-1}u_{n-1}\ast u_{n-1} + ,\quad + \frac{2e}{\rho_n}=\int dx\ (1-u_n(x))v(x) + . + $$ + \item $\int dx\ u_n(x)<\frac1{\rho_n}$: integrating, + $$ + 0=\frac{2e}{\rho_n}-4e\int u_n+2e\rho_{n-1}\left(\int u_{n-1}\right)^2 + < + \frac{2e}{\rho_n}-2e\int u_n + $$ + (since $\int u_{n-1}<\frac1{\rho_{n-1}}$ and $\int u_{n-1}\leqslant\int u_n$). +\end{itemize} +\vfill +\eject + +\title{Existence of a solution (sketch)} +\begin{itemize} + $$ + -\Delta u_n=(1-u_n)v-4eu+2e\rho_{n-1}u_{n-1}\ast u_{n-1} + ,\quad + \frac{2e}{\rho_n}=\int dx\ (1-u_n(x))v(x) + . + $$ + \item $u_n(x)\leqslant 1$: since $v\geqslant 0$, + \begin{itemize} + \item for $x\in\Sigma:=\{x:\ u_n(x)>1\}$, + $$ + -\Delta u_n<-4e+2e\rho_{n-1}u_{n-1}\ast u_{n-1} + \leqslant-2e + <0 + $$ + (since $u_{n-1}\ast u_{n-1}\leqslant\|u_{n-1}\|_\infty\| u_{n-1}\|_1<\frac1{\rho_{n-1}}$). + \item Therefore $u_n$ is subharmonic on $\Sigma$, so it reaches its maximum on $\partial\Sigma$. + But, for $x\in\partial\Sigma$, $u_n(x)=1$, so $u_n(x)\leqslant 1$ in $\Sigma$, so $\Sigma=\emptyset$. + \end{itemize} +\end{itemize} +\vfill +\eject + +\title{Uniqueness} +\begin{itemize} + \item In addition, one can prove that the limiting $u$ is the unique non-negative integrable solution of the simple equation, for every fixed $e$. + + \item In addition, we prove that $e\mapsto\rho(e)$ is continuous, and $\rho(0)=0$ and $\rho(\infty)=\infty$, which allows us to compute solutions for the problem at fixed $\rho$. + + \item In order to show uniqueness of the solution of the simple equation for fixed $\rho$, one would have to show that $e\mapsto\rho(e)$ is monotone. + + \item Nevertheless, all non-negative integrable solutions are obtained by taking the limit of the sequence $u_n$ with the appropriate $e$. +\end{itemize} +\vfill +\eject + +\title{Asymptotics (sketch)} +\vskip-10pt +\begin{itemize} + $$ + -\Delta u=(1-u)v-4eu+2e\rho u\ast u + ,\quad + e=\frac\rho2\int dx\ (1-u(x))v(x) + . + $$ + \item When $\rho$ is small, $e$ is small as well, so the solution $u$ is {\it not too far from} the solution of the scattering equation + $$ + (-\Delta+v)\varphi=v + . + $$ + + \item The energy of $\varphi$ is + $$ + \frac\rho 2\int dx\ (1-\varphi(x))v(x)=2\pi\rho a + $$ + which yields the first term in the expansion. +\end{itemize} +\vfill +\eject + +\title{Asymptotics (sketch)} + $$ + -\Delta u=(1-u)v-4eu+2e\rho u\ast u + ,\quad + \frac{2e}\rho=\int dx\ (1-u(x))v(x) + . + $$ +\begin{itemize} + \item We work in Fourier space: + $$ + \rho \hat u(k)=\frac{k^2}{4e}+1-\sqrt{\left(\frac{k^2}{4e}+1\right)^2-\frac\rho{2e}\hat S(k)} + $$ + where $\hat S$ is the Fourier transform of $(1-u)v$. + + \item Small $e$ is related to small $k$. We approximate $\hat S(k)$ by $\hat S(0)=\frac{2e}\rho$, and control the error terms. +\end{itemize} +\vfill +\eject + +\title{Decay (sketch)} +$$ + u=(-\Delta+4e)^{-1}\left((1-u)v+2e\rho u\ast u\right) + ,\quad + e=\frac\rho2\int dx\ (1-u(x))v(x) +$$ +\begin{itemize} + \item $(-\Delta+4e)^{-1}$ has an exponentially decaying kernel, so $u$ cannot decay faster than $2e\rho u\ast u$. + + \item This is true for algebraically decaying functions: if $u\sim \alpha|x|^{-n}$ with $n>3$, then + $$ + u\ast u\sim \frac{2\alpha\int u}{|x|^n}. + $$ + + \item But why $|x|^{-4}$? +\end{itemize} +\vfill +\eject + +\title{Decay (sketch)} +$$ + u=(-\Delta+4e)^{-1}\left((1-u)v+2e\rho u\ast u\right) +$$ +\begin{itemize} + \item $w:=2e\rho (-\Delta+4e)^{-1}u$ satisfies + $$ + w=2e\rho (-\Delta+4e)^{-2}(1-u)v+w\ast w\geqslant w\ast w + ,\quad + \int w=\frac12 + . + $$ + \item {\bf Theorem} \href{https://arxiv.org/abs/2002.04184}{[Carlen, Jauslin, Lieb, Loss, 2020]}: for $0\leqslant \alpha<1$, + $$ + \int dx\ |x|w(x)=\infty + ,\quad + \int dx\ |x|^\alpha w(x)<\infty + . + $$ + Furthermore, $w\geqslant 0$. +\end{itemize} +\vfill +\eject + +\title{Full equation} +\hfil\includegraphics[height=5.5cm]{erho_fulleq.pdf} + +\hfil{\footnotesize Monte Carlo computation courtesy of M. Holzmann} +\vfill +\eject + +\title{Condensate fraction} +\hfil\includegraphics[height=5.5cm]{condensate.pdf} + +\hfil{\footnotesize Monte Carlo computation courtesy of M. Holzmann} +\vfill + +\title{Conclusion} +\vfill +\begin{itemize} + \item Simple equation: correct asymptotics for the ground state energy at both high and low densities. + + \item Condensate fraction seems right at low densities. + + \item Intriguing non-linear PDE. + + \item Proved existence, asymptotics, and decay rate. + + \item Full equation: does even better for the energy and condensate fraction. +\end{itemize} +\vfill +\eject + +\title{Open problems and conjectures} +\begin{itemize} + \item Monotonicity of $e\mapsto\rho(e)$, and concavity of $e\mapsto\frac1{\rho(e)}$ (would imply uniqueness). (So far, we have proofs for small and large $\rho$.) + + \item Condensate fraction: prove that $0\leqslant\eta\leqslant 1$. (Again, we have a proof for small and large $\rho$.) + + \item Other equations: interpolate between full equation and simple equation. + + \item Potentials which are not $\geqslant 0$? +\end{itemize} + +\end{document} diff --git a/Makefile b/Makefile new file mode 100644 index 0000000..74cd1ca --- /dev/null +++ b/Makefile @@ -0,0 +1,50 @@ +PROJECTNAME=$(basename $(wildcard *.tex)) +LIBS=$(notdir $(wildcard libs/*)) +FIGS=$(notdir $(wildcard figs/*.fig)) +PNGS=$(notdir $(wildcard figs/*.png)) + +PDFS=$(addsuffix .pdf, $(PROJECTNAME)) +SYNCTEXS=$(addsuffix .synctex.gz, $(PROJECTNAME)) + +all: $(PROJECTNAME) + +$(PROJECTNAME): $(LIBS) $(FIGS) $(PNGS) + pdflatex -file-line-error $@.tex + pdflatex -synctex=1 $@.tex + +$(SYNCTEXS): $(LIBS) $(FIGS) $(PNGS) + pdflatex -synctex=1 $(patsubst %.synctex.gz, %.tex, $@) + + +$(LIBS): + ln -fs libs/$@ ./ + + +$(FIGS): + make -C figs/$@ + for pdf in $$(find figs/$@/ -name '*.pdf'); do ln -fs "$$pdf" ./ ; done + +$(PNGS): + ln -fs figs/$@ ./ + + +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) $(SYNCTEXS) + +clean: clean-aux clean-tex clean-libs clean-figs @@ -0,0 +1,32 @@ +This directory contains the source files to typeset the presentation, and +generate the figures. This can be accomplished by running + make + +This document uses a custom class file, located in the 'libs' directory, which +defines a number of commands. + + +* Dependencies: + + pdflatex + TeXlive packages: + amsfonts + array + graphics + hyperref + latex + pgf + standalone + GNU make + gnuplot + +* Files: + + Jauslin_Harvard_RM_2020.tex: + main LaTeX file + + libs: + custom LaTeX class file + + figs: + source code for the figures diff --git a/figs/plots.fig/Makefile b/figs/plots.fig/Makefile new file mode 100644 index 0000000..9b08148 --- /dev/null +++ b/figs/plots.fig/Makefile @@ -0,0 +1,28 @@ +PROJECTNAME=erho_effective erho_fulleq condensate + +PDFS=$(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 $(PDFS) + +clean: clean-libs clean-aux clean-tex diff --git a/figs/plots.fig/condensate.gnuplot b/figs/plots.fig/condensate.gnuplot new file mode 100644 index 0000000..8b4579a --- /dev/null +++ b/figs/plots.fig/condensate.gnuplot @@ -0,0 +1,36 @@ +set ylabel "$\\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 "condensate_simpleq.dat" u 1:(1-$2) w l ls 1, \ + "condensate_fulleq.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/plots.fig/condensate_fulleq.dat b/figs/plots.fig/condensate_fulleq.dat new file mode 100644 index 0000000..d2ed0d4 --- /dev/null +++ b/figs/plots.fig/condensate_fulleq.dat @@ -0,0 +1,100 @@ + #1.000000000000000e-06 -8.614938818503196e-02 + #1.202264434617413e-06 -9.766116625085511e-02 + #1.445439770745928e-06 -1.086260326967837e-01 + #1.737800828749376e-06 -1.188900378151884e-01 + #2.089296130854041e-06 -1.165715185508008e-01 + #2.511886431509582e-06 -1.250759588981834e-01 + #3.019951720402019e-06 -1.268149860317770e-01 + #3.630780547701017e-06 -1.008774209546726e-01 + #4.365158322401657e-06 -6.384109793944306e-02 + #5.248074602497723e-06 -3.305204372052289e-02 + #6.309573444801930e-06 -1.363639580237857e-02 + #7.585775750291836e-06 -2.687137270988418e-03 + #9.120108393559096e-06 3.166008919824121e-03 + #1.096478196143185e-05 6.184918017260721e-03 + #1.318256738556407e-05 7.747932088893341e-03 + #1.584893192461114e-05 8.662355141522138e-03 + 1.905460717963248e-05 9.371765974117721e-03 + 2.290867652767775e-05 1.009387581263716e-02 + 2.754228703338163e-05 1.091616583083455e-02 + 3.311311214825908e-05 1.186061437823890e-02 + 3.981071705534969e-05 1.292387505733936e-02 + 4.786300923226380e-05 1.409873146023454e-02 + 5.754399373371566e-05 1.538267140810235e-02 + 6.918309709189363e-05 1.677890896567674e-02 + 8.317637711026709e-05 1.829411171824110e-02 + 1.000000000000000e-04 1.993571803225050e-02 + 1.202264434617413e-04 2.171031767662337e-02 + 1.445439770745928e-04 2.362335416481030e-02 + 1.737800828749376e-04 2.567961076697717e-02 + 2.089296130854039e-04 2.788370415580528e-02 + 2.511886431509580e-04 3.024006412149300e-02 + 3.019951720402016e-04 3.275234236798458e-02 + 3.630780547701014e-04 3.542253918502022e-02 + 4.365158322401661e-04 3.825019662026136e-02 + 5.248074602497728e-04 4.123183951806994e-02 + 6.309573444801930e-04 4.436063221009928e-02 + 7.585775750291835e-04 4.762610773130148e-02 + 9.120108393559096e-04 5.101385275574772e-02 + 1.096478196143185e-03 5.450513498525032e-02 + 1.318256738556408e-03 5.807655754936158e-02 + 1.584893192461114e-03 6.169986685522461e-02 + 1.905460717963246e-03 6.534202152307987e-02 + 2.290867652767772e-03 6.896557615548764e-02 + 2.754228703338166e-03 7.252937827034577e-02 + 3.311311214825911e-03 7.598954163862429e-02 + 3.981071705534973e-03 7.930064515549705e-02 + 4.786300923226385e-03 8.241709976189890e-02 + 5.754399373371567e-03 8.529461702611295e-02 + 6.918309709189363e-03 8.789170543663596e-02 + 8.317637711026709e-03 9.017112178408174e-02 + 1.000000000000000e-02 9.210121105163713e-02 + 1.202264434617413e-02 9.365706524811174e-02 + 1.445439770745928e-02 9.482141728116293e-02 + 1.737800828749376e-02 9.558518071743499e-02 + 2.089296130854041e-02 9.594757348717294e-02 + 2.511886431509582e-02 9.591581884687068e-02 + 3.019951720402019e-02 9.550446752089987e-02 + 3.630780547701010e-02 9.473440574899994e-02 + 4.365158322401656e-02 9.363161664666107e-02 + 5.248074602497723e-02 9.222577960370333e-02 + 6.309573444801930e-02 9.054883426175536e-02 + 7.585775750291836e-02 8.863366924323736e-02 + 9.120108393559097e-02 8.651307558708890e-02 + 1.096478196143185e-01 8.421902020041082e-02 + 1.318256738556407e-01 8.178218705614894e-02 + 1.584893192461114e-01 7.923166661365826e-02 + 1.905460717963248e-01 7.659468332934523e-02 + 2.290867652767775e-01 7.389632123698403e-02 + 2.754228703338169e-01 7.115928555205950e-02 + 3.311311214825908e-01 6.840377345182166e-02 + 3.981071705534969e-01 6.564750307407688e-02 + 4.786300923226380e-01 6.290588873608968e-02 + 5.754399373371566e-01 6.019229370079152e-02 + 6.918309709189363e-01 5.751827233449629e-02 + 8.317637711026709e-01 5.489373839406184e-02 + 1.000000000000000e+00 5.232704754857587e-02 + 1.202264434617413e+00 4.982503104737237e-02 + 1.445439770745928e+00 4.739304037479557e-02 + 1.737800828749376e+00 4.503505262022169e-02 + 2.089296130854041e+00 4.275385260331126e-02 + 2.511886431509582e+00 4.055126928839553e-02 + 3.019951720402019e+00 3.842841870725856e-02 + 3.630780547701010e+00 3.638590295621058e-02 + 4.365158322401657e+00 3.442393313982928e-02 + 5.248074602497723e+00 3.254237317563782e-02 + 6.309573444801930e+00 3.074072814466525e-02 + 7.585775750291836e+00 2.901811533232729e-02 + 9.120108393559097e+00 2.737325456775722e-02 + 1.096478196143185e+01 2.580449985960452e-02 + 1.318256738556407e+01 2.430991392870668e-02 + 1.584893192461114e+01 2.288736930953625e-02 + 1.905460717963248e+01 2.153465030968419e-02 + 2.290867652767775e+01 2.024953133089283e-02 + 2.754228703338169e+01 1.902981682025423e-02 + 3.311311214825908e+01 1.787334174054898e-02 + 3.981071705534969e+01 1.677794371478593e-02 + 4.786300923226381e+01 1.574142505712074e-02 + 5.754399373371567e+01 1.476152324305837e-02 + 6.918309709189363e+01 1.383590285833535e-02 + 8.317637711026708e+01 1.296217324309031e-02 diff --git a/figs/plots.fig/condensate_simpleq.dat b/figs/plots.fig/condensate_simpleq.dat new file mode 100644 index 0000000..348121c --- /dev/null +++ b/figs/plots.fig/condensate_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/plots.fig/erho.dat b/figs/plots.fig/erho.dat new file mode 100644 index 0000000..837439f --- /dev/null +++ b/figs/plots.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/plots.fig/erho_effective.gnuplot b/figs/plots.fig/erho_effective.gnuplot new file mode 100644 index 0000000..f26252e --- /dev/null +++ b/figs/plots.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/plots.fig/erho_fulleq.dat b/figs/plots.fig/erho_fulleq.dat new file mode 100644 index 0000000..351d1b9 --- /dev/null +++ b/figs/plots.fig/erho_fulleq.dat @@ -0,0 +1,100 @@ + 1.000000000000000e-06 7.943042518656766e-06 0 + 1.202264434617413e-06 9.550219866068997e-06 0 + 1.445439770745928e-06 1.148608224097378e-05 1 + 1.737800828749376e-06 1.381647407426905e-05 1 + 2.089296130854041e-06 1.662160583174429e-05 0 + 2.511886431509582e-06 2.000065135391551e-05 0 + 3.019951720402019e-06 2.406839054942614e-05 0 + 3.630780547701017e-06 2.896662133595565e-05 1 + 4.365158322401657e-06 3.486570260772683e-05 1 + 5.248074602497723e-06 4.197087478032896e-05 1 + 6.309573444801930e-06 5.052956242205629e-05 1 + 7.585775750291836e-06 6.084048678334965e-05 1 + 9.120108393559096e-06 7.326450648917462e-05 1 + 1.096478196143185e-05 8.823760552067889e-05 1 + 1.318256738556407e-05 1.062866339996179e-04 1 + 1.584893192461114e-05 1.280484412743087e-04 1 + 1.905460717963248e-05 1.542931396948374e-04 1 + 2.290867652767775e-05 1.859523935537466e-04 1 + 2.754228703338163e-05 2.241538298379074e-04 1 + 3.311311214825908e-05 2.702629184292266e-04 1 + 3.981071705534969e-05 3.259339774051344e-04 1 + 4.786300923226380e-05 3.931723354869787e-04 1 + 5.754399373371566e-05 4.744101435386617e-04 1 + 6.918309709189363e-05 5.725988899895806e-04 1 + 8.317637711026709e-05 6.913223659756494e-04 1 + 1.000000000000000e-04 8.349346745163116e-04 1 + 1.202264434617413e-04 1.008728918608530e-03 1 + 1.445439770745928e-04 1.219143475424315e-03 1 + 1.737800828749376e-04 1.474014314386416e-03 1 + 2.089296130854039e-04 1.782883700975914e-03 1 + 2.511886431509580e-04 2.157377911005317e-03 1 + 3.019951720402016e-04 2.611669336976909e-03 1 + 3.630780547701014e-04 3.163041683927843e-03 1 + 4.365158322401661e-04 3.832580921405091e-03 1 + 5.248074602497728e-04 4.646019387820095e-03 1 + 6.309573444801930e-04 5.634766055532872e-03 1 + 7.585775750291835e-04 6.837162598523666e-03 1 + 9.120108393559096e-04 8.300012713479526e-03 1 + 1.096478196143185e-03 1.008044129788173e-02 1 + 1.318256738556408e-03 1.224815077758103e-02 1 + 1.584893192461114e-03 1.488815434797412e-02 1 + 1.905460717963246e-03 1.810408049926405e-02 1 + 2.290867652767772e-03 2.202216044849479e-02 1 + 2.754228703338166e-03 2.679603069994577e-02 1 + 3.311311214825911e-03 3.261250778551406e-02 1 + 3.981071705534973e-03 3.969852233927642e-02 1 + 4.786300923226385e-03 4.832943621884326e-02 1 + 5.754399373371567e-03 5.883901075761193e-02 1 + 6.918309709189363e-03 7.163134806415740e-02 1 + 8.317637711026709e-03 8.719519272244317e-02 1 + 1.000000000000000e-02 1.061210611088454e-01 1 + 1.202264434617413e-02 1.291217632376783e-01 1 + 1.445439770745928e-02 1.570570011615084e-01 1 + 1.737800828749376e-02 1.909628719282619e-01 1 + 2.089296130854041e-02 2.320872756251715e-01 1 + 2.511886431509582e-02 2.819324351385837e-01 1 + 3.019951720402019e-02 3.423059810454135e-01 1 + 3.630780547701010e-02 4.153823512868898e-01 1 + 4.365158322401656e-02 5.037766102499891e-01 1 + 5.248074602497723e-02 6.106332154610473e-01 1 + 6.309573444801930e-02 7.397327648968161e-01 1 + 7.585775750291836e-02 8.956203622431048e-01 1 + 9.120108393559097e-02 1.083759966304908e+00 1 + 1.096478196143185e-01 1.310719973979596e+00 1 + 1.318256738556407e-01 1.584396355238566e+00 1 + 1.584893192461114e-01 1.914280945866737e+00 1 + 1.905460717963248e-01 2.311784046064119e+00 1 + 2.290867652767775e-01 2.790622317703228e+00 1 + 2.754228703338169e-01 3.367285183378040e+00 1 + 3.311311214825908e-01 4.061595587917465e+00 1 + 3.981071705534969e-01 4.897384186423424e+00 1 + 4.786300923226380e-01 5.903299886083452e+00 1 + 5.754399373371566e-01 7.113784322007290e+00 1 + 6.918309709189363e-01 8.570243441380599e+00 1 + 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/plots.fig/erho_fulleq.gnuplot b/figs/plots.fig/erho_fulleq.gnuplot new file mode 100644 index 0000000..2927ead --- /dev/null +++ b/figs/plots.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/plots.fig/holzmann_2019-12-25.dat b/figs/plots.fig/holzmann_2019-12-25.dat new file mode 100644 index 0000000..96689cb --- /dev/null +++ b/figs/plots.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 |