diff --git a/flake.nix b/flake.nix index 5f85282..04c1e07 100644 --- a/flake.nix +++ b/flake.nix @@ -8,49 +8,50 @@ outputs = { self, nixpkgs, flake-utils }: with flake-utils.lib; eachSystem allSystems (system: - let - pkgs = nixpkgs.legacyPackages.${system}; - tex = pkgs.texlive.combine { - inherit (pkgs.texlive) scheme-medium latexmk koma-script babel-english - physics mathtools amsmath fontspec booktabs siunitx caption biblatex float - pgfplots microtype fancyvrb csquotes setspace newunicodechar hyperref - cleveref multirow bbold unicode-math biblatex-phys xpatch beamerposter - type1cm changepage lualatex-math footmisc wrapfig2 curve2e pict2e wrapfig - appendixnumberbeamer sidecap appendix orcidlink ncctools bigfoot crop xcolor; - }; - in rec { - packages = { - watch = pkgs.writeShellScriptBin "watch-latex" '' - ${tex}/bin/latexmk - while ${pkgs.inotify-tools}/bin/inotifywait --include ".*\.(sty|tex|pgf|pdf)" -e modify -r .; do - ${tex}/bin/latexmk - done - ''; - document = pkgs.stdenvNoCC.mkDerivation rec { - name = "masters-thesis"; - src = self; - buildInputs = [ pkgs.coreutils tex pkgs.biber]; - phases = ["unpackPhase" "buildPhase" "installPhase"]; - buildPhase = '' - export PATH="${pkgs.lib.makeBinPath buildInputs}"; - mkdir -p .cache/texmf-var - mkdir -p output/src - env TEXMFHOME=.cache TEXMFVAR=.cache/texmf-var \ - OSFONTDIR=${pkgs.gyre-fonts}/share/fonts:${pkgs.liberation_ttf}/share/fonts:${pkgs.lato}/share/fonts/lato:${pkgs.raleway}/share/fonts:${pkgs.lmodern}/share/fonts \ - latexmk ./index.tex + let + pkgs = nixpkgs.legacyPackages.${system}; + tex = pkgs.texlive.combine { + inherit (pkgs.texlive) scheme-medium latexmk koma-script babel-english + physics mathtools amsmath fontspec booktabs siunitx caption biblatex float + pgfplots microtype fancyvrb csquotes setspace newunicodechar hyperref + cleveref multirow bbold unicode-math biblatex-phys xpatch beamerposter + type1cm changepage lualatex-math footmisc wrapfig2 curve2e pict2e wrapfig + appendixnumberbeamer sidecap appendix orcidlink ncctools bigfoot crop xcolor; + }; + in + rec { + packages = { + watch = pkgs.writeShellScriptBin "watch-latex" '' + ${tex}/bin/latexmk + while ${pkgs.inotify-tools}/bin/inotifywait --include ".*\.(sty|tex|pgf|pdf)" -e modify -r .; do + ${tex}/bin/latexmk + done ''; - installPhase = '' - mkdir -p $out - cp output/index.pdf $out/ + document = pkgs.stdenvNoCC.mkDerivation rec { + name = "masters-thesis"; + src = self; + buildInputs = [ pkgs.coreutils tex pkgs.biber ]; + phases = [ "unpackPhase" "buildPhase" "installPhase" ]; + buildPhase = '' + export PATH="${pkgs.lib.makeBinPath buildInputs}"; + mkdir -p .cache/texmf-var + mkdir -p output/src + env TEXMFHOME=.cache TEXMFVAR=.cache/texmf-var \ + OSFONTDIR=${pkgs.gyre-fonts}/share/fonts:${pkgs.liberation_ttf}/share/fonts:${pkgs.lato}/share/fonts/lato:${pkgs.raleway}/share/fonts:${pkgs.lmodern}/share/fonts \ + latexmk ./index.tex + ''; + installPhase = '' + mkdir -p $out + cp output/index.pdf $out/ + ''; + }; + }; + defaultPackage = packages.document; + devShell = pkgs.mkShellNoCC { + buildInputs = [ packages.watch pkgs.openjdk ] ++ packages.document.buildInputs; + shellHook = '' + export OSFONTDIR=${pkgs.gyre-fonts}/share/fonts:${pkgs.liberation_ttf}/share/fonts:${pkgs.lato}/share/fonts/lato:${pkgs.raleway}/share/fonts:${pkgs.lmodern}/share/fonts ''; }; - }; - defaultPackage = packages.document; - devShell = pkgs.mkShellNoCC { - buildInputs = [packages.watch pkgs.openjdk] ++ packages.document.buildInputs; - shellHook = '' - export OSFONTDIR=${pkgs.gyre-fonts}/share/fonts:${pkgs.liberation_ttf}/share/fonts:${pkgs.lato}/share/fonts/lato:${pkgs.raleway}/share/fonts:${pkgs.lmodern}/share/fonts - ''; - }; - }); + }); } diff --git a/talk_short/figs/01/flow.pdf b/talk_short/figs/01/flow.pdf new file mode 100644 index 0000000..2d7a45c Binary files /dev/null and b/talk_short/figs/01/flow.pdf differ diff --git a/talk_short/figs/01/flow.pgf b/talk_short/figs/01/flow.pgf new file mode 100644 index 0000000..e8516be --- /dev/null +++ b/talk_short/figs/01/flow.pgf @@ -0,0 +1,39784 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{3.307043in}{2.645634in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{0.500000,0.500000,0.500000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{3.307043in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{3.307043in}{2.645634in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{2.645634in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{0.898039,0.898039,0.898039}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetstrokeopacity{0.000000}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.742014in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{3.157043in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{3.157043in}{2.495634in}}% +\pgfpathlineto{\pgfqpoint{0.742014in}{2.495634in}}% +\pgfpathlineto{\pgfqpoint{0.742014in}{0.552778in}}% +\pgfpathclose% +\pgfusepath{fill}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.742014in}{0.552778in}}{\pgfqpoint{2.415029in}{1.942857in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.851788in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{0.851788in}{2.495634in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.851788in}{0.552778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.851788in,y=0.455556in,,top]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 0}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.742014in}{0.552778in}}{\pgfqpoint{2.415029in}{1.942857in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{1.217701in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{1.217701in}{2.495634in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.217701in}{0.552778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.217701in,y=0.455556in,,top]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 5}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.742014in}{0.552778in}}{\pgfqpoint{2.415029in}{1.942857in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{1.583615in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{1.583615in}{2.495634in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.583615in}{0.552778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.583615in,y=0.455556in,,top]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 10}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.742014in}{0.552778in}}{\pgfqpoint{2.415029in}{1.942857in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{1.949528in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{1.949528in}{2.495634in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.949528in}{0.552778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.949528in,y=0.455556in,,top]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 15}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.742014in}{0.552778in}}{\pgfqpoint{2.415029in}{1.942857in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{2.315442in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{2.315442in}{2.495634in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{2.315442in}{0.552778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.315442in,y=0.455556in,,top]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 20}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.742014in}{0.552778in}}{\pgfqpoint{2.415029in}{1.942857in}}% +\pgfusepath{clip}% +\pgfsetrectcap% 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+\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.681355in,y=0.455556in,,top]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 25}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.742014in}{0.552778in}}{\pgfqpoint{2.415029in}{1.942857in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{3.047269in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{3.047269in}{2.495634in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% 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+\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.610166in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{0.610166in}{1.836142in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.610166in}{0.552778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% 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+\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.088079in}{0.552778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.088079in,y=0.455556in,,top]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 1}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.514583in}{0.552778in}}{\pgfqpoint{2.102817in}{1.283364in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{1.565992in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{1.565992in}{1.836142in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.565992in}{0.552778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.565992in,y=0.455556in,,top]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 2}% +\end{pgfscope}% +\begin{pgfscope}% 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+\begin{pgfscope}% +\pgfsys@transformshift{2.043905in}{0.552778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.043905in,y=0.455556in,,top]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 3}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.514583in}{0.552778in}}{\pgfqpoint{2.102817in}{1.283364in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{2.521817in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{2.521817in}{1.836142in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% 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only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{2.767400in}{2.213920in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{0.500000,0.500000,0.500000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{2.767400in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{2.767400in}{2.213920in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{2.213920in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathclose% 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are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{3.307043in}{2.645634in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{0.500000,0.500000,0.500000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{3.307043in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{3.307043in}{2.645634in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{2.645634in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathclose% 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For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{3.307043in}{2.645634in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{0.500000,0.500000,0.500000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{3.307043in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{3.307043in}{2.645634in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{2.645634in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathclose% 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+\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{1.006570in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{1.006570in}{2.495634in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.006570in}{0.552778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.006570in,y=0.455556in,,top]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 0}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.904167in}{0.552778in}}{\pgfqpoint{2.252876in}{1.942857in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{1.689260in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{1.689260in}{2.495634in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.689260in}{0.552778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.689260in,y=0.455556in,,top]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 10}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.904167in}{0.552778in}}{\pgfqpoint{2.252876in}{1.942857in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{2.371950in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{2.371950in}{2.495634in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{2.371950in}{0.552778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.371950in,y=0.455556in,,top]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 20}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.904167in}{0.552778in}}{\pgfqpoint{2.252876in}{1.942857in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{3.054640in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{3.054640in}{2.495634in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.054640in}{0.552778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=3.054640in,y=0.455556in,,top]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 30}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.030605in,y=0.301333in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle τ\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.904167in}{0.552778in}}{\pgfqpoint{2.252876in}{1.942857in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.904167in}{0.633916in}}% +\pgfpathlineto{\pgfqpoint{3.157043in}{0.633916in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.904167in}{0.633916in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.446344in, y=0.595361in, left, base]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont \ensuremath{-}0.175}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.904167in}{0.552778in}}{\pgfqpoint{2.252876in}{1.942857in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.904167in}{0.887075in}}% +\pgfpathlineto{\pgfqpoint{3.157043in}{0.887075in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.904167in}{0.887075in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.446344in, y=0.848520in, left, base]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont \ensuremath{-}0.150}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.904167in}{0.552778in}}{\pgfqpoint{2.252876in}{1.942857in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.904167in}{1.140234in}}% +\pgfpathlineto{\pgfqpoint{3.157043in}{1.140234in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.904167in}{1.140234in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.446344in, y=1.101679in, left, base]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont \ensuremath{-}0.125}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.904167in}{0.552778in}}{\pgfqpoint{2.252876in}{1.942857in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.904167in}{1.393393in}}% +\pgfpathlineto{\pgfqpoint{3.157043in}{1.393393in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.904167in}{1.393393in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.446344in, y=1.354837in, left, base]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont \ensuremath{-}0.100}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.904167in}{0.552778in}}{\pgfqpoint{2.252876in}{1.942857in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.904167in}{1.646552in}}% +\pgfpathlineto{\pgfqpoint{3.157043in}{1.646552in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.904167in}{1.646552in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% 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+\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.904167in}{1.899711in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.446344in, y=1.861155in, left, base]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont \ensuremath{-}0.050}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.904167in}{0.552778in}}{\pgfqpoint{2.252876in}{1.942857in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.904167in}{2.152870in}}% +\pgfpathlineto{\pgfqpoint{3.157043in}{2.152870in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.904167in}{2.152870in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% 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+%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. 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main LaTeX file. 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+%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{3.307043in}{2.645634in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{0.500000,0.500000,0.500000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{3.307043in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{3.307043in}{2.645634in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{2.645634in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathclose% 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instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. 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directory as the main LaTeX file. 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100644 index 0000000..5502ba3 --- /dev/null +++ b/talk_short/figs/05/cholesky.pgf @@ -0,0 +1,1242 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.405701in}{1.321710in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{0.500000,0.500000,0.500000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{4.405701in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{4.405701in}{1.321710in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{1.321710in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathclose% 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diff --git a/talk_short/figs/05/flow.pgf b/talk_short/figs/05/flow.pgf new file mode 100644 index 0000000..ae126a6 --- /dev/null +++ b/talk_short/figs/05/flow.pgf @@ -0,0 +1,15160 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. 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Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. 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For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{3.307043in}{2.645634in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{0.500000,0.500000,0.500000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{3.307043in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{3.307043in}{2.645634in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{2.645634in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathclose% 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+\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.998417in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{0.998417in}{2.298803in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.998417in}{0.552778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.998417in,y=0.455556in,,top]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 0}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.895625in}{0.552778in}}{\pgfqpoint{2.261418in}{1.746025in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{1.409584in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{1.409584in}{2.298803in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.409584in}{0.552778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.409584in,y=0.455556in,,top]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 10}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.895625in}{0.552778in}}{\pgfqpoint{2.261418in}{1.746025in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{1.820751in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{1.820751in}{2.298803in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.820751in}{0.552778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=1.820751in,y=0.455556in,,top]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 20}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.895625in}{0.552778in}}{\pgfqpoint{2.261418in}{1.746025in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{2.231917in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{2.231917in}{2.298803in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{2.231917in}{0.552778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.231917in,y=0.455556in,,top]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 30}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.895625in}{0.552778in}}{\pgfqpoint{2.261418in}{1.746025in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{2.643084in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{2.643084in}{2.298803in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{2.643084in}{0.552778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.643084in,y=0.455556in,,top]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 40}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.895625in}{0.552778in}}{\pgfqpoint{2.261418in}{1.746025in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{3.054251in}{0.552778in}}% +\pgfpathlineto{\pgfqpoint{3.054251in}{2.298803in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{-0.048611in}}{\pgfqpoint{0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{-0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.054251in}{0.552778in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=3.054251in,y=0.455556in,,top]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 50}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=2.026334in,y=0.301333in,,top]{\color{textcolor}\rmfamily\fontsize{10.000000}{12.000000}\selectfont \(\displaystyle τ\)}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.895625in}{0.552778in}}{\pgfqpoint{2.261418in}{1.746025in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.895625in}{0.632143in}}% +\pgfpathlineto{\pgfqpoint{3.157043in}{0.632143in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.895625in}{0.632143in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.470625in, y=0.593587in, left, base]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 0.0000}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.895625in}{0.552778in}}{\pgfqpoint{2.261418in}{1.746025in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.895625in}{0.993706in}}% +\pgfpathlineto{\pgfqpoint{3.157043in}{0.993706in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.895625in}{0.993706in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.470625in, y=0.955151in, left, base]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 0.0005}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.895625in}{0.552778in}}{\pgfqpoint{2.261418in}{1.746025in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.895625in}{1.355270in}}% +\pgfpathlineto{\pgfqpoint{3.157043in}{1.355270in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.895625in}{1.355270in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.470625in, y=1.316715in, left, base]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 0.0010}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.895625in}{0.552778in}}{\pgfqpoint{2.261418in}{1.746025in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.895625in}{1.716834in}}% +\pgfpathlineto{\pgfqpoint{3.157043in}{1.716834in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.895625in}{1.716834in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.470625in, y=1.678279in, left, base]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 0.0015}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.895625in}{0.552778in}}{\pgfqpoint{2.261418in}{1.746025in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.895625in}{2.078398in}}% +\pgfpathlineto{\pgfqpoint{3.157043in}{2.078398in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{0.895625in}{2.078398in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.470625in, y=2.039843in, left, base]{\color{textcolor}\rmfamily\fontsize{8.000000}{9.600000}\selectfont 0.0020}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% 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a/talk_short/figs/05/flow_conv_0.svg b/talk_short/figs/05/flow_conv_0.svg new file mode 100644 index 0000000..600025c --- /dev/null +++ b/talk_short/figs/05/flow_conv_0.svg @@ -0,0 +1,3019 @@ + + + + + + + + 1980-01-01T00:00:00+00:00 + image/svg+xml + + + Matplotlib v3.5.1, https://matplotlib.org/ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 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Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{3.307043in}{2.645634in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{0.500000,0.500000,0.500000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{3.307043in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{3.307043in}{2.645634in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{2.645634in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathclose% 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necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. 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loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. 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Inkscape, but the package 'color.sty' is not loaded}% + \renewcommand\color[2][]{}% + }% + \providecommand\transparent[1]{% + \errmessage{(Inkscape) Transparency is used (non-zero) for the text in Inkscape, but the package 'transparent.sty' is not loaded}% + \renewcommand\transparent[1]{}% + }% + \providecommand\rotatebox[2]{#2}% + \newcommand*\fsize{\dimexpr\f@size pt\relax}% + \newcommand*\lineheight[1]{\fontsize{\fsize}{#1\fsize}\selectfont}% + \ifx\svgwidth\undefined% + \setlength{\unitlength}{225.12314203bp}% + \ifx\svgscale\undefined% + \relax% + \else% + \setlength{\unitlength}{\unitlength * \real{\svgscale}}% + \fi% + \else% + \setlength{\unitlength}{\svgwidth}% + \fi% + \global\let\svgwidth\undefined% + \global\let\svgscale\undefined% + \makeatother% + \begin{picture}(1,0.35954775)% + \lineheight{1}% + \setlength\tabcolsep{0pt}% + \put(0,0){\includegraphics[width=\unitlength,page=1]{shovel.pdf}}% + 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\put(0.84038056,0.30920962){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}$J(\omega)$\end{tabular}}}}% + \put(0.96273157,0.27894832){\color[rgb]{0,0,0}\makebox(0,0)[lt]{\lineheight{1.25}\smash{\begin{tabular}[t]{l}\tiny{$\omega$}\end{tabular}}}}% + \end{picture}% +\endgroup% diff --git a/talk_short/figs/drawings/shovel.png b/talk_short/figs/drawings/shovel.png new file mode 100644 index 0000000..f30f9c1 Binary files /dev/null and b/talk_short/figs/drawings/shovel.png differ diff --git a/talk_short/figs/drawings/shovel.svg b/talk_short/figs/drawings/shovel.svg new file mode 100644 index 0000000..be45b69 --- /dev/null +++ b/talk_short/figs/drawings/shovel.svg @@ -0,0 +1,477 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + $\ket{\uparrow}$ + + + $\ket{\downarrow}$ + + $H_{\sys}$ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + $H_{\bath}$ + + + + $L(τ)$ + + + + + + + + + + + + $J(\omega)$ + 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+\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{0.000000in}{0.000000in}}{\pgfqpoint{0.000000in}{0.048611in}}{% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{0.048611in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{3.476743in}{2.469051in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=3.476743in,y=2.566273in,,bottom]{\color{textcolor}\rmfamily\fontsize{7.000000}{8.400000}\selectfont 10}% +\end{pgfscope}% +\begin{pgfscope}% 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+\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{1.521626in}{2.003547in}}% +\pgfpathlineto{\pgfqpoint{3.569843in}{2.003547in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfsys@defobject{currentmarker}{\pgfqpoint{-0.048611in}{0.000000in}}{\pgfqpoint{-0.000000in}{0.000000in}}{% +\pgfpathmoveto{\pgfqpoint{-0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{-0.048611in}{0.000000in}}% +\pgfusepath{stroke,fill}% +}% +\begin{pgfscope}% +\pgfsys@transformshift{1.521626in}{2.003547in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.333333,0.333333,0.333333}% +\pgfsetstrokecolor{textcolor}% 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a/talk_short/figs/interaction_orders/k_weights.pdf b/talk_short/figs/interaction_orders/k_weights.pdf new file mode 100644 index 0000000..d04ce71 Binary files /dev/null and b/talk_short/figs/interaction_orders/k_weights.pdf differ diff --git a/talk_short/figs/interaction_orders/k_weights.pgf b/talk_short/figs/interaction_orders/k_weights.pgf new file mode 100644 index 0000000..24ae12a --- /dev/null +++ b/talk_short/figs/interaction_orders/k_weights.pgf @@ -0,0 +1,2764 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.574804in}{2.827385in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{0.500000,0.500000,0.500000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{4.574804in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{4.574804in}{2.827385in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{2.827385in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathclose% 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+\begin{pgfscope}% +\pgfsys@transformshift{0.540139in}{1.819364in}% +\pgfsys@useobject{currentmarker}{}% +\end{pgfscope}% +\end{pgfscope}% +\begin{pgfscope}% +\definecolor{textcolor}{rgb}{0.000000,0.000000,0.000000}% +\pgfsetstrokecolor{textcolor}% +\pgfsetfillcolor{textcolor}% +\pgftext[x=0.300875in, y=1.785628in, left, base]{\color{textcolor}\rmfamily\fontsize{7.000000}{8.400000}\selectfont 0.6}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfpathrectangle{\pgfqpoint{0.540139in}{0.536667in}}{\pgfqpoint{3.914665in}{2.170718in}}% +\pgfusepath{clip}% +\pgfsetrectcap% +\pgfsetroundjoin% +\pgfsetlinewidth{0.803000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.540139in}{2.214040in}}% +\pgfpathlineto{\pgfqpoint{4.454804in}{2.214040in}}% +\pgfusepath{stroke}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetroundjoin% +\definecolor{currentfill}{rgb}{0.000000,0.000000,0.000000}% 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For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.000000in}{4.000000in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetstrokeopacity{0.000000}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{4.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{4.000000in}{4.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{4.000000in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathclose% +\pgfusepath{}% +\end{pgfscope}% +\begin{pgfscope}% +\pgfsetbuttcap% 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diff --git a/talk_short/figs/modcoup/delta_dependence.pdf b/talk_short/figs/modcoup/delta_dependence.pdf new file mode 100644 index 0000000..3c71970 Binary files /dev/null and b/talk_short/figs/modcoup/delta_dependence.pdf differ diff --git a/talk_short/figs/modcoup/omegas_total.pdf b/talk_short/figs/modcoup/omegas_total.pdf new file mode 100644 index 0000000..fca9c9f Binary files /dev/null and b/talk_short/figs/modcoup/omegas_total.pdf differ diff --git a/talk_short/figs/norm_est/norm_estimate_delta.pdf b/talk_short/figs/norm_est/norm_estimate_delta.pdf new file mode 100644 index 0000000..3f72645 Binary files /dev/null and b/talk_short/figs/norm_est/norm_estimate_delta.pdf differ diff --git a/talk_short/figs/norm_est/norm_estimate_delta.pgf b/talk_short/figs/norm_est/norm_estimate_delta.pgf new file mode 100644 index 0000000..39e2ba6 --- /dev/null +++ b/talk_short/figs/norm_est/norm_estimate_delta.pgf @@ -0,0 +1,6704 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. For loading figures +%% from other directories you can use the `import` package +%% \usepackage{import} +%% +%% and then include the figures with +%% \import{}{.pgf} +%% +%% Matplotlib used the following preamble +%% \usepackage{fontspec} +%% +\begingroup% +\makeatletter% +\begin{pgfpicture}% +\pgfpathrectangle{\pgfpointorigin}{\pgfqpoint{4.574804in}{4.241077in}}% +\pgfusepath{use as bounding box, clip}% +\begin{pgfscope}% +\pgfsetbuttcap% +\pgfsetmiterjoin% +\definecolor{currentfill}{rgb}{1.000000,1.000000,1.000000}% +\pgfsetfillcolor{currentfill}% +\pgfsetlinewidth{0.000000pt}% +\definecolor{currentstroke}{rgb}{0.500000,0.500000,0.500000}% +\pgfsetstrokecolor{currentstroke}% +\pgfsetdash{}{0pt}% +\pgfpathmoveto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{4.574804in}{0.000000in}}% +\pgfpathlineto{\pgfqpoint{4.574804in}{4.241077in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{4.241077in}}% +\pgfpathlineto{\pgfqpoint{0.000000in}{0.000000in}}% +\pgfpathclose% 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diff --git a/talk_short/figs/norm_est/norm_estimate_omega.pdf b/talk_short/figs/norm_est/norm_estimate_omega.pdf new file mode 100644 index 0000000..f55f808 Binary files /dev/null and b/talk_short/figs/norm_est/norm_estimate_omega.pdf differ diff --git a/talk_short/figs/norm_est/norm_estimate_omega.pgf b/talk_short/figs/norm_est/norm_estimate_omega.pgf new file mode 100644 index 0000000..dfdc71f --- /dev/null +++ b/talk_short/figs/norm_est/norm_estimate_omega.pgf @@ -0,0 +1,4553 @@ +%% Creator: Matplotlib, PGF backend +%% +%% To include the figure in your LaTeX document, write +%% \input{.pgf} +%% +%% Make sure the required packages are loaded in your preamble +%% \usepackage{pgf} +%% +%% Also ensure that all the required font packages are loaded; for instance, +%% the lmodern package is sometimes necessary when using math font. +%% \usepackage{lmodern} +%% +%% Figures using additional raster images can only be included by \input if +%% they are in the same directory as the main LaTeX file. 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a/talk_short/figs/one_bath_syst/k_systematics_consistency.pdf b/talk_short/figs/one_bath_syst/k_systematics_consistency.pdf new file mode 100644 index 0000000..dcc703c Binary files /dev/null and b/talk_short/figs/one_bath_syst/k_systematics_consistency.pdf differ diff --git a/talk_short/figs/one_bath_syst/k_systematics_flow.pdf b/talk_short/figs/one_bath_syst/k_systematics_flow.pdf new file mode 100644 index 0000000..8a618dd Binary files /dev/null and b/talk_short/figs/one_bath_syst/k_systematics_flow.pdf differ diff --git a/talk_short/figs/one_bath_syst/k_systematics_interaction.pdf b/talk_short/figs/one_bath_syst/k_systematics_interaction.pdf new file mode 100644 index 0000000..ac6154e Binary files /dev/null and b/talk_short/figs/one_bath_syst/k_systematics_interaction.pdf differ diff --git a/talk_short/figs/one_bath_syst/k_systematics_system.pdf b/talk_short/figs/one_bath_syst/k_systematics_system.pdf new file mode 100644 index 0000000..dff7108 Binary files /dev/null and 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a/talk_short/figs/one_bath_syst/omega_energy_overview.pdf b/talk_short/figs/one_bath_syst/omega_energy_overview.pdf new file mode 100644 index 0000000..b757f3b Binary files /dev/null and b/talk_short/figs/one_bath_syst/omega_energy_overview.pdf differ diff --git a/talk_short/figs/one_bath_syst/omega_initial_slip.pdf b/talk_short/figs/one_bath_syst/omega_initial_slip.pdf new file mode 100644 index 0000000..87fd9d4 Binary files /dev/null and b/talk_short/figs/one_bath_syst/omega_initial_slip.pdf differ diff --git a/talk_short/figs/one_bath_syst/omega_interaction.pdf b/talk_short/figs/one_bath_syst/omega_interaction.pdf new file mode 100644 index 0000000..b9a88b4 Binary files /dev/null and b/talk_short/figs/one_bath_syst/omega_interaction.pdf differ diff --git a/talk_short/figs/one_bath_syst/omega_interaction.pgf b/talk_short/figs/one_bath_syst/omega_interaction.pgf new file mode 100644 index 0000000..253378e --- /dev/null +++ b/talk_short/figs/one_bath_syst/omega_interaction.pgf @@ -0,0 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+\usepackage[justification=centering]{caption} +\usepackage[list=true, font=small, +labelformat=brace, position=top]{subcaption} +\usepackage[tbtags]{mathtools} +\usepackage{amssymb} +\usepackage{physics} +\usepackage{cleveref} +\usepackage{graphicx} + +\usepackage{appendixnumberbeamer} +\graphicspath{ {./figs/} {./figs/drawings} } +\usepackage{tikz} +\usepackage{pgfplots} +\usetikzlibrary{calc,matrix,intersections,fillbetween} + + +\usetheme{default} +\usecolortheme{dolphin} +\usefonttheme{professionalfonts} +%\usepackage{newmathpx} +\institute[TUD] % (optional) +{ + TU Dresden +} + +\setbeamertemplate{itemize items}[default] +\setbeamertemplate{enumerate items}[default] +\setbeamertemplate{blocks}[shadow=true] +\setbeamercolor{block title}{use=structure,bg=structure.fg!50, fg=white} +\setbeamercolor{block body}{use=structure,bg=structure.fg!10} + +\AtBeginSection[] +{ + \begin{frame} + \tableofcontents[currentsection] + \end{frame} +} + + +\AtBeginSubsection[] +{ + \begin{frame} + \tableofcontents[currentsubsection] + \end{frame} + } + +\setbeamertemplate{footline}[frame number] +% \setbeamertemplate{bibliography item}{\insertbiblabel} + +\usepackage{pgfpages} +% \setbeameroption{show notes on second screen} + +\makeatletter +\def\beamer@framenotesbegin{% at beginning of slide + \usebeamercolor[fg]{normal text} + \gdef\beamer@noteitems{}% + \gdef\beamer@notes{}% +} +\makeatother + +% Plots +% \newcommand{\plot}[1]{% +% \ifdraft{\includegraphics[draft=false]{#1.pdf}}{\input{./figs/#1.pgf}}} + + + +\addbibresource{references.bib} +\synctex=1 +\title{Bath Observables with HOPS} +\subtitle{Energy Flow in Strongly Coupled Open Quantum Systems} + +\author{\underline{Valentin Boettcher}, Richard Hartmann, + Konstantin Beyer, Walter Strunz} +\titlegraphic{ + \includegraphics[width=2cm]{figs/Logo_TU_Dresden.pdf} +} +\institute{Institute for Theoretical Physics, Dresden, Germany} +\date{17.08.2022} +\beamertemplatenavigationsymbolsempty + +\begin{document} +\hypersetup{pageanchor=false} +\begin{frame}[plain] + \titlepage + %\includegraphics[width=3cm]{figs/Logo_TU_Dresden.pdf} +\end{frame} + +%\hypersetup{pageanchor=true} +\pagenumbering{arabic} +\begin{frame} + \tableofcontents +\end{frame} + + +\section{Introduction} +\label{sec:intro} + +\subsection{Motivation} + +\begin{frame} + \begin{block}{Situation} + Consider an open quantum system + \begin{equation} + \label{eq:openthermo} + H=\underbrace{H_\sys}_{\text{"small"}}\; +\; + \underbrace{H_\inter}_{\mathrm{?}} \;+\; + \underbrace{H_\bath}_{\text{"big", simple}} + \end{equation} + with \([H_S, H_B] = 0\). + \end{block} + \pause + \begin{itemize}[<+->] + \item weak coupling \(H_\inter\approx 0\) + thermodynamics of open systems + are somewhat understood \footcite{Rivas2019Oct,Talkner2020Oct} + \item strong coupling: \(\ev{H_\inter} \sim \ev{H_\sys}\) + \(\implies\) we can't neglect the interaction \(\implies\) + thermodynamics? + \note[item]{we do quantum mechanics \(\implies\) can't separate bath + and system, especially not dynamics!} + \item but what is clear: \emph{need to get access to exact dynamics + of \(H_\inter,H_\bath\)} + \end{itemize} +\end{frame} +\begin{frame} + \begin{center} + \huge{Is that possible? \pause{}Yes.}\\\pause{} + \huge{Using HOPS :)} + \pause{} + \end{center} + \begin{block}{Sneak Peek} + We will be able to calculate + \(\dv{\ev{H_\bath}}{t}\) (and \(\ev{H_\inter}\)). + \begin{itemize} + \item and still more general observables (omitted) + \end{itemize} + \end{block} + \pause{} + \begin{itemize}[<+->] + \item won't call this \emph{heat-flow} because it isn't + \emph{the} thermodynamic heat flow + \item nevertheless: may be interesting \emph{qualitative} measure + for energy flow + \end{itemize} +\end{frame} + +\subsection{Technical Basics} +\begin{frame}{Standard Model of Open Systems} + In the following we will work with models of the form\footnote{Sometimes this + is called the ``Standard Model of Open Systems''.} + \begin{equation} + \label{eq:openmodel} + H = H_\sys(t) + ∑_{n=1}^N \qty[H_\bath\nth + \qty(L_n^†(t)B_n + \hc)], + \end{equation} + + where + \note[item]{mention dimension system h} + \note[item]{special because of separation of the bath couplings} + \begin{itemize} + \item \(H_\sys\) is the System Hamiltonian + \item \(H_B\nth = ∑_λω_λ\nth a_λ^{(n),†}a_λ\nth\) + \item \(B_n=∑_{λ} g_λ\nth a_λ\nth\). + \end{itemize} +\end{frame} +\begin{frame}{What remains of the Bath?} + \begin{block}{Bath Correlation Function} + \[α(t-s) = \ev{B(t)B(s)} \qty(\overset{T=0}{=} ∑_λ + \abs{g_λ}^2\,\eu^{-\iu ω_λ (t-s)})= \frac{1}{π} ∫J(ω) \eu^{-\iu ω + t}\dd{ω}\] + \end{block} + \pause + \begin{block}{Spectral Density} + \[J(ω) = π ∑_{λ} \abs{g_{λ}}^{2}δ(ω-ω_{λ})\] + \begin{itemize} + \item in thermodynamic limit \(\to\) smooth function + \item here usually: Ohmic SD \(J(ω)=η ω \eu^{-ω/ω_c}\) (think phonons) + \end{itemize} + \end{block} +\end{frame} +% \begin{frame} +% \begin{tikzpicture} +% \def\xmin{-.9} +% \def\xmax{.9} +% \def\spacing{1/4} +% \def\maincolor{black} + +% \foreach \n in {0,...,4}{ +% \node (.2\n,.5\n) {test}; +% \draw[\maincolor,domain=\xmin:\xmax,samples=100,smooth,name +% path=harmonic] +% plot (\x,{2*(\x)^2}); + +% \foreach \i in {0,...,5}{ +% \draw[name path=level\i,draw=none] (\xmin,{\spacing * (\i + 1/2)}) -- +% (\xmax,{\spacing * (\i + 1/2)}); +% \draw[name intersections={of=harmonic and level\i}]; +% \draw[\maincolor] (intersection-1) -- (intersection-2); +% } +% } +% \end{tikzpicture} +% \end{frame} + + +\begin{frame}{NMQSD (Zero Temperature)} + Open system dynamics formulated as a \emph{stochastic} differential equation: + \begin{equation} + \label{eq:multinmqsd} + ∂_t\ket{ψ_t(\vb{η}^\ast_t)} = -\iu H(t) \ket{ψ_t(\vb{η}^\ast_t)} + + \vb{L}\cdot\vb{η}^\ast_t\ket{ψ_t(\vb{η}^\ast_t)} - ∑_{n=1}^N L_n^†(t)∫_0^t\dd{s}α_n(t-s)\fdv{\ket{ψ_t(\vb{η}^\ast_t)}}{η^\ast_n(s)}, + \end{equation} + with + \begin{equation} + \label{eq:processescorr} + \begin{aligned} + \mathcal{M}(η_n(t)) &=0, & \mathcal{M}(η_n(t)η_m(s)) &= 0, + & \mathcal{M}(η_n(t)η_m(s)^\ast) &= δ_{nm}α_n(t-s), + \end{aligned} + \end{equation} + by projecting on coherent bath states.\footnote{For details see: + \cite{Diosi1998Mar}} + + System state can be recovered by averaging over \(η\) + \begin{equation} + \label{eq:recover_rho} + ρ_{\sys}(t) = \tr_{\bath}\bqty{\ketbra{ψ(t)}} = + \mathcal{M}_{\vb{η}_{t}^\ast}\bqty{\ketbra{ψ_t(\vb{η}_t)}{ψ_t(\vb{η}^\ast_t)}}. +\end{equation} +\end{frame} + +\begin{frame}{HOPS} + Using \(α_n(τ)=∑_{\mu}^{M_n}G_μ\nth\eu^{-W_μ\nth τ}\) we define + \begin{equation} + \label{eq:dops} + D_μ\nth(t) \equiv ∫_0^t\dd{s}G_μ\nth\eu^{-W_μ\nth (t-s)}\fdv{η^\ast_n(s)} + \end{equation} + and + \( + D^{\underline{\vb{k}}} \equiv + ∏_{n=1}^N∏_{μ=1}^{M_n} + {\sqrt{\frac{\underline{\vb{k}}_{n,μ}!}{\qty(G\nth_μ)^{\underline{\vb{k}}_{n,μ}}}} + \frac{1}{i^{\underline{\vb{k}}_{n,μ}}}}\qty(D_μ\nth)^{\underline{\vb{k}}_{n,μ}}\), + \( + ψ_{t}^{\kmat} \equiv D^\kmatψ_{t}\) + we find + \begin{multline} + \label{eq:multihops} + \dot{ψ}_{t}^\kmat = \qty[-\iu H_\sys(t) + \vb{L}(t)\cdot\vb{η}_{t}^\ast - + ∑_{n=1}^N∑_{μ=1}^{M_n}\kmat_{n,μ}W\nth_μ]ψ_{t}^\kmat \\+ + \iu ∑_{n=1}^N∑_{μ=1}^{M_n}\sqrt{G\nth_μ}\qty[\sqrt{\kmat_{n,μ}} L_n(t)ψ_{t}^{\kmat - + \mat{e}_{n,μ}} + \sqrt{\qty(\kmat_{n,μ} + 1)} L^†_n(t)ψ_{t}^{\kmat + + \mat{e}_{n,μ}} ]. + \end{multline} +\end{frame} + + +\section{Bath Observables with HOPS} +\begin{frame}{Zero Temperature, One Bath, Linear NMQSD} + We want to calculate + \begin{equation} + \label{eq:heatflowdef} + J = - \dv{\ev{H_\bath}}{t} = \ev{L^†∂_t B(t) + L∂_t B^†(t)}_\inter. + \end{equation} + \pause{} \ldots some manipulations \ldots{}\pause{} + \begin{block}{Result (NMQSD)} + \begin{equation} + \label{eq:final_flow_nmqsd} + J(t) = -\i \mathcal{M}_{η^\ast}\bra{\psi(η, + t)}L^†\dot{D}_t\ket{\psi(η^\ast,t)} + \cc + \end{equation} + \end{block} + with \(\dot{D}_t = ∫_0^t\dd{s} \dot{\alpha}(t-s)\fdv{η^\ast_s}\).\pause{} + \begin{block}{Result (HOPS)} + \begin{equation} + \label{eq:hopsflowfock} + J(t) = - ∑_\mu\sqrt{G_\mu}W_\mu + \mathcal{M}_{η^\ast}\bra{\psi^{(0)}(η, + t)}L^†\ket{\psi^{\vb{e}_\mu}(η^\ast,t)} + \cc + \end{equation} + \end{block} +\end{frame} + +\begin{frame}{Generalizations} + \begin{itemize} + \item finite temperatures + \item nonlinear NMQSD/HOPS + \item multiple baths straight forward\note[item]{due to simple + structure of coupling} + \item interaction energy: ``removing the dot''\ldots{} + \item general ``collective'' bath observables \(O_\sys\otimes + (B^a)^\dag B^b\) with \(B=∑_{λ}g_{λ}a_{λ}\) + \end{itemize} + \note[item]{can be calculated along with sample trajectory with little effort} +\end{frame} + + + + +\section{Applications} + + +\subsection{Energy Shovel} +\begin{frame} + \frametitle{Model} + + \begin{figure} + \centering + \input{figs/drawings/shovel.pdf_tex} + \end{figure} + \begin{block}{} + \begin{equation} + \label{eq:one_qubit_model} + H = \frac{1}{2} σ_z + \frac{1}{2} ∑_λ\qty(g_λ σ_x^† a_λ + g_λ^\ast + σ_x a_λ^†) + ∑_λ ω_λ a_λ^\dag a_λ,\;\ket{ψ_{0}}_{\sys} = \ket{\downarrow} + \end{equation} + \begin{itemize} + \item \(L(τ) = \sin^2(\frac{Δ}{2} τ)σ_x\) + \item initial state of total system: \(ρ_{0} = \ketbra{\downarrow} + \otimes \frac{\eu^{-β H_{\bath}}}{Z}\) + \end{itemize} + \end{block} +\end{frame} + +\begin{frame} + \frametitle{Extracting Energy from One Bath} + \begin{itemize} + \item how much energy can be \emph{unitarily} extracted? + \(\implies\) \(ΔE_{\mathrm{max}}=\frac{1}{β}\qrelent{ρ_{\sys}}{ρ_{\sys}^{β}}\) + \end{itemize} + \begin{figure}[h] + \centering + \only<1>{\includegraphics[height=.65\textheight]{figs/modcoup/omegas_total}} + \only<2>{\includegraphics[height=.65\textheight]{figs/modcoup/delta_dependence}} + \end{figure} + \note[item]{energy normalized to ergo} + \note[item]{vert lines bath memory time} +\end{frame} + + +\subsection{Otto Cycle} +\begin{frame} + \frametitle{Otto Cycle (proof of concept)} + \begin{block}{Model} + Spin-Boson model with compression of \(H_{\sys}\) and modulation + of \(L\). + \end{block} + \begin{itemize} + \item classical toy model of the quantum heat engine community\footcite{Geva1992Feb} + \end{itemize} + \begin{figure}[h] + \centering + \includegraphics{figs/otto/modulation} + \end{figure} +\end{frame} +\begin{frame} + \begin{figure}[h] + \centering + \includegraphics{figs/otto/energy_cont} + \end{figure} +\end{frame} +\begin{frame} + \begin{figure}[h] + \centering + \includegraphics{figs/otto/energy_strobe} + \end{figure} +\end{frame} +\begin{frame} + \begin{figure}[h] + \centering + \includegraphics{figs/otto/power} + \end{figure} + \begin{itemize} + \item \(\bar{P} = 1.98 \cdot 10^{-3} \pm 2.3 \cdot 10^{-5}\), + \(η\approx 20\%\), \(T_{c}=1\), \(T_{h}=20\) + \item no tuning of parameters, except for resonant coupling + \item long bath memory \(ω_{c}=1\), but weak-ish coupling + \end{itemize} +\end{frame} +\begin{frame}{Questions (for the future)} + \begin{itemize} + \item better performance through ``overlapping'' phases? + \item strong coupling any good? + \item non-Markovianity + strong coupling any good? + \item what is the optimal efficiency and power? (probably no + advantage here) + \end{itemize} +\end{frame} + +\subsection{Anti-Zeno Engine} +\begin{frame} + \frametitle{Anti-Zeno Engine} + \begin{block}{Question} + Is there a use for non-Markovianity in quantum heat engines? + \end{block} + \begin{itemize} + \item \cite{Mukherjee2020Jan} claims that one can exploit the + time-energy uncertainty for quantum advantage\footnote{I'd be + careful to call this quantum advantage.} + \end{itemize} + + \begin{block}{Model} + Qubit coupled to two baths of different + temperatures (\(T_c, T_h\)) + \begin{equation} + \label{eq:antizenomodel} + H_\sys= \frac12 \qty[ω_0 + γ Δ\sin(Δ t)]σ_z,\, L_{c,h}=\frac12 σ_x + \end{equation} + \note[item]{frictionless dynamics} + \end{block} +\end{frame} + +\begin{frame} + \begin{figure}[h] + \centering + \includegraphics{figs/anti_zeno/with_gap_coupling_diagram} + \end{figure} + \begin{itemize} + \item couple for \(n\) modulation periods slightly of resonance + \item for smaller \(n\) the \(\sin((ω-(ω_{0}\pm Δ))τ)/((ω-(ω_{0}\pm + Δ)) τ)\) has a greater overlap + \(\implies\) controls power output + \end{itemize} +\end{frame} + +\begin{frame} + \begin{figure} + \centering + \begin{subfigure}[t]{.49\linewidth} + \centering + \includegraphics[width=\linewidth]{anti_zeno/anti_zeno_without_cool} + \caption{\tval{anti_zeno/power_without_cool}} + \end{subfigure} + \begin{subfigure}[t]{.49\linewidth} + \centering + \includegraphics[width=\linewidth]{anti_zeno/anti_zeno_with_cool} + \caption{ + \tval{anti_zeno/power_with_cool}} + \end{subfigure} + \end{figure} + \begin{exampleblock}{Parameters} + {\tval{anti_zeno/delta}, \tval{anti_zeno/gamma}, \tval{anti_zeno/omega_alpha}, + \tval{anti_zeno/omega_zero}, \tval{anti_zeno/tc}, \tval{anti_zeno/th}} + \end{exampleblock} + \begin{itemize} + \item this is not properly converged yet \(\rightarrow\) newer + results: no advantage at these temperatures / coupling strengths + \item new simulations with temperatures from paper + (\(β_{h(c)}=0.0005(0.005)\)) are promising + \begin{itemize} + \item interesting \(\rightarrow\) no good steady state power in this case + (insufficient samples?) + \end{itemize} + \end{itemize} +\end{frame} + + +\section{Outlook} +\label{sec:outlook} +\begin{frame}{On the ``To Do'' List} + \begin{itemize} + \item verify/falsify weak coupling results in the literature + (engines) + \item three-level systems: there is an experimental paper ;) + \item parameter scan of two qubit model + \item filter modes + \item \ldots + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Lessons Learned} + \begin{itemize} + \item careful convergence checks pay off + \item surveying literature is important + \item properly documenting observations is a great help + and should be done as early as possible + \item applications should be carefully chosen to answer interesting + questions + \item numerics are helpful, but physical insights are important + \item comparison with some experiments would have been nice + \end{itemize} +\end{frame} + +\appendix +\begin{frame}[allowframebreaks]{References} + \printbibliography +\end{frame} + +\begin{frame}{Model} + \begin{equation} + \label{eq:qbmhamiltonian} + H = \frac{Ω}{4}\qty(p^2+q^2) + \frac{1}{2} q + \sum_λ\qty(g_λ^\ast b_λ + g_λ + b^†_λ)+\sum_λ\omega_λ b^†_λ b_λ, + \end{equation} + \pause + \ldots leading to \ldots + \begin{align} + \dot{q} &=Ω p \label{eq:qdot}\\ + \dot{p} &= -Ω q - \int_0^t \Im[α_0(t-s)] q(s)\dd{s} + W(t) \label{eq:pdot} + \\ + \dot{b}_λ &= -\iu g_λ \frac{q}{2} - \iu\omega_λ b_λ + \end{align} + with the operator noise + \(W(t)=-\sum_λ \qty(g_λ^\ast b_λ(0) + \eu^{-\iu\omega_λ t } + g_λ b_λ^†(0) + \eu^{\iu\omega_λ t })\), + \(\ev{W(t)W(s)}=α(t-s)\) and \(α_0 \equiv \eval{α}_{T=0}\). +\end{frame} + +\begin{frame} + Solution through a matrix \(G(t)\) with \(G(0)=\id\) and + \begin{equation} + \label{eq:eqmotprop} + \dot{G}(t) = A G(t) - \int_0^t K(t-s) G(s)\dd{s},\quad A=\mqty(0 & + Ω \\ -Ω & 0), \quad K(t)=\mqty(0 & 0\\ \Im[α_0(t)] & 0). + \end{equation} + \pause + Then + \begin{equation} + \label{eq:qpsol} + \mqty(q(t)\\ p(t)) = G(t)\mqty(q(0)\\ p(0)) + \int_0^tG(t-s) + \mqty(0\\ W(s))\dd{s}. + \end{equation} + \begin{itemize} + \item ``exact'' solution via laplace transform and BCF expansion + + residue theorem + \end{itemize} +\end{frame} +\begin{frame}{Result} + \begin{block}{Solution} + \begin{equation} + \label{eq:gfinal} + G(t) = \sum_{l=1}^{N+1}\qty[R_l \mqty(\tilde{z}_l & Ω \\ \frac{\tilde{z}_l^2}{Ω} & \tilde{z}_l)\eu^{\tilde{z}_l \cdot + t} + \cc] + \end{equation} + with \(R_l={f_0(\tilde{z}_l)}/{p'(\tilde{z}_l)}\), \(f_0,p\) + polynomials, \(\tilde{z}_l\) roots of \(p\). + \note[item]{Simple Structure, but lots of algebra -> computer} + \end{block} + \pause + \begin{itemize} + \item note: \(G\) doesn't depend on temperature + \item solution very sensitive to precision of the fits and roots + \end{itemize} +\end{frame} + +\begin{frame}{Bath Energy Derivative} + \begin{equation} + \label{eq:bathderiv_1} + \begin{aligned} + \ev{\dot{H}_B} &= ∑_λ ω_λ \qty(\ev{b_λ^†\dot{b}_λ} + \cc) \\ + &= + \begin{aligned}[t] + -\frac{1}{2}\Im&\qty[∫_0^t\dd{s}\ev{q(t)q(s)}\dot{α}_0(t-s)] \\&+ + \frac12 G_{12}(t)[α(t)-α_0(t)] + -\frac{Ω}{2}∫_0^t\dd{s} G_{11}(s)\qty[α(s)-α_0(s)] + \end{aligned} + \end{aligned} + \end{equation} + \begin{itemize} + \item becomes huge sum of exponentials (thanks Mathematica) + \note[item]{initially forgot last term, took some time to find} + \end{itemize} +\end{frame} + + + +\begin{frame}{One Bath, Finite Temperature} + \begin{block}{Parameters} + \tval{04/omega}, Ohmic BCF + \(\frac{η}{π}\qty({ω_c}/({1+\iu ω_c τ}))^2\) with + (\(α(0)=0.64,\, ω_c=2\)), \(N=10^{5}\) samples, \(15\) Hilbert + space dimensions, \(\ket{ψ(0)}_{\sys} = \ket{1}_{\sys}\), \(T=1\) + \end{block} + \note[item]{left out zero temperature} + \begin{figure}[t] + \centering + \includegraphics{figs/analytic_comp/flow_comp_nonzero.pdf} + % \caption{\label{fig:comp_finite_t} The bath energy flow \(-J\) of + % the quantum Brownian motion model for different parameters of the + % ohmic bath correlation function \cref{eq:ohmic_bcf} in the finite + % temperature \(T=1\) case. The presentation is equivalent to + % \cref{fig:comp_zero_t}.} + \end{figure} +\end{frame} + + +\begin{frame}{Two Baths, Finite Temperature (Gradient)} + \begin{block}{Parameters} + \(Ω=Λ=1\), symmetric Ohmic BCFs with + (\(α(0)=0.25,\, ω_c=2\)), \(N=10^{4}\) samples, \(9\) Hilbert + space dimensions, \(\ket{ψ(0)}_{\sys} = \ket{0,0}_{\sys}\), + \(T=0.6\), \(γ=0.5\) + \end{block} + \begin{figure}[h] + \centering + \begin{subfigure}[t]{.49\linewidth} + \includegraphics{figs/analytic_comp/comparison_two_5bcf_5ho.pdf} + \end{subfigure} + \begin{subfigure}[t]{.49\linewidth} + \includegraphics{figs/analytic_comp/comparison_two_ho.pdf} + \end{subfigure} + \end{figure} +\end{frame} + + +\begin{frame} + \begin{block}{Situation (Longer)} + Consider an open quantum system + \begin{equation} + \label{eq:openthermo} + H=\underbrace{H_\sys}_{\text{"small"}}\; +\; + \underbrace{H_\inter}_{\mathrm{?}} \;+\; + \underbrace{H_\bath}_{\text{"big", simple}} + \end{equation} + with \([H_S, H_B] = 0\). + \end{block} + \pause + \begin{itemize}[<+->] + \item weak coupling \(H_\inter\approx 0\) + thermodynamics\footnote{even in strong coupling equilibrium\ldots{}} of open systems + are somewhat understood \footcite{Rivas2019Oct,Talkner2020Oct} + \item strong coupling: \(\ev{H_\inter} \sim \ev{H_\sys}\) + \(\implies\) we can't neglect the interaction \(\implies\) + thermodynamics? + \item we do quantum mechanics \(\implies\) can't separate bath + and system\uncover<+->{, especially not dynamics!} + \item no consensus about strong coupling thermodynamics: + \note[item]{won't resolve within scope of masters thesis} + \item but what is clear: \emph{need to get access to exact dynamics + of \(H_\inter,H_\bath\)} + \end{itemize} +\end{frame} + + +\begin{frame}{Generalizations} + \begin{block}{Finite Temperature} + \begin{equation} + \label{eq:nonlinhopsflowfock} + J(t) = J_0(t) + \qty[\ev{L^†∂_t ξ(t)} + \cc] + \end{equation} + with \(\mathcal{M}(ξ(t))=0=\mathcal{M}(ξ(t) ξ(s))\), + \( + \mathcal{M}\left(ξ(t) ξ^{*}(s)\right)=\frac{1}{\pi} ∫_{0}^{∞} \mathrm{d} ω \bar{n}(\beta ω) J(ω) e^{-\mathrm{i} ω(t-s)} + \) + and \(J(ω)=π\sum_λ\abs{g_λ}^2δ(w-ω_λ)\).\footnote{\(∂_t ξ(t)\) exists if correlation function is smooth} + \end{block} + \begin{itemize} + \item finite temperatures + \item nonlinear NMQSD/HOPS + \item multiple baths straight forward\note[item]{due to simple + structure of coupling} + \item interaction energy: ``removing the dot''\ldots{} + \item general ``collective'' bath observables \(O_\sys\otimes + (B^a)^\dag B^b\) with \(B=∑_{λ}g_{λ}a_{λ}\) + \end{itemize} + \note[item]{can be calculated along with sample trajectory with little effort} +\end{frame} + +\begin{frame} + \frametitle{More Papers on Thermo} + \cite{Rivas2019Oct,Talkner2020Oct,Motz2018Nov,Wiedmann2020Mar,Senior2020Feb,Kato2015Aug,Kato2016Dec,Strasberg2021Aug,Talkner2016Aug,Bera2021Feb,Bera2021Jun,Esposito2015Dec} +\end{frame} + +\begin{frame}{Ohmic SD BCF} + \begin{columns} + \begin{column}{.49\textwidth} + \plot{01/ohmic_sd} + \end{column} + \begin{column}{.49\textwidth} + \plot{01/ohmic_bcf} + \end{column} + \end{columns} +\end{frame} +\begin{frame}{NMQSD (Zero Temperature)} + Expanding in a Bargmann (unnormalized) coherent state basis~\cite{klauder1968fundamentals} + \(\qty{\ket{\vb{z}^{(1)},\vb{z}^{(2)},\ldots}= + \ket{\underline{\vb{z}}}}\) + + \begin{equation} + \label{eq:projected} + \ket{ψ(t)} = ∫∏_{n=1}^N{\qty(\frac{\dd{\vb{z}\nth}}{π^{N_n}}\eu^{-\abs{\vb{z}}^2})}\ket{ψ(t,\underline{\vb{z}}^\ast)}\ket{\underline{\vb{z}}}, + \end{equation} + we obtain + \note[item]{interpret the integral in a montecarlo sense} + \begin{equation} + \label{eq:multinmqsd} + ∂_tψ_t(\vb{η}^\ast_t) = -\iu H ψ_t(\vb{η}^\ast_t) + + \vb{L}\cdot\vb{η}^\ast_tψ_t(\vb{η}^\ast_t) - ∑_{n=1}^N L_n^†∫_0^t\dd{s}α_n(t-s)\fdv{ψ_t(\vb{η}^\ast_t)}{η^\ast_n(s)}, + \end{equation} + with + \begin{equation} + \label{eq:processescorr} + \begin{aligned} + \mathcal{M}(η^\ast_n(t)) &=0, & \mathcal{M}(η_n(t)η_m(s)) &= 0, + & \mathcal{M}(η_n(t)η_m(s)^\ast) &= δ_{nm}α_n(t-s), + \end{aligned} + \end{equation} + where + \(α_n(t-s)=∑_λ\abs{g_λ\nth}^2\eu^{-\iu + ω_λ\nth(t-s)}=\ev{B(t)B(s)}_{I,ρ(0)}\) \cite{Strunz2001Habil} + (fourier transf. of spectral density + \(J(ω) = π ∑_λ\abs{g_λ}^2δ(ω-ω_λ)\)). +\end{frame} +\begin{frame}{Fock-Space Embedding} + As in \refcite{Gao2021Sep} we can define + \begin{equation} + \label{eq:fockpsi} + \ket{Ψ} = \sum_\kmat\ket{\psi^\kmat}\otimes \ket{\kmat} + \end{equation} + where + \(\ket{\kmat}=\bigotimes_{n=1}^N\bigotimes_{μ=1}^{N_n}\ket{\kmat_{n,μ}}\) + are bosonic Fock-states. + + Now \cref{eq:multihops} becomes + \begin{equation} + \label{eq:fockhops} + ∂_t\ket{Ψ} = \qty[-\iu H_\sys + \vb{L}\cdot\vb{η}^\ast - + ∑_{n=1}^N∑_{μ=1}^{M_n}b_{n,μ}^\dag b_{n,μ} W\nth_μ + + \iu ∑_{n=1}^N∑_{μ=1}^{M_n} \sqrt{G_{n,μ}} \qty(b^†_{n,μ}L_n + b_{n,μ}L^†_n)] \ket{Ψ}. + \end{equation} + \pause + \(\implies\) possible to derive an upper bound for the norm of + \(\ket{\psi^\kmat}\) \pause \(\implies\) new truncation scheme + \note[item]{looks somewhat like a non-hermitian hamiltonian} +\end{frame} + +\begin{frame}{Multiple Baths} + \begin{itemize} + \item theory generalizes easily to \(N\) baths + \item generalized our HOPS code to \(N\) baths + \note[item]{added docstrings and typehints to (almost) everything} + \note[item]{added (some tests) and CI that ensures they aren't broken} + \item solving a model with two coupled HOs is now possible + \note[item]{but with much anguish, root precision, bcf fit!!} + \begin{equation} + \label{eq:hamiltonian} + \begin{aligned} + H &= ∑_{i\in\qty{1,2}} \qty[H^{(i)}_O + q_iB^{(i)} + H_B^{(i)}] + \frac{γ}{4}(q_1-q_2)^2, + \end{aligned} + \end{equation} + where \(H_O^{(i)}= \frac{Ω_i}{4}\qty(p_i^2+q_i^2)\), \(B^{(i)}=\sum_λ\qty(g^{(i),\ast}_λb^{(i)}_λ + g^{(i)}_λ + b^{(i),†}_λ)\) and \(H_B^{(i)}=\sum_λ\omega_λ b^{(i),†}_λ b^{(i)}_λ\). + \end{itemize} +\end{frame} + + +\subsection{One Bath} +\begin{frame} + \frametitle{One Bath, Zero Temperature} + \begin{block}{Model: Spin-Boson} + \begin{equation} + \label{eq:one_qubit_model} + H = \frac{1}{2} σ_z + \frac{1}{2} ∑_λ\qty(g_λ σ_x^† a_λ + g_λ^\ast + σ_x a_λ^†) + ∑_λ ω_λ a_λ^\dag a_λ,\;\ket{ψ_{0}}_{\sys} = \ket{\uparrow} + \end{equation} + \end{block} + \begin{itemize} + \item<+-> how do we check convergence:\pause + \begin{itemize} + \item old: difference of results to some ``good'' configuration\pause + \item new: consistency with energy conservation + \end{itemize} + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Example: Dependence of the Interaction Energy on Stochastic Process + Sampling} + \begin{figure}[h] + \centering + \includegraphics{figs/one_bath_syst/stocproc_systematics_interaction} + \end{figure} + \begin{itemize} + \item \(α(0)=1.6\) and \(ω_{c}=4\) \(\implies\) stress HOPS through + fast decaying BCF + \item ``perfect'' results only with very high + accuracy\footnote{smaller \(\varsigma\) is better} \(\varsigma\) + \item good qualitative results for less extreme configurations + (common theme) + \end{itemize} +\end{frame} + +\begin{frame} + \frametitle{Various Cutoff Frequencies} + \begin{figure}[h] + \centering + \includegraphics[height=.9\textheight]{figs/one_bath_syst/omega_energy_overview} + \note[item]{marked differences between trajcetories -> non-markov, + strong coup} + \end{figure} +\end{frame} + +\begin{frame}{Non-Markovian Dynamics} + \begin{figure}[h] + \centering + \only<1>{\includegraphics{figs/one_bath_syst/markov_analysis}} + \only<2>{\includegraphics{figs/one_bath_syst/markov_analysis_longer}} + \end{figure} + \begin{itemize} + \item<+-> interaction strengths chosen for approx. same interaction + energy + \item<+-> timing important for energy transfer ``performance'' + \end{itemize} +\end{frame} + +\begin{frame} + \begin{center} + \begin{alertblock}{Beware :)} + The following is WIP and has not been written up properly yet. + \end{alertblock} + \end{center} +\end{frame} + + +\section{Other Projects} +\begin{frame}[allowframebreaks] + \begin{itemize} + \item stabilized normalization in nonlinear HOPS + \begin{figure} + \centering + \plot{05/norm} + \end{figure} + \item stochastic process sampling via Cholesky decomposition + \note[item]{allows to generate processes that match up to a point in + time} + \note[item]{allows to extend stochastic processes to arbitrary times} + \note[item]{could be useful for steady state studies and long-time + propagation} + \begin{figure} + \centering + \plot{05/cholesky} + \end{figure} + \item norm based truncation scheme + \begin{itemize} + \note[item]{needs further investigation} + \item promising at ``friendly'' coupling strengths + \end{itemize} + \begin{figure} + \centering + \plot{06/convergence} + \end{figure} + \end{itemize} +\end{frame} + +\end{document} + + + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% TeX-output-dir: "output" +%%% TeX-engine: luatex +%%% End: diff --git a/talk_short/latexmkrc b/talk_short/latexmkrc new file mode 100644 index 0000000..ef8f9b0 --- /dev/null +++ b/talk_short/latexmkrc @@ -0,0 +1,5 @@ +$pdf_mode = 4; +@default_files = ('index.tex'); +$out_dir = 'output'; +set_tex_cmds( '--shell-escape %O %S' ); +$pdf_previewer = 'start zathura output/index.pdf' diff --git a/talk_short/output/index.pdf b/talk_short/output/index.pdf new file mode 100644 index 0000000..63fea9c Binary files /dev/null and b/talk_short/output/index.pdf differ diff --git a/talk_short/references.bib b/talk_short/references.bib new file mode 100644 index 0000000..a4c0c0c --- /dev/null +++ b/talk_short/references.bib @@ -0,0 +1,1321 @@ +@misc{vzitkovic2010, + title = {Introduction to stochastic processes-lecture notes}, + author = {{\v{Z}}itkovi{\'c}, Gordan}, + year = 2010, + publisher = {Austin, University of Texas-Department of + Mathematics}, + url = + {https://web.ma.utexas.edu/users/gordanz/notes/introduction_to_stochastic_processes.pdf} +} + 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Rev. E}, + volume = 87, + number = 4, + pages = 042123, + year = 2013, + month = apr, + issn = {2470-0053}, + publisher = {American Physical Society}, + doi = {10.1103/PhysRevE.87.042123} +} + +@article{Lobejko2021Feb, + author = {{\L}obejko, Marcin}, + title = {{The tight Second Law inequality for coherent + quantum systems and finite-size heat baths}}, + journal = {Nat. Commun.}, + volume = 12, + number = 918, + pages = {1--6}, + year = 2021, + month = feb, + issn = {2041-1723}, + publisher = {Nature Publishing Group}, + doi = {10.1038/s41467-021-21140-4} +} + +@article{Skrzypczyk2014Jun, + author = {Skrzypczyk, Paul and Short, Anthony J. and Popescu, + Sandu}, + title = {{Work extraction and thermodynamics for individual + quantum systems}}, + journal = {Nat. Commun.}, + volume = 5, + number = 4185, + pages = {1--8}, + year = 2014, + month = jun, + issn = {2041-1723}, + publisher = {Nature Publishing Group}, + doi = {10.1038/ncomms5185} +} + +@article{Klatzow2019Mar, + author = {Klatzow, James and Becker, Jonas N. and Ledingham, + Patrick M. and Weinzetl, Christian and Kaczmarek, + Krzysztof T. and Saunders, Dylan J. and Nunn, Joshua + and Walmsley, Ian A. and Uzdin, Raam and Poem, + Eilon}, + title = {{Experimental Demonstration of Quantum Effects in + the Operation of Microscopic Heat Engines}}, + journal = {Phys. Rev. Lett.}, + volume = 122, + number = 11, + pages = 110601, + year = 2019, + month = mar, + issn = {1079-7114}, + publisher = {American Physical Society}, + doi = {10.1103/PhysRevLett.122.110601} +} + +@article{Wyss2017Jul, + author = {Wyss, Walter}, + title = {{Two Non-Commutative Binomial Theorems}}, + journal = {arXiv}, + year = 2017, + month = jul, + eprint = {1707.03861}, + doi = {10.48550/arXiv.1707.03861} +} + +@article{Kolar2012Aug, + author = + {Kol{\ifmmode\acute{a}\else\'{a}\fi}{\ifmmode\check{r}\else\v{r}\fi}, + M. and Gelbwaser-Klimovsky, D. and Alicki, R. and + Kurizki, G.}, + title = {{Quantum Bath Refrigeration towards Absolute Zero: + Challenging the Unattainability Principle}}, + journal = {Phys. Rev. Lett.}, + volume = 109, + number = 9, + pages = 090601, + year = 2012, + month = aug, + issn = {1079-7114}, + publisher = {American Physical Society}, + doi = {10.1103/PhysRevLett.109.090601} +} + +@article{Welford1962Aug, + author = {Welford, B. P.}, + title = {{Note on a Method for Calculating Corrected Sums of + Squares and Products}}, + journal = {Technometrics}, + volume = 4, + number = 3, + pages = {419--420}, + year = 1962, + month = aug, + issn = {0040-1706}, + publisher = {Taylor {\&} Francis}, + doi = {10.1080/00401706.1962.10490022} +} + +@book{Knuth1997, + added-at = {2007-10-23T15:51:41.000+0200}, + address = {Boston, MA, USA}, + author = {Knuth, Donald E.}, + isbn = 0201896842, + keywords = {algorithms}, + publisher = {Addison-Wesley Longman Publishing Co., Inc.}, + timestamp = {2007-10-23T15:51:49.000+0200}, + title = {The art of computer programming, volume 2 (3rd ed.): + seminumerical algorithms}, + url = {http://portal.acm.org/citation.cfm?id=270146}, + year = 1997 +} + +@article{Magazzu2018Apr, + author = {Magazz{\ifmmode\grave{u}\else\`{u}\fi}, L. and + Forn-D{\ifmmode\acute{\imath}\else\'{\i}\fi}az, + P. and Belyansky, R. and Orgiazzi, J.-L. and + Yurtalan, M. A. and Otto, M. R. and Lupascu, A. and + Wilson, C. M. and Grifoni, M.}, + title = {{Probing the strongly driven spin-boson model in a + superconducting quantum circuit}}, + journal = {Nat. Commun.}, + volume = 9, + number = 1403, + pages = {1--8}, + year = 2018, + month = apr, + issn = {2041-1723}, + publisher = {Nature Publishing Group}, + doi = {10.1038/s41467-018-03626-w} +} + +@book{Breuer2002Jun, + author = {Breuer, Heinz-Peter and Petruccione, Francesco}, + title = {{The Theory of Open Quantum Systems}}, + year = {2002}, + month = jun, + isbn = {978-0-19852063-4}, + publisher = {Oxford University Press}, + address = {Oxford, England, UK}, + url = {https://global.oup.com/academic/product/the-theory-of-open-quantum-systems-9780198520634} +} diff --git a/talk_short/talk.org b/talk_short/talk.org new file mode 100644 index 0000000..d432217 --- /dev/null +++ b/talk_short/talk.org @@ -0,0 +1,150 @@ +These are the planning and notes for the talk for "Wissenschaftliches +Arbeiten". + +There is a total time of 20 minutes to fill, which is going to be +a pretty tough upper bound. + +#+begin_src emacs-lisp :results none + (defun total-time () + (interactive) + (let ((total 0)) + (message + (number-to-string + (apply + #'+ + (org-map-entries + #'(lambda () + (string-to-number + (or (cdr (assoc "DURATION" (org-entry-properties))) "0"))))))))) +#+end_src + + +* Introduction +** DONE General Model :WAITING: +:PROPERTIES: +:DURATION: 2 +:END: + +- hamiltonian multiple baths +- (def. BCFs) + +** DONE Motivation +:PROPERTIES: +:DURATION: 2 +:END: +- weak coupling/equilibrium well settled +- strong coupling: no consensus (lots of citations) +- won't be settled in a masters thesis but -> + - access to bath/interaction observables with exact dynamics would + be helpful +- this where hopsflow will come in +- also: nice maintainable tooling would be good + +** DONE NMQSD +:PROPERTIES: +:DURATION: 2 +:END: + +- nmqsd equation +- not much more + +** DONE HOPS +:PROPERTIES: +:DURATION: 2 +:END: +- hops for multiple baths +- with new normalization + +* Bath Energy +** DONE Formulas and Generalizations +:PROPERTIES: +:DURATION: 2 +:END: +- short derivation +- explain hurdles +- explain nonzero + +** DONE Interaction Energy +:PROPERTIES: +:DURATION: 1 +:END: +- straight forward -> remove dot + +* Analytical Verification +** Model +:PROPERTIES: +:DURATION: 2 +:END: + +- for one HO +- give valentin credit +** Solution +:PROPERTIES: +:DURATION: 5 +:END: + +- give valentin credit +- general idea +- formula for laplace transform of exponential +- trick with mathematica +** Comparison +:PROPERTIES: +:DURATION: 2 +:END: + +- one bath case for zero and nonzero temperature +** Quick review of the two HO case +:PROPERTIES: +:DURATION: 3 +:END: + +- explain that generalization is straight forward +- problems with numerics (sensitive to bcf) +- show comparison + +* Applications +** One Bath, Zero +- quick mention of use as convergence check, no details + - it is hard to get "perfect" convergence, but qualitative picture + is ok pretty fast +- quick mention of resonance effect -> already present in weak coupling +- non show that non markovianity has to be exploited pretty rigorously +- point out initial slip, mention that this has to do with initial pure dephasing +- dependence of the energy change on shape of bcf -> beyond weak + coupling and non-markovianity +** One Bath with Modulation +- take the figure from the poster +- explain ergotropy bound +- show relevance of non-markovianity +** Show a picture of a circular process +- just as demo, not looked into this +** show plots of anti zeno engine +- say wip +- explain anti zeno engine +- hard to reproduce -> weak coupling but very high temperatures +- ideally hops allows us to go beyond the restrictive setting in the + paper + +* HOPS Related, No Details +:PROPERTIES: +:DURATION: 3 +:END: + +- code and docs and tests and poetry +- auto norm +- new cutoff +- tree hops + +* Outlook +:PROPERTIES: +:DURATION: 3 +:END: + +- concrete models + - sweep + - three baths +- steady state detection -> pseudo eigenstates? +- higher order moments of bath energy + - may bring insight into role of aux states + - better cutoff for multi bath (not as many cross terms) +- concrete importance sampling diff --git a/talk_short/values/01/bcf_scale.tex b/talk_short/values/01/bcf_scale.tex new file mode 100644 index 0000000..327f174 --- /dev/null +++ b/talk_short/values/01/bcf_scale.tex @@ -0,0 +1 @@ +\(η=0.5\) \ No newline at end of file diff --git a/talk_short/values/01/cutoff_freq.tex b/talk_short/values/01/cutoff_freq.tex new file mode 100644 index 0000000..f6c8280 --- /dev/null +++ b/talk_short/values/01/cutoff_freq.tex @@ -0,0 +1 @@ +\(ω_c=2\) \ No newline at end of file diff --git a/talk_short/values/01/samples.tex b/talk_short/values/01/samples.tex new file mode 100644 index 0000000..08eb9b1 --- /dev/null +++ b/talk_short/values/01/samples.tex @@ -0,0 +1 @@ +\(N=8000\) \ No newline at end of file diff --git a/talk_short/values/02/bcf_scale.tex b/talk_short/values/02/bcf_scale.tex new file mode 100644 index 0000000..327f174 --- /dev/null +++ b/talk_short/values/02/bcf_scale.tex @@ -0,0 +1 @@ +\(η=0.5\) \ No newline at end of file diff --git a/talk_short/values/02/cutoff_freq.tex b/talk_short/values/02/cutoff_freq.tex new file mode 100644 index 0000000..f6c8280 --- /dev/null +++ b/talk_short/values/02/cutoff_freq.tex @@ -0,0 +1 @@ +\(ω_c=2\) \ No newline at end of file diff --git a/talk_short/values/02/samples.tex b/talk_short/values/02/samples.tex new file mode 100644 index 0000000..75b25e6 --- /dev/null +++ b/talk_short/values/02/samples.tex @@ -0,0 +1 @@ +\(N=10000\) \ No newline at end of file diff --git a/talk_short/values/02/temp.tex b/talk_short/values/02/temp.tex new file mode 100644 index 0000000..ec1839d --- /dev/null +++ b/talk_short/values/02/temp.tex @@ -0,0 +1 @@ +\(T=1.5\) \ No newline at end of file diff --git a/talk_short/values/04/bcf_scale.tex b/talk_short/values/04/bcf_scale.tex new file mode 100644 index 0000000..1124f53 --- /dev/null +++ b/talk_short/values/04/bcf_scale.tex @@ -0,0 +1 @@ +\(η=0.2\) \ No newline at end of file diff --git a/talk_short/values/04/cutoff_freq.tex b/talk_short/values/04/cutoff_freq.tex new file mode 100644 index 0000000..f6c8280 --- /dev/null +++ b/talk_short/values/04/cutoff_freq.tex @@ -0,0 +1 @@ +\(ω_c=2\) \ No newline at end of file diff --git a/talk_short/values/04/max_HO_level.tex b/talk_short/values/04/max_HO_level.tex new file mode 100644 index 0000000..eff73be --- /dev/null +++ b/talk_short/values/04/max_HO_level.tex @@ -0,0 +1 @@ +\(15\) \ No newline at end of file diff --git a/talk_short/values/04/omega.tex b/talk_short/values/04/omega.tex new file mode 100644 index 0000000..ca41841 --- /dev/null +++ b/talk_short/values/04/omega.tex @@ -0,0 +1 @@ +\(Ω=1\) \ No newline at end of file diff --git a/talk_short/values/04/samples.tex b/talk_short/values/04/samples.tex new file mode 100644 index 0000000..75b25e6 --- /dev/null +++ b/talk_short/values/04/samples.tex @@ -0,0 +1 @@ +\(N=10000\) \ No newline at end of file diff --git a/talk_short/values/04/temp.tex b/talk_short/values/04/temp.tex new file mode 100644 index 0000000..60b50c7 --- /dev/null +++ b/talk_short/values/04/temp.tex @@ -0,0 +1 @@ +\(T=0.5\) \ No newline at end of file diff --git a/talk_short/values/05/bcf_scale.tex b/talk_short/values/05/bcf_scale.tex new file mode 100644 index 0000000..1124f53 --- /dev/null +++ b/talk_short/values/05/bcf_scale.tex @@ -0,0 +1 @@ +\(η=0.2\) \ No newline at end of file diff --git a/talk_short/values/05/bcf_terms.tex b/talk_short/values/05/bcf_terms.tex new file mode 100644 index 0000000..7566d7b --- /dev/null +++ b/talk_short/values/05/bcf_terms.tex @@ -0,0 +1 @@ +\(K=12\) \ No newline at end of file diff --git a/talk_short/values/05/cutoff_freq.tex b/talk_short/values/05/cutoff_freq.tex new file mode 100644 index 0000000..f6c8280 --- /dev/null +++ b/talk_short/values/05/cutoff_freq.tex @@ -0,0 +1 @@ +\(ω_c=2\) \ No newline at end of file diff --git a/talk_short/values/05/gamma.tex b/talk_short/values/05/gamma.tex new file mode 100644 index 0000000..6c0d4b5 --- /dev/null +++ b/talk_short/values/05/gamma.tex @@ -0,0 +1 @@ +\(γ=0.5\) \ No newline at end of file diff --git a/talk_short/values/05/max_HO_level.tex b/talk_short/values/05/max_HO_level.tex new file mode 100644 index 0000000..76de674 --- /dev/null +++ b/talk_short/values/05/max_HO_level.tex @@ -0,0 +1 @@ +\(9\) \ No newline at end of file diff --git a/talk_short/values/05/omega.tex b/talk_short/values/05/omega.tex new file mode 100644 index 0000000..ca41841 --- /dev/null +++ b/talk_short/values/05/omega.tex @@ -0,0 +1 @@ +\(Ω=1\) \ No newline at end of file diff --git a/talk_short/values/05/samples.tex b/talk_short/values/05/samples.tex new file mode 100644 index 0000000..784bcb0 --- /dev/null +++ b/talk_short/values/05/samples.tex @@ -0,0 +1 @@ +\(N=5191\) \ No newline at end of file diff --git a/talk_short/values/05/temp.tex b/talk_short/values/05/temp.tex new file mode 100644 index 0000000..3b9f188 --- /dev/null +++ b/talk_short/values/05/temp.tex @@ -0,0 +1 @@ +\(T=0.6\) \ No newline at end of file diff --git a/talk_short/values/analytic/bcf_scale.tex b/talk_short/values/analytic/bcf_scale.tex new file mode 100644 index 0000000..1124f53 --- /dev/null +++ b/talk_short/values/analytic/bcf_scale.tex @@ -0,0 +1 @@ +\(η=0.2\) \ No newline at end of file diff --git a/talk_short/values/analytic/bcf_terms.tex b/talk_short/values/analytic/bcf_terms.tex new file mode 100644 index 0000000..7566d7b --- /dev/null +++ b/talk_short/values/analytic/bcf_terms.tex @@ -0,0 +1 @@ +\(K=12\) \ No newline at end of file diff --git a/talk_short/values/analytic/bcf_zero.tex b/talk_short/values/analytic/bcf_zero.tex new file mode 100644 index 0000000..f507137 --- /dev/null +++ b/talk_short/values/analytic/bcf_zero.tex @@ -0,0 +1 @@ +\(α(0)=0.3\) \ No newline at end of file diff --git a/talk_short/values/analytic/cutoff_freq.tex b/talk_short/values/analytic/cutoff_freq.tex new file mode 100644 index 0000000..f6c8280 --- /dev/null +++ b/talk_short/values/analytic/cutoff_freq.tex @@ -0,0 +1 @@ +\(ω_c=2\) \ No newline at end of file diff --git a/talk_short/values/analytic/gamma.tex b/talk_short/values/analytic/gamma.tex new file mode 100644 index 0000000..6c0d4b5 --- /dev/null +++ b/talk_short/values/analytic/gamma.tex @@ -0,0 +1 @@ +\(γ=0.5\) \ No newline at end of file diff --git a/talk_short/values/analytic/max_HO_level.tex b/talk_short/values/analytic/max_HO_level.tex new file mode 100644 index 0000000..76de674 --- /dev/null +++ b/talk_short/values/analytic/max_HO_level.tex @@ -0,0 +1 @@ +\(9\) \ No newline at end of file diff --git a/talk_short/values/analytic/omega.tex b/talk_short/values/analytic/omega.tex new file mode 100644 index 0000000..297467e --- /dev/null +++ b/talk_short/values/analytic/omega.tex @@ -0,0 +1 @@ +\(Ω_i=1\) \ No newline at end of file diff --git a/talk_short/values/analytic/samples.tex b/talk_short/values/analytic/samples.tex new file mode 100644 index 0000000..784bcb0 --- /dev/null +++ b/talk_short/values/analytic/samples.tex @@ -0,0 +1 @@ +\(N=5191\) \ No newline at end of file diff --git a/talk_short/values/analytic/temp.tex b/talk_short/values/analytic/temp.tex new file mode 100644 index 0000000..3b9f188 --- /dev/null +++ b/talk_short/values/analytic/temp.tex @@ -0,0 +1 @@ +\(T=0.6\) \ No newline at end of file diff --git a/talk_short/values/anti_zeno/delta.tex b/talk_short/values/anti_zeno/delta.tex new file mode 100644 index 0000000..edd9111 --- /dev/null +++ b/talk_short/values/anti_zeno/delta.tex @@ -0,0 +1 @@ +\(Δ=11\) \ No newline at end of file diff --git a/talk_short/values/anti_zeno/gamma.tex b/talk_short/values/anti_zeno/gamma.tex new file mode 100644 index 0000000..6c0d4b5 --- /dev/null +++ b/talk_short/values/anti_zeno/gamma.tex @@ -0,0 +1 @@ +\(γ=0.5\) \ No newline at end of file diff --git a/talk_short/values/anti_zeno/omega_alpha.tex b/talk_short/values/anti_zeno/omega_alpha.tex new file mode 100644 index 0000000..9f5f72a --- /dev/null +++ b/talk_short/values/anti_zeno/omega_alpha.tex @@ -0,0 +1 @@ +\(α(0)=1.0\) \ No newline at end of file diff --git a/talk_short/values/anti_zeno/omega_zero.tex b/talk_short/values/anti_zeno/omega_zero.tex new file mode 100644 index 0000000..99e9cf2 --- /dev/null +++ b/talk_short/values/anti_zeno/omega_zero.tex @@ -0,0 +1 @@ +\(ω_0=20\) \ No newline at end of file diff --git a/talk_short/values/anti_zeno/power_with_cool.tex b/talk_short/values/anti_zeno/power_with_cool.tex new file mode 100644 index 0000000..98e928e --- /dev/null +++ b/talk_short/values/anti_zeno/power_with_cool.tex @@ -0,0 +1 @@ +\(P=-0.068\pm 0.010\) \ No newline at end of file diff --git a/talk_short/values/anti_zeno/power_without_cool.tex b/talk_short/values/anti_zeno/power_without_cool.tex new file mode 100644 index 0000000..46325cb --- /dev/null +++ b/talk_short/values/anti_zeno/power_without_cool.tex @@ -0,0 +1 @@ +\(P=-0.058\pm 0.014\) \ No newline at end of file diff --git a/talk_short/values/anti_zeno/tc.tex b/talk_short/values/anti_zeno/tc.tex new file mode 100644 index 0000000..f76853a --- /dev/null +++ b/talk_short/values/anti_zeno/tc.tex @@ -0,0 +1 @@ +\(T_c=8\) \ No newline at end of file diff --git a/talk_short/values/anti_zeno/th.tex b/talk_short/values/anti_zeno/th.tex new file mode 100644 index 0000000..29dfde1 --- /dev/null +++ b/talk_short/values/anti_zeno/th.tex @@ -0,0 +1 @@ +\(T_h=40\) \ No newline at end of file diff --git a/talk_short/values/modcoup/init_slip_alpha.tex b/talk_short/values/modcoup/init_slip_alpha.tex new file mode 100644 index 0000000..f95d9a6 --- /dev/null +++ b/talk_short/values/modcoup/init_slip_alpha.tex @@ -0,0 +1 @@ +\(α(0)=0.4\) \ No newline at end of file diff --git a/talk_short/values/modcoup/initial_slip_cuttoff.tex b/talk_short/values/modcoup/initial_slip_cuttoff.tex new file mode 100644 index 0000000..0453ad3 --- /dev/null +++ b/talk_short/values/modcoup/initial_slip_cuttoff.tex @@ -0,0 +1 @@ +\(ω_c=1.0\) \ No newline at end of file diff --git a/talk_short/values/modcoup/omega_alpha.tex b/talk_short/values/modcoup/omega_alpha.tex new file mode 100644 index 0000000..9f5f72a --- /dev/null +++ b/talk_short/values/modcoup/omega_alpha.tex @@ -0,0 +1 @@ +\(α(0)=1.0\) \ No newline at end of file diff --git a/talk_short/values/modcoup/omega_delta.tex b/talk_short/values/modcoup/omega_delta.tex new file mode 100644 index 0000000..784e3e4 --- /dev/null +++ b/talk_short/values/modcoup/omega_delta.tex @@ -0,0 +1 @@ +\(Δ=5.0\) \ No newline at end of file diff --git a/talk_short/values/one_bath/delta_bcf_wc.tex b/talk_short/values/one_bath/delta_bcf_wc.tex new file mode 100644 index 0000000..f6c8280 --- /dev/null +++ b/talk_short/values/one_bath/delta_bcf_wc.tex @@ -0,0 +1 @@ +\(ω_c=2\) \ No newline at end of file diff --git a/talk_short/values/one_bath/omega_bcf_str.tex b/talk_short/values/one_bath/omega_bcf_str.tex new file mode 100644 index 0000000..f95d9a6 --- /dev/null +++ b/talk_short/values/one_bath/omega_bcf_str.tex @@ -0,0 +1 @@ +\(α(0)=0.4\) \ No newline at end of file diff --git a/talk_short/values/one_bath/δ_bcf_wc.tex b/talk_short/values/one_bath/δ_bcf_wc.tex new file mode 100644 index 0000000..f6c8280 --- /dev/null +++ b/talk_short/values/one_bath/δ_bcf_wc.tex @@ -0,0 +1 @@ +\(ω_c=2\) \ No newline at end of file