Bose Einstein Distribution
Illustrating the change in the real part of the Bose-Einstein distribution, i.e. the average occupancy of the ground state of a bosonic system, from doubling the temperature. Pulled from arxiv:1712.09863.
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bose-einstein-distribution.tex (40 lines)
\documentclass{standalone}
\usepackage{pgfplots,mathtools}
\pgfplotsset{compat=newest}
\usetikzlibrary{intersections}
\let\Re\relax
\DeclareMathOperator{\Re}{Re}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
domain = 0:2, ymax = 5,
xlabel = $\Re(p_0)$,
ylabel = $n_\text{B}(p_0)$,
ticks=none, smooth,
thick, axis lines = left,
every tick/.style = {thick},
width=8cm, height=7cm]
\def\nB#1{1/(e^(x/#1) - 1) + 1/2}
\addplot[name path=T1, color=red] {\nB{0.5}};
\addplot[name path=T2, color=yellow] {\nB{1}};
\addplot[name path=T3, color=blue] {\nB{2}};
\addplot[draw=none, name path=aux] {3*x};
\end{axis}
\draw[shorten >=2, shorten <=2, name intersections={of=T1 and aux, name=int1}, name intersections={of=T2 and aux, name=int2}] (int1-1) edge[->, bend left] node[midway, below right=-1pt, font=\scriptsize] {$2 \cdot T$} (int2-1);
\draw[shorten >=2, shorten <=2, name intersections={of=T3 and aux, name=int3}] (int2-1) edge[->, bend left] node[midway, below right=-1pt, font=\scriptsize] {$2 \cdot T$} (int3-1);
\end{tikzpicture}
\end{document}
Typst
bose-einstein-distribution.typ (68 lines)
#import "@preview/cetz:0.3.2": canvas, draw
#import "@preview/cetz-plot:0.1.1": plot
#import draw: content, line, bezier
#set page(width: auto, height: auto, margin: 8pt)
// Bose-Einstein distribution function
#let n_B(x, T) = {
if x == 0 or T == 0 { return 0.5 }
let ratio = x / T
1 / (calc.exp(ratio) - 1) + 0.5
}
#canvas({
draw.set-style(axes: (y: (label: (anchor: "south-east", angle: 90deg)), x: (label: (anchor: "north-east"))))
plot.plot(
size: (8, 7),
x-label: $"Re"(p_0)$,
y-label: $n_"B" (p_0)$,
x-min: 0,
y-min: 0,
y-max: 5,
x-tick-step: none,
y-tick-step: none,
axis-style: "left",
{
// Plot distributions for different temperatures
for (T, color) in ((0.5, red), (1, orange), (2, blue)) {
plot.add(
style: (stroke: color + 1.5pt),
domain: (0.01, 2),
samples: 150,
x => n_B(x, T),
)
}
},
)
// Add curved arrows between intersection points
// We approximate the intersection points since CeTZ doesn't have direct intersection support
let arrow-style = (
end: "stealth",
stroke: black + 1pt,
fill: black,
)
// First arrow (T=0.5 to T=1)
bezier(
(1.8, 1.7), // start point
(2.4, 2.4), // end point
(2, 2.3), // control point
mark: arrow-style,
name: "arrow1",
)
content("arrow1.mid", text(size: 8pt)[$2 dot T$], anchor: "south-east")
// Second arrow (T=1 to T=2)
bezier(
(2.4, 2.5), // start point
(3.5, 3.2), // end point
(2.9, 3.3), // control point
mark: arrow-style,
name: "arrow2",
)
content("arrow2.mid", text(size: 8pt)[$2 dot T$], anchor: "south-east")
})