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Fluctuations

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physicsstatistical mechanics

Number fluctuations of the occupation probability〈nk〉of a single mode k in an ideal Bose and Fermi gas in the grand canonical ensemble. Used in Exercise Sheet 11 of Statistical Physics by Manfred Salmhofer (2016), available at https://janosh.dev/physics/statistical-physics.


Fluctuations

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fluctuations.tex (43 lines)

\documentclass{standalone}

\usepackage{pgfplots, mathtools}
\pgfplotsset{compat=newest}

\begin{document}
\begin{tikzpicture}
  \begin{axis}[
      xlabel = $T$,
      ylabel = $\Delta n_k^+$,
      smooth,thick,
      axis lines = center,
      every tick/.style = thick]

    \def\beta{1/x}
    \def\ek{1}
    \def\mu{0}
    \def\bosefluc{1/(2*sinh(\beta/2 * (\ek - \mu)))^2}
    \addplot[color=blue,domain = 0:4.2]{\bosefluc};

  \end{axis}
\end{tikzpicture}

\begin{tikzpicture}
  \begin{axis}[
      xlabel = $T$,
      ylabel = $\Delta n_k^-$,
      smooth,thick,
      ymax = 0.28,
      axis lines = center,
      every tick/.style = thick,
      yticklabel style = /pgf/number format/fixed]

    \def\beta{1/x}
    \def\ek{1}
    \def\mu{0}
    \def\fermfluc{1/(2 + 2*cosh(\beta * (\ek - \mu)))}
    \addplot[color=blue,domain = 0:4.2]{\fermfluc};

  \end{axis}
\end{tikzpicture}
\end{document}