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.

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% 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. \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}

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