Energy fluctuations of finite free-electron Fermi gas

TL;DR

This paper analyzes the energy distribution of finite free-electron Fermi gases, revealing non-Gaussian effects and skewed distributions in small systems, especially relevant for mesoscopic conductors at low temperatures.

Contribution

It provides an analytical solution for the energy distribution of small free-electron Fermi gases, highlighting non-Gaussian features absent in large systems.

Findings

Energy distribution becomes skewed in small systems.

Distribution vanishes at low energies, showing a sharp cutoff.

Non-Gaussian effects are significant when heat capacity is low.

Abstract

We discuss the energy distribution of free-electron Fermi-gas, a problem with a textbook solution of Gaussian energy fluctuations in the limit of a large system. We find that for a small system, characterized solely by its heat capacity $C$, the distribution can be solved analytically, and it is both skewed and it vanishes at low energies, exhibiting a sharp drop to zero at the energy corresponding to the filled Fermi sea. The results are relevant from the experimental point of view, since the predicted non-Gaussian effects become pronounced when $C/k_B \lesssim 10^3$ ($k_B$ is the Boltzmann constant), a regime that can be easily achieved for instance in mesoscopic metallic conductors at sub-kelvin temperatures.