Energy fluctuations of finite free-electron Fermi gas

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.

References in corpus (3)

• Fast electron thermometry towards ultra-sensitive calorimetric detection
• Incomplete measurement of work in a dissipative two level system
• Microwave nanobolometer based on proximity Josephson junctions

Cited by in corpus (6)

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• Full counting statistics of the subsystem energy in the free fermions and the quantum spin chains
• Quantifying non-Markovianity due to driving and a finite-size environment in an open quantum system
• A model for calorimetric measurements in an open quantum system
• Comparison between quantum jumps and master equation in the presence of a finite environment
• Calorimetric measurement of work for a driven harmonic oscillator