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arXiv · 1001.5365

Level density of a Fermi gas and integer partitions: a Gumbel-like finite-size correction

Jérôme Roccia·Patricio Leboeuf
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Abstract

We investigate the many-body level density of gas of non-interacting fermions. We determine its behavior as a function of the temperature and the number of particles. As the temperature increases, and beyond the usual Sommerfeld expansion that describes the degenerate gas behavior, corrections due to a finite number of particles lead to Gumbel-like contributions. We discuss connections with the partition problem in number theory, extreme value statistics as well as differences with respect to the Bose gas.

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Jérôme Roccia, Patricio Leboeuf. 2010-03-20. Level density of a Fermi gas and integer partitions: a Gumbel-like finite-size correction. https://doi.org/10.1103/physrevc.81.044301

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