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

Abstract

We investigate the many-body level density of a gas of noninteracting 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, and differences with respect to the Bose gas.

Authors:
 [1];  [2]
  1. Institut de Physique et Chimie des Materiaux de Strasbourg, UMR 7504, CNRS-UdS, 23 rue du Loess, BP 43, F-67034 Strasbourg Cedex 2 (France)
  2. Laboratoire de Physique Theorique et Modeles Statistiques, CNRS, Universite Paris Sud, UMR 8626, F-91405 Orsay Cedex (France)
Publication Date:
OSTI Identifier:
21388910
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 81; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevC.81.044301; (c) 2010 The American Physical Society
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; BOSE-EINSTEIN GAS; CORRECTIONS; ENERGY-LEVEL DENSITY; EXPANSION; FERMI GAS; FERMIONS; MANY-BODY PROBLEM; TEMPERATURE DEPENDENCE

Citation Formats

Roccia, Jerome, and Leboeuf, Patricio. Level density of a Fermi gas and integer partitions: A Gumbel-like finite-size correction. United States: N. p., 2010. Web. doi:10.1103/PHYSREVC.81.044301.
Roccia, Jerome, & Leboeuf, Patricio. Level density of a Fermi gas and integer partitions: A Gumbel-like finite-size correction. United States. doi:10.1103/PHYSREVC.81.044301.
Roccia, Jerome, and Leboeuf, Patricio. 2010. "Level density of a Fermi gas and integer partitions: A Gumbel-like finite-size correction". United States. doi:10.1103/PHYSREVC.81.044301.
@article{osti_21388910,
title = {Level density of a Fermi gas and integer partitions: A Gumbel-like finite-size correction},
author = {Roccia, Jerome and Leboeuf, Patricio},
abstractNote = {We investigate the many-body level density of a gas of noninteracting 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, and differences with respect to the Bose gas.},
doi = {10.1103/PHYSREVC.81.044301},
journal = {Physical Review. C, Nuclear Physics},
number = 4,
volume = 81,
place = {United States},
year = 2010,
month = 4
}
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