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

Jérôme Roccia ¹, Patricio Leboeuf ²

Physical Review C 81 (2010) 044301

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.

• 1. Institut de Physique et Chimie des Matériaux de Strasbourg (IPCMS),
  Université de Strasbourg – CNRS : UMR7504
• 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
  CNRS : UMR8626 – Université Paris XI – Paris Sud