Fluctuations in the level density of a Fermi gas

P. Leboeuf ¹, A. G. Monastra ², A. Relano ³

Physical Review Letters 94 (2005) 102502

We present a theory that accurately describes the counting of excited states of a noninteracting fermionic gas. At high excitation energies the results reproduce Bethe\’s theory. At low energies oscillatory corrections to the many–body density of states, related to shell effects, are obtained. The fluctuations depend non-trivially on energy and particle number. Universality and connections with Poisson statistics and random matrix theory are established for regular and chaotic single–particle motion.

• 1. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
  CNRS : UMR8626 – Université Paris XI – Paris Sud
• 2. Institut fur Theoretische Physik,
  Technische Universitat Dresden
• 3. Departamento de Fisica Atomica, Molecular y Nuclear,
  Universidad Complutense de Madrid