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

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.

5 pages, 1 figure, one figure added, accepted for publication in Phys. Rev. C

References in corpus (4)

• General Logarithmic Corrections to Black Hole Entropy
• Level Density of a Bose Gas and Extreme Value Statistics
• On the Quantum Density of States and Partitioning an Integer
• Level density of a Fermion gas: average growth, fluctuations, universality

Cited by in corpus (4)

• Statistical mechanics approach in the counting of integer partitions
• Microscopic electronic configurations after ultrafast magnetization dynamics
• A geometrical approach to the mean density of states in many-body quantum systems
• Boltzmann Distribution on "Short" Integer Partitions with Power Parts: Limit Laws and Sampling