Thermodynamics of small Fermi systems: quantum statistical fluctuations

Abstract

We investigate the probability distribution of the quantum fluctuations of thermodynamic functions of finite, ballistic, phase-coherent Fermi gases. Depending on the chaotic or integrable nature of the underlying classical dynamics, on the thermodynamic function considered, and on temperature, we find that the probability distributions are dominated either (i) by the local fluctuations of the single-particle spectrum on the scale of the mean level spacing, or (ii) by the long-range modulations of that spectrum produced by the short periodic orbits. In case (i) the probability distributions are computed using the appropriate local universality class, uncorrelated levels for integrable systems and random matrix theory for chaotic ones. In case (ii) all the moments of the distributions can be explicitly computed in terms of periodic orbit theory, and are system-dependent, non-universal, functions. The dependence on temperature and number of particles of the fluctuations is explicitly computed in all cases, and the different relevant energy scales are displayed.

24 pages, 7 figures, 5 tables

References in corpus (2)

• Quantum Transport in Semiconductor Nanostructures
• Nuclear masses: evidence of order-chaos coexistence

Cited by in corpus (8)

• Semiclassical Theory of Bardeen-Cooper-Schrieffer Pairing-Gap Fluctuations
• Correlations in Nuclear Masses
• Double-magicity of proton drip-line nucleus ${}^{22}$Si with \textit{ab initio} calculation
• Average ground-state energy of finite Fermi systems
• Fluctuations in the level density of a Fermi gas
• Quantum thermodynamic fluctuations of a chaotic Fermi-gas model
• On the ground--state energy of finite Fermi systems
• Quantum Chaos and Regularity in Ultracold Fermi Gases