Fermi-Dirac statistics and the number theory

Abstract

We relate the Fermi-Dirac statistics of an ideal Fermi gas in a harmonic trap to partitions of given integers into distinct parts, studied in number theory. Using methods of quantum statistical physics we derive analytic expressions for cumulants of the probability distribution of the number of different partitions.

7pages, 2 figures, epl.cls, revised version

References in corpus (6)

• Anomalous fluctuations of the condensate in interacting Bose gases
• Condensate Fluctuations in Trapped Bose Gases: Canonical vs. Microcanonical Ensemble
• On the Quantum Density of States and Partitioning an Integer
• Microcanonical fluctuations of the condensate in weakly interacting Bose gases
• Asymptotics of the number partitioning distribution
• Exact ground state number fluctuations of trapped ideal and interacting fermions

Cited by in corpus (6)

• Quantum theory of bright matter wave solitons in harmonic confinement
• Grand-canonical condensate fluctuations in weakly interacting Bose-Einstein condensates of light
• A statistical mechanical approach to restricted integer partition functions
• Statistical-mechanical description of quantum entanglement
• On the fluctuations of the number of atoms in the condensate
• Stochastic Dynamics of Growing Young Diagrams and Their Limit Shapes