From creation and annihilation operators to statistics

Abstract

A procedure to derive the partition function of non-interacting particles with exotic or intermediate statistics is presented. The partition function is directly related to the associated creation and annihilation operators that obey some specific commutation or anti-commutation relations. The cases of Gentile statistics, quons, Polychronakos statistics, and ewkons are considered. Ewkons statistics was recently derived from the assumption of free diffusion in energy space (Phys. Rev. E 94, 062115, 2016); an ideal gas of ewkons has negative pressure, a feature that makes them suitable for the description of dark energy.

15 pages, 1 figure

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• Improved Cosmological Constraints from New, Old and Combined Supernova Datasets
• Thermodynamic Geometry of Fractional Statistics
• Fractional exclusion statistics in general systems with interaction
• Quantum statistics of classical particles derived from the condition of free diffusion coefficient