Thermodynamics of ideal quantum gas with fractional statistics in D dimensions

TL;DR

This paper provides exact thermodynamic analysis of a quantum gas with fractional statistics across various dimensions, revealing how statistical interactions influence physical properties and phase transitions.

Contribution

It offers explicit formulas for thermodynamic quantities of fractional statistics gases in arbitrary dimensions, highlighting the crossover between bosonic and fermionic behaviors.

Findings

Isochoric heat capacity is independent of g in 2D.

Bose-Einstein condensation occurs at nonzero temperature in all dimensions.

Velocity of sound relates simply to thermodynamic response functions.

Abstract

We present exact and explicit results for the thermodynamic properties (isochores, isotherms, isobars, response functions, velocity of sound) of a quantum gas in dimensions D>=1 and with fractional exclusion statistics 0<=g<=1 connecting bosons (g=0) and fermions (g=1). In D=1 the results are equivalent to those of the Calogero-Sutherland model. Emphasis is given to the crossover between boson-like and fermion-like features, caused by aspects of the statistical interaction that mimic long-range attraction and short-range repulsion. The full isochoric heat capacity and the leading low-T term of the isobaric expansivity in D=2 are independent of g. The onset of Bose-Einstein condensation along the isobar occurs at a nonzero transition temperature in all dimensions. The T-dependence of the velocity of sound is in simple relation to isochores and isobars. The effects of soft container walls are accounted for rigorously for the case of a pure power-law potential.