What is between Fermi-Dirac and Bose-Einstein Statistics?

TL;DR

This paper explores intermediate quantum statistics introduced by Haldane, analyzing how it interpolates between Fermi-Dirac and Bose-Einstein distributions and examining its thermodynamic properties.

Contribution

It provides an explicit solution for the distribution function and investigates thermodynamic behavior across temperature regimes for particles with intermediate statistics.

Findings

Distribution function interpolates between Fermi-Dirac and Bose-Einstein

Explicit solution for the transcendental distribution equation

Thermodynamic properties characterized in different temperature limits

Abstract

We overwiev the properties of a quantum gas of particles with the intermediate statistics defined by Haldane. Although this statistics has no direct connection to the symmetry of the multiparticle wave function, the statistical distribution function interpolates continuously between the Fermi-Dirac and the Bose-Einstein limits. We present an explicit solution of the transcendental equation for the didtribution function in a general case, as well as determine the thermodynamic properties in both low- and high-temperature limits.