Thermodynamics of an one-dimensional ideal gas with fractional exclusion statistics

TL;DR

This paper demonstrates that particles in the Calogero-Sutherland Model follow fractional exclusion statistics, deriving their energy distribution, partition function, and virial expansion, revealing unique statistical properties of the system.

Contribution

It provides a detailed analysis of fractional exclusion statistics in the Calogero-Sutherland Model, including explicit derivations of distribution functions and virial coefficients.

Findings

Particles obey fractional exclusion statistics as per Haldane.

Partition function factorizes like an ideal gas.

Only the second virial coefficient encodes the statistics.

Abstract

We show that the particles in the Calogero-Sutherland Model obey fractional exclusion statistics as defined by Haldane. We construct anyon number densities and derive the energy distribution function. We show that the partition function factorizes in the form characteristic of an ideal gas. The virial expansion is exactly computable and interestingly it is only the second virial coefficient that encodes the statistics information.