High temperature expansion, Virial coefficients and Exclusion statistics

TL;DR

This paper explores the extension of exclusion statistics to infinite-dimensional spaces, calculating virial coefficients and validating Haldane's definition through high-temperature expansions and particle distribution analysis.

Contribution

It reproduces virial coefficients for anionic gases and demonstrates the usefulness of high-temperature expansion in defining mutual exclusion statistics.

Findings

Reproduces third virial coefficients for single-species gases.

Calculates second mixed virial coefficients for multicomponent gases.

Validates Haldane's exclusion statistics through high-temperature expansion.

Abstract

We follow the generalisation of exclusion statistics to infinite dimensional Hilbert space as envisaged in Phys. Rev. Lett. {\bf{72}}, 3629, 1994. We reproduce the third virial coefficients at leading order for single species of anionic gas and 2nd mixed virial coefficients for multicomponent anionic gas. We argue that this particular method can be useful in determining definition of mutual exclusion statistics. We demonstrate this by taking high temperature expansion of two particle partition function of well known systems and show that it follows Haldane's definition of exclusion statistics. We also discuss equilibrium particle distributions at thermodynamic limit.