The virial expansion of a classical interacting system

TL;DR

This paper derives the classical virial expansion for a one-dimensional system of particles with inverse square interactions, providing new insights into the equation of state and fractional exclusion statistics.

Contribution

It offers a concise re-derivation of the classical partition function and extends the virial expansion to fractional exclusion statistics in this system.

Findings

Classical partition function for the Calogero-Sutherland-Moser model is re-derived.

Equation of state is calculated for both trapped and homogeneous gases.

Classical limit of Wu's distribution function is obtained and used for virial expansion.

Abstract

We consider N particles interacting pair-wise by an inverse square potential in one dimension (Calogero-Sutherland-Moser model). When trapped harmonically, its classical canonical partition function for the repulsive regime is known in the literature. We start by presenting a concise re-derivation of this result. The equation of state is then calculated both for the trapped and the homogeneous gas. Finally, the classical limit of Wu's distribution function for fractional exclusion statistics is obtained and we re-derive the classical virial expansion of the homogeneous gas using this distribution function.