An improved calculation of the Third Virial Coefficient of a free anyon Gas

TL;DR

This paper presents an improved method for calculating the third virial coefficient of a free anyon gas by focusing on the nonlinear contribution of three confined anyons, simplifying previous complex calculations.

Contribution

It introduces a streamlined calculation approach that isolates the nonlinear state contributions, avoiding cancellations and aligning with recent analytical proposals.

Findings

Numerical results match the analytical form suggested by recent studies.

The method simplifies the calculation of virial coefficients for anyon gases.

The approach confirms the significance of nonlinear state contributions in virial calculations.

Abstract

For three anyons confined in a harmonic oscillator, only the class of states that interpolate nonlinearly with the statistical parameter contributes to the third virial coefficient of a free anyon gas. Rather than evaluating the full three-body partition function as was done in an earlier publication (Phys. Rev. {\bf A46}, 4693 (1992)), here only the nonlinear contribution is calculated, thus avoiding delicate cancellations between the irrelevant linear part and the two-body partition function. Our numerical results are consistent with the simple analytical form suggested recently by Myrheim and Olaussen.