The Third Virial Coefficient of Free Anyons

TL;DR

This paper calculates the third virial coefficient for free anyons using a path integral approach, demonstrating its finiteness and providing numerical results that align with Fourier series convergence in the statistics angle.

Contribution

It introduces a path integral method to compute the third virial coefficient of free anyons and confirms its finiteness with numerical calculations.

Findings

The third virial coefficient of free anyons is finite.

Numerical results agree with Fourier series convergence.

The method confirms theoretical predictions about anyon statistics.

Abstract

We use a path integral representation for the partition function of non-interacting anyons confined in a harmonic oscillator potential in order to prove that the third virial coefficient of free anyons is finite, and to calculate it numerically. Our results together with previously known results are consistent with a rapidly converging Fourier series in the statistics angle.