Statistics of Anyon Gas and the Factorizable Property of Thermodynamic Quantities

TL;DR

This paper investigates the statistical properties of anyon gases, deriving their thermodynamic quantities and demonstrating a factorization property that links them to Bose and Fermi gases, supported by high-temperature and low-temperature analyses.

Contribution

It establishes the factorizable property of thermodynamic quantities of anyon gases, connecting them to Bose and Fermi gases through a rigorous theoretical framework.

Findings

Thermodynamic quantities of anyon gas can be factorized into Bose and Fermi components.

High-temperature and low-temperature limits support the derived factorization.

The factorization is rooted in the equivalence between anyon statistics and boson-fermion transmutation.

Abstract

The statistical distribution function of anyon is used to find the eighth viral coefficient in the high-temperature limit and the equation of state in the low-temperature limit. The perturbative results indicate that the thermodynamic quantities, $Q(\alpha)$, of the free anyon gas may be factorized in the terms characteristic of the ideal Bose ($\alpha =0$) and fermion ($\alpha =1$) gases, i.e., $Q(\alpha) = \alpha Q(1) + (1-\alpha) Q(0)$. It is shown that the factorizable property of the thermodynamic quantities, to all orders, can be established from the property of the equivalence between the anyon statistics and statistics in a system with boson-fermion transmutation, which was found by us in a recent paper (hep-th/0308095; Phys. Rev. E 51 (1995) 3729)