From Random Matrix Theory to Statistical Mechanics - Anyon Gas

TL;DR

This paper bridges random matrix theory and statistical mechanics to analyze an anyon gas, deriving a formal momentum distribution and validating it against known low-density hard-sphere gas results.

Contribution

It introduces a novel approach connecting random matrix models with statistical mechanical descriptions of anyon gases, extending previous methods.

Findings

Derived a formal expression for the momentum distribution of anyon gas.

Found agreement with known low-density hard-sphere gas results.

Discussed various limiting cases consistent with classical results.

Abstract

Motivated by numerical experiments and studies of quantum systems which are classically chaotic, we take a Random Matrix description of a Hard-sphere gas to Statistical Mechanical description. We apply this to Anyon gas and obtain a formal expression for the momentum distribution. Various limiting situations are discussed and are found in agreement with the well-known results on Hard-sphere gas in low-density regime.