Statistical mechanics and thermodynamics for multispecies exclusion statistics

TL;DR

This paper systematically studies the thermodynamics of ideal fractional exclusion statistics with mutual interactions, deriving general expansions and analyzing multispecies anyons, linking exclusion statistics to physical models.

Contribution

It introduces a unified virial expansion for systems with fractional exclusion statistics and solves the multispecies anyon problem in the lowest Landau level for arbitrary charges and masses.

Findings

Derived a general form of the cluster and virial expansions.

Analyzed thermodynamics for symmetric statistics matrices at constant density.

Solved the multispecies anyon problem in the lowest Landau level.

Abstract

Statistical mechanics and thermodynamics for ideal fractional exclusion statistics with mutual statistical interactions is studied systematically. We discuss properties of the single-state partition functions and derive the general form of the cluster expansion. Assuming a certain scaling of the single-particle partition functions, relevant to systems of noninteracting particles with various dispersion laws, both in a box and in an external harmonic potential, we derive a unified form of the virial expansion. For the case of a symmetric statistics matrix at a constant density of states, the thermodynamics is analyzed completely. We solve the microscopic problem of multispecies anyons in the lowest Landau level for arbitrary values of particle charges and masses (but the same sign of charges). Based on this, we derive the equation of state which has the form implied by exclusion statistics, with the statistics matrix coinciding with the exchange statistics matrix of anyons. Relation to one-dimensional integrable models is discussed.