From Fractional Exclusion Statistics Back to Bose and Fermi Distributions

TL;DR

This paper demonstrates how fractional exclusion statistics systems can be equivalently described as gases of quasiparticles obeying Bose or Fermi distributions, providing a reverse mapping from FES to traditional distributions.

Contribution

It introduces a method to represent FES systems as quasiparticle gases obeying Bose or Fermi statistics, reversing the usual approach.

Findings

FES systems can be described as quasiparticle gases obeying Bose or Fermi distributions.

The quasiparticle energies are derived from FES equations for equilibrium distributions.

An example using the effective mass approximation illustrates the procedure.

Abstract

Fractional exclusion statistics (FES) is a generalization of the Bose and Fermi statistics. Typically, systems of interacting particles are described as ideal FES systems and the properties of the FES systems are calculated from the properties of the interacting systems. In this paper I reverse the process and I show that a FES system may be described in general as a gas of quasiparticles which obey Bose or Fermi distributions; the energies of the newly defined quasiparticles are calculated starting from the FES equations for the equilibrium particle distribution. In the end I use a system in the effective mass approximation as an example to show how the procedure works.