Statistical correlations in an ideal gas of particles obeying fractional exclusion statistics

TL;DR

This paper investigates the thermodynamic properties and correlation functions of particles obeying fractional exclusion statistics, highlighting the effects of dimensionality and statistical parameters through analytical and numerical methods.

Contribution

It provides new analytical and numerical results on thermodynamics and correlations in fractional exclusion statistics, emphasizing the role of dimensionality and density effects.

Findings

Chemical potential ratio varies with scaled density.

Friedel oscillations emerge near the fermion limit.

Dimensionality influences thermodynamic behavior.

Abstract

After a brief discussion of the concepts of fractional exchange and fractional exclusion statistics, we report partly analytical and partly numerical results on thermodynamic properties of assemblies of particles obeying fractional exclusion statistics. The effect of dimensionality is one focal point, the ratio mu/kB T of chemical potential to thermal energy being obtained numerically as a function of a scaled particle density. Pair correlation functions are also presented as a function of the statistical parameter, with `Friedel' oscillations developing close to the fermion limit, for sufficiently large density.