Exclusion statistics for particles with a discrete spectrum

Authors

Stéphane Ouvry, Paris-Saclay University
Alexios P. Polychronakos, CUNY Graduate CenterFollow

Document Type

Article

Publication Date

2021

Abstract

We formulate and study the microscopic statistical mechanics of systems of particles with exclusion statistics in a discrete one-body spectrum. The statistical mechanics of these systems can be expressed in terms of effective single-level grand partition functions obeying a generalization of the standard thermodynamic exclusion statistics equation of state. We derive explicit expressions for the thermodynamic potential in terms of microscopic cluster coefficients and show that the mean occupation numbers of levels satisfy a nesting relation involving a number of adjacent levels determined by the exclusion parameter. We apply the formalism to the harmonic Calogero model and point out a relation with the Ramanujan continued fraction identity and appropriate generalizations.

Comments

This work was originally published in Nuclear Physics B, available at https://doi.org/10.1016/j.nuclphysb.2021.115573

This work is distributed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).