An interpolation between Bose, Fermi and Maxwell-Boltzmann statistics based on Jack Polynomials

TL;DR

This paper introduces a novel interpolation framework between Bose, Fermi, and Maxwell-Boltzmann statistics using Jack polynomials, enabling new forms of exclusion statistics with potential physical applications.

Contribution

It proposes a mathematically grounded interpolation method connecting different quantum statistics through Jack polynomials, extending the concept of exclusion statistics.

Findings

Defines a new interpolation between statistical weights

Uses properties of Jack polynomials for physical modeling

Suggests a new form of exclusion statistics

Abstract

An interpolation between the canonical partition functions of Bose, Fermi and Maxwell-Boltzmann statistics is proposed. This interpolation makes use of the properties of Jack polynomials and leads to a physically appealing interpolation between the statistical weights of the three statistics. This, in turn, can be used to define a new exclusion statistics in the spirit of the work of Haldane.