Fractional statistic

TL;DR

This paper refines Haldane's formula for fractional statistics, providing a finite-size correction and a geometric interpretation, enhancing understanding of particle configurations beyond the thermodynamic limit.

Contribution

The authors introduce a new finite-size formula for fractional statistics and offer a geometric interpretation using composite particles, extending prior theoretical frameworks.

Findings

New finite-size formula for fractional statistics

Geometric interpretation via composite particles

Consistency with thermodynamic limit results

Abstract

We improve Haldane's formula which gives the number of configurations for $N$ particles on $d$ states in a fractional statistic defined by the coupling $g=l/m$. Although nothing is changed in the thermodynamic limit, the new formula makes sense for finite $N=pm+r$ with $p$ integer and $0<r\leq m.$ A geometrical interpretation of fractional statistic is given in terms of ''composite particles''.