Exclusion statistics: A resolution of the problem of negative weights

TL;DR

This paper introduces a new formulation for occupation probabilities in systems with fractional exclusion statistics, resolving issues of negative probabilities through revised counting rules.

Contribution

It provides a novel set of counting rules for exclusion statistics that eliminate negative weights, based on an exactly solvable model.

Findings

New counting rules prevent negative probabilities

Derived from an exactly solvable exclusion statistics model

Applicable to systems obeying Haldane's fractional exclusion statistics

Abstract

We give a formulation of the single particle occupation probabilities for a system of identical particles obeying fractional exclusion statistics of Haldane. We first derive a set of constraints using an exactly solvable model which describes an ideal exclusion statistics system and deduce the general counting rules for occupancy of states obeyed by these particles. We show that the problem of negative probabilities may be avoided with these new counting rules.