# Modeling free anyons at the bosonic and fermionic ends

## TL;DR

This paper proposes a modified statistical model for free anyons that interpolates between bosonic and fermionic behaviors, matching known virial coefficients and calculating an effective excitation spectrum.

## Contribution

It introduces a new functional form for the occupation numbers of free anyons, extending the Gibbs factor to better describe their unique statistics.

## Key findings

- Virial coefficients match those of free anyons up to the fifth order.
- The model accurately reproduces the bosonic and fermionic limits.
- An effective excitation spectrum for anyons is derived.

## Abstract

The topology of two-dimensional movement allows for existing of anyons -- particles obeying statistics intermediate between that of bosons and fermions. In this article, the functional form of the occupation numbers of free anyons is suggested as a modification of the Gibbs factor in the Bose and Fermi statistics. The proposed expressions are studied in the bosonic and fermionic limits. The obtained virial coefficients coincide with those of free anyons up to the fourth and fifth virial coefficients (the proposed approach can be extended for higher ones as well) and up to the second order in the anyonic parameter. The effective excitation spectrum corresponding to anyons is calculated.