Fractional statistics and finite bosonic system: A one-dimensional case

TL;DR

This paper establishes an equivalence between finite 1D Bose systems and fractional Gentile statistics, providing a model for harmonically trapped Bose gases and generalizing to systems with power energy spectra.

Contribution

It introduces a novel equivalence between finite 1D Bose systems and fractional Gentile statistics, extending the understanding of quantum statistical models.

Findings

Finite 1D Bose systems are equivalent to systems obeying fractional Gentile statistics.

The model is applied to harmonically trapped Bose gases.

Results are generalized for systems with power energy spectra.

Abstract

The equivalence is established between the one-dimensional (1D) Bose-system with a finite number of particles and the system obeying the fractional (intermediate) Gentile statistics, in which the maximum occupation of single-particle energy levels is limited. The system of 1D harmonic oscillators is considered providing the model of harmonically trapped Bose-gas. The results are generalized for the system with power energy spectrum.