Fractional exclusion statistics and the Random Matrix Boson Ensemble

TL;DR

This paper explores the energy spectrum of bosonic random matrix ensembles, revealing a generalized beta distribution that aligns with fractional exclusion statistics, bridging random matrix theory and quantum statistical models.

Contribution

It demonstrates that the energy spectrum of the bosonic ensemble follows a generalized beta distribution, connecting it with fractional exclusion statistics introduced by Haldane.

Findings

Energy spectrum follows a generalized beta distribution.

Distribution matches that of non-interacting quasiparticles obeying fractional exclusion statistics.

Links random matrix ensembles with quantum statistical models.

Abstract

The k-body Gaussian Embedded Ensemble of Random Matrices is considered for N bosons distributed on two single-particle levels. When k = N, the ensemble is equivalent to the Gaussian Orthogonal Ensemble (GOE), and when k = 2 it corresponds to the Two-body Random Ensemble (TBRE) for bosons. It is shown that the energy spectrum leads to a rank function which is of the form of a discrete generalized beta distribution. The same distribution is obtained assuming N non-interacting quasiparticles that obey the fractional exclusion statistics introduced by Haldane two decades ago.