Fractional exclusion statistics and the Random Matrix Boson Ensemble
Atomic Physics
2012-04-02 v1 Statistical Mechanics
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.
Cite
@article{arxiv.1203.6694,
title = {Fractional exclusion statistics and the Random Matrix Boson Ensemble},
author = {Saul Hernández-Quiroz and Manuel Beltrán and Luis Benet and Jorge Flores and Germinal Cocho},
journal= {arXiv preprint arXiv:1203.6694},
year = {2012}
}