Fractional exclusion statistics and the Random Matrix Boson Ensemble
Abstract
The kbody Gaussian Embedded Ensemble of Random Matrices is considered for N bosons distributed on two singleparticle levels. When k = N, the ensemble is equivalent to the Gaussian Orthogonal Ensemble (GOE), and when k = 2 it corresponds to the Twobody 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 noninteracting quasiparticles that obey the fractional exclusion statistics introduced by Haldane two decades ago.
 Publication:

arXiv eprints
 Pub Date:
 March 2012
 DOI:
 10.48550/arXiv.1203.6694
 arXiv:
 arXiv:1203.6694
 Bibcode:
 2012arXiv1203.6694H
 Keywords:

 Physics  Atomic Physics;
 Condensed Matter  Statistical Mechanics