Impact of localization on Dyson's circular ensemble
Condensed Matter
2009-10-28 v1
Abstract
A wide variety of complex physical systems described by unitary matrices have been shown numerically to satisfy level statistics predicted by Dyson's circular ensemble. We argue that the impact of localization in such systems is to provide certain restrictions on the eigenvalues. We consider a solvable model which takes into account such restrictions qualitatively and find that within the model a gap is created in the spectrum, and there is a transition from the universal Wigner distribution towards a Poisson distribution with increasing localization.
Keywords
Cite
@article{arxiv.cond-mat/9510005,
title = {Impact of localization on Dyson's circular ensemble},
author = {K. A. Muttalib and M. E. H. Ismail},
journal= {arXiv preprint arXiv:cond-mat/9510005},
year = {2009}
}
Comments
To be published in J. Phys. A