Spectral correlations in systems undergoing a transition from periodicity to disorder
Disordered Systems and Neural Networks
2009-10-31 v1 Mesoscale and Nanoscale Physics
Abstract
We study the spectral statistics for extended yet finite quasi 1-d systems which undergo a transition from periodicity to disorder. In particular we compute the spectral two-point form factor, and the resulting expression depends on the degree of disorder. It interpolates smoothly between the two extreme limits -- the approach to Poissonian statistics in the (weakly) disordered case, and the universal expressions derived for the periodic case. The theoretical results agree very well with the spectral statistics obtained numerically for chains of chaotic billiards and graphs.
Keywords
Cite
@article{arxiv.cond-mat/9811322,
title = {Spectral correlations in systems undergoing a transition from periodicity to disorder},
author = {T. Dittrich and B. Mehlig and H. Schanz and Uzy Smilansky and Peter Pollner and Gabor Vattay},
journal= {arXiv preprint arXiv:cond-mat/9811322},
year = {2009}
}
Comments
16 pages, Latex