Correlated random band matrices: localization-delocalization transitions
Mesoscale and Nanoscale Physics
2009-10-31 v1 Disordered Systems and Neural Networks
Statistical Mechanics
Abstract
We study the statistics of eigenvectors in correlated random band matrix models. These models are characterized by two parameters, the band width B(N) of a Hermitian N times N matrix and the correlation parameter C(N) describing correlations of matrix elements along diagonal lines. The correlated band matrices show a much richer phenomenology than models without correlation as soon as the correlation parameter scales sufficiently fast with matrix size. In particular, for B(N) and C(N) increasing like the square root of N the model shows a localization-delocalization transition of the quantum Hall type.
Cite
@article{arxiv.cond-mat/9911467,
title = {Correlated random band matrices: localization-delocalization transitions},
author = {Martin Janssen and Krystian Pracz},
journal= {arXiv preprint arXiv:cond-mat/9911467},
year = {2009}
}
Comments
12 pages, 11 postscript figures