Weak disorder expansion for localization lengths of quasi-1D systems
Disordered Systems and Neural Networks
2007-05-23 v1 Mesoscale and Nanoscale Physics
Mathematical Physics
math.MP
Abstract
A perturbative formula for the lowest Lyapunov exponent of an Anderson model on a strip is presented. It is expressed in terms of an energy dependent doubly stochastic matrix, the size of which is proportional to the strip width. This matrix and the resulting perturbative expression for the Lyapunov exponent are evaluated numerically. Dependence on energy, strip width and disorder strength are thoroughly compared with the results obtained by the standard transfer matrix method. Good agreement is found for all energies in the band of the free operator and this even for quite large values of the disorder strength.
Keywords
Cite
@article{arxiv.cond-mat/0405125,
title = {Weak disorder expansion for localization lengths of quasi-1D systems},
author = {Rudolf A. Roemer and Hermann Schulz-Baldes},
journal= {arXiv preprint arXiv:cond-mat/0405125},
year = {2007}
}
Comments
4 pages with 5 .eps figures included