One-dimensional Anderson Localization: Devil's staircase of Statistical Anomalies
Disordered Systems and Neural Networks
2015-05-13 v1 Mesoscale and Nanoscale Physics
Abstract
The statistics of wavefunctions in the one-dimensional (1d) Anderson model of localization is considered. It is shown that at any energy that corresponds to a rational filling factor f=p/q there is a statistical anomaly which is seen in expansion of the generating function (GF) to the order (q-2) in the disorder parameter. We study in detail the principle anomaly at that appears in the leading order. The transfer-matrix equation of the Fokker-Planck type with a two-dimensional internal space is derived for GF. It is shown that the zero-mode variant of this equation is integrable and a solution for the generating function is found in the thermodynamic limit.
Keywords
Cite
@article{arxiv.0806.2118,
title = {One-dimensional Anderson Localization: Devil's staircase of Statistical Anomalies},
author = {V. E. Kravtsov and V. I. Yudson},
journal= {arXiv preprint arXiv:0806.2118},
year = {2015}
}
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4 pages RevTex, 1 picture