A mean-field theory of Anderson localization
Disordered Systems and Neural Networks
2008-09-16 v1
Abstract
Anderson model of noninteracting disordered electrons is studied in high spatial dimensions. We find that off-diagonal one- and two-particle propagators behave as gaussian random variables w.r.t. momentum summations. With this simplification and with the electron-hole symmetry we reduce the parquet equations for two-particle irreducible vertices to a single algebraic equation for a local vertex. We find a disorder-driven bifurcation point in this equation signalling vanishing of diffusion and onset of Anderson localization. There is no bifurcation in where all states are localized. A natural order parameter for Anderson localization pops up in the construction.
Cite
@article{arxiv.cond-mat/0402471,
title = {A mean-field theory of Anderson localization},
author = {V. Janis and J. Kolorenc},
journal= {arXiv preprint arXiv:cond-mat/0402471},
year = {2008}
}
Comments
REVTeX4, 4 pages, 2 EPS figures