Anderson localization at large disorder

TL;DR

This paper investigates Anderson localization at high disorder levels, revealing non-monotonic energy dependence and analyzing small-site models to understand localization phenomena across dimensions.

Contribution

It introduces analytical solutions for two- and three-site models that capture key features of localization at large disorder, validated by numerical simulations.

Findings

Inverse participation number shows non-monotonic energy dependence

Two-site approximation captures essential localization features

Three-site model improves understanding of localization behavior

Abstract

The localization of one-electron states in the large (but finite) disorder limit is investigated. The inverse participation number shows a non--monotonic behavior as a function of energy owing to anomalous behavior of few-site localization. The two-site approximation is solved analytically and shown to capture the essential features found in numerical simulations on one-, two- and three-dimensional systems. Further improvement has been obtained by solving a three-site model.