Anomalous Localization in Low-Dimensional Systems with Correlated Disorder

TL;DR

This review explores how correlations in disorder affect Anderson localization in one-dimensional systems, highlighting the emergence of mobility edges and comparing theoretical predictions with experimental microwave transmission results.

Contribution

It provides a unified analysis of localization in correlated disordered systems, emphasizing the role of long-range correlations and effective mobility edges across various models.

Findings

Correlations can induce effective mobility edges in 1D systems.

Localization length depends on disorder correlations and model parameters.

Theoretical and numerical results align with microwave transmission experiments.

Abstract

This review presents a unified view on the problem of Anderson localization in one-dimensional weakly disordered systems with short-range and long-range statistical correlations in random potentials. The following models are analyzed: the models with continuous potentials, the tight-binding models of the Anderson type, and various Kronig-Penney models with different types of perturbations. Main attention is payed to the methods of obtaining the localization length in dependence on the controlling parameters of the models. Specific interest is in an emergence of effective mobility edges due to certain long-range correlations in a disorder. The predictions of the theoretical and numerical analysis are compared to recent experiments on microwave transmission through randomly filled waveguides.