Physical interpretation of the spectral approach to delocalization in infinite disordered systems

TL;DR

This paper introduces a spectral approach to understanding delocalization in infinite disordered systems, offering a boundary-condition-independent perspective and applying it to numerical simulations in 2D and 3D.

Contribution

It provides a novel spectral analysis method for localization problems, with a physical interpretation and application to disordered systems in multiple dimensions.

Findings

Delocalization occurs at W<=0.6 in 2D.

Delocalization occurs at W<=5 in 3D.

Spectral analysis avoids boundary condition issues in localization studies.

Abstract

In this paper we introduce the spectral approach to delocalization in infinite disordered systems and provide a physical interpretation in context of the classical model of Edwards and Thouless. We argue that spectral analysis is an important contribution to localization problems since it avoids issues related to the use of boundary conditions. Applying the method to 2D and 3D numerical simulations with various amount of disorder W shows that delocalization occurs for W<=0.6 in 2D and for W<=5 for 3D.