Weak disorder expansion for localization lengths of quasi-1D systems

TL;DR

This paper introduces a perturbative formula for the Lyapunov exponent in quasi-1D Anderson models, enabling efficient numerical evaluation and comparison with traditional methods across various energies and disorder strengths.

Contribution

It presents a novel perturbative approach to compute localization lengths in quasi-1D systems, validated against standard transfer matrix results.

Findings

Good agreement with transfer matrix results across energies

Effective for large disorder strengths

Perturbative formula simplifies localization length calculations

Abstract

A perturbative formula for the lowest Lyapunov exponent of an Anderson model on a strip is presented. It is expressed in terms of an energy dependent doubly stochastic matrix, the size of which is proportional to the strip width. This matrix and the resulting perturbative expression for the Lyapunov exponent are evaluated numerically. Dependence on energy, strip width and disorder strength are thoroughly compared with the results obtained by the standard transfer matrix method. Good agreement is found for all energies in the band of the free operator and this even for quite large values of the disorder strength.