Perturbation theory for Lyapunov exponents of an Anderson model on a strip

TL;DR

This paper develops a perturbative formalism to bound the inverse localization length in an Anderson model on a strip, relating it to the Lyapunov exponents of random symplectic matrix products.

Contribution

It introduces a new perturbation approach to analyze Lyapunov exponents in disordered systems, providing bounds on localization length for small disorder.

Findings

Inverse localization length is bounded by L/λ^2 for small λ

Develops a formalism for calculating Lyapunov exponents perturbatively

Provides bounds relevant for Anderson localization on strips

Abstract

It is proven that the inverse localization length of an Anderson model on a strip of width $L$ is bounded above by $L/\lambda^2$ for small values of the coupling constant $\lambda$ of the disordered potential. For this purpose, a formalism is developed in order to calculate the bottom Lyapunov exponent associated with random products of large symplectic matrices perturbatively in the coupling constant of the randomness.