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

Abstract

It is proven that the inverse localization length of an Anderson model on a strip of width $L$ is bounded above by $L/λ^2$ for small values of the coupling constant $λ$ 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.