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 $L/{\lambda }^2$ 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.

to appear in GAFA