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

摘要

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 A 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.