Absence of diffusion in the Anderson tight binding model for large disorder or low energy

Abstract

We prove that the Green's function of the Anderson tight binding Hamiltonian decays exponentially fast at long distances on ℤv, with probability 1. We must assume that either the disorder is large or the energy is sufficiently low. Our proof is based on perturbation theory about an infinite sequence of block Hamiltonians and is related to KAM methods. © 1983 Springer-Verlag.