The Fermi-Pasta-Ulam paradox, Anderson Localization problem and the the generalized diffusion approach

The goal of this paper is two-fold. First, based on the interpretation of a quantum tight-binding model in terms of a classical Hamiltonian map, we consider the Anderson localization (AL) problem as the Fermi-Pasta-Ulam (FPU) effect in a modified dynamical system containing both stable and unstable (inverted) modes. Delocalized states in the AL are analogous to the stable quasi-periodic motion in FPU; whereas localized states are analogous to thermalization, respectively. The second aim is to use the classical Hamilton map for a simplified derivation of exact equations for the localization operator H(z). The letter was presented earlier [J.Phys.: Condens. Matter 14 (2002) 13777] treating the AL as a generalized diffusion in a dynamical system. We demonstrate that counter-intuitive results of our studies of the AL are similar to the FPU counter-intuitivity. PACS numbers: 05.40.-a , 05.45.-a , 72.15.Rn ∗Electronic address: [email protected]