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

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

2008-11-12

arxiv.org/abs/0811.1832v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

20 pages

Scientific paper

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 \textit{exact} equations for the localization operator $H(z)$. The letter was presented earlier [J.Phys.: Condens. Matter {\bf 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.

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