Spreading in disordered lattices with different nonlinearities

Department of Physics and Astronomy, Potsdam University - 14476 Potsdam, Germany, EU

Received: 18 February 2010
Accepted: 6 April 2010

Abstract

We study the spreading of initially localized states in a nonlinear disordered lattice described by the nonlinear Schrödinger equation with random on-site potentials —a nonlinear generalization of the Anderson model of localization. We use a nonlinear diffusion equation to describe the subdiffusive spreading. To confirm the self-similar nature of the evolution we characterize the peak structure of the spreading states with help of Rényi entropies and in particular with the structural entropy. The latter is shown to remain constant over a wide range of time. Furthermore, we report on the dependence of the spreading exponents on the nonlinearity index in the generalized nonlinear Schrödinger disordered lattice, and show that these quantities are in accordance with previous theoretical estimates, based on assumptions of weak and very weak chaoticity of the dynamics.