Spreading in Disordered Lattices with Different Nonlinearities

Details Spreading in Disordered Lattices with Different Nonlinearities Spreading in Disordered Lattices with Different Nonlinearities

2010-02-18

arxiv.org/abs/1002.3470v2

M. Mulansky and A. Pikovsky 2010 EPL 90 10015

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 6 figures

Scientific paper

10.1209/0295-5075/90/10015

We study the spreading of initially localized states in a nonlinear disordered lattice described by the nonlinear Schr\"odinger 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 R\'enyi 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 Schr\"odinger 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.

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