Spreading of waves in nonlinear disordered media

Details Spreading of waves in nonlinear disordered media Spreading of waves in nonlinear disordered media

2010-01-15

arxiv.org/abs/1001.2673v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

24 pages, 3 figures

Scientific paper

We analyze mechanisms and regimes of wave packet spreading in nonlinear disordered media. We predict that wave packets can spread in two regimes of strong and weak chaos. We discuss resonance probabilities, nonlinear diffusion equations, and predict a dynamical crossover from strong to weak chaos. The crossover is controlled by the ratio of nonlinear frequency shifts and the average eigenvalue spacing of eigenstates of the linear equations within one localization volume. We consider generalized models in higher lattice dimensions and obtain critical values for the nonlinearity power, the dimension, and norm density, which influence possible dynamical outcomes in a qualitative way.

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