Universal subdiffusion of nonlinear waves in two dimensions with disorder

Details Universal subdiffusion of nonlinear waves in two dimensions with disorder Universal subdiffusion of nonlinear waves in two dimensions with disorder

2012-03-14

arxiv.org/abs/1203.3053v1

Nonlinear Sciences

Chaotic Dynamics

6 pages, 6 figures, 1 table

Scientific paper

We follow the dynamics of nonlinear waves in two-dimensional disordered lattices with tunable nonlinearity. In the absence of nonlinear terms Anderson localization traps the packet in space. For the nonlinear case a destruction of Anderson localization is found. The packet spreads subdiffusively, and its second moment grows in time asymptotically as $t^\alpha$. We perform fine statistical averaging and test theoretical predictions for $\alpha$. Along with a precise confirmation of the predictions in [Chemical Physics \textbf{375}, 548 (2010)], we also find potentially long lasting intermediate deviations due to a growing number of surface resonances of the wave packet.

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