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arXiv · 1203.3053

Universal subdiffusion of nonlinear waves in two dimensions with disorder

T. V. Laptyeva·J. D. Bodyfelt·S. Flach
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Abstract

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 $t^α$. We perform fine statistical averaging and test theoretical predictions for $α$. 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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T. V. Laptyeva, J. D. Bodyfelt, S. Flach. 2012-03-14. Universal subdiffusion of nonlinear waves in two dimensions with disorder. https://arxiv.org/abs/1203.3053

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