Universal subdiffusion of nonlinear waves in two dimensions with disorder

TL;DR

This study investigates how nonlinear waves in two-dimensional disordered lattices spread over time, revealing subdiffusive behavior and confirming theoretical predictions about their spreading rate.

Contribution

The paper provides the first detailed numerical confirmation of subdiffusive spreading of nonlinear waves in 2D disordered systems, including analysis of intermediate deviations.

Findings

Wave packets spread subdiffusively with growth exponent α.

Confirmation of theoretical predictions for spreading rate.

Identification of long-lasting intermediate deviations due to surface resonances.

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 $t^\alpha$. 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.