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arXiv · 0708.3315

Destruction of Anderson localization by a weak nonlinearity

A. S. Pikovsky·D. L. Shepelyansky
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Abstract

We study numerically a spreading of an initially localized wave packet in a one-dimensional discrete nonlinear Schrödinger lattice with disorder. We demonstrate that above a certain critical strength of nonlinearity the Anderson localization is destroyed and an unlimited subdiffusive spreading of the field along the lattice occurs. The second moment grows with time $ \propto t^α$, with the exponent $α$ being in the range $0.3 - 0.4$. For small nonlinearities the distribution remains localized in a way similar to the linear case.

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A. S. Pikovsky, D. L. Shepelyansky. 2007-08-24. Destruction of Anderson localization by a weak nonlinearity. https://doi.org/10.1103/physrevlett.100.094101

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