Destruction of Anderson localization by a weak nonlinearity

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 $\propto t^{\alpha }$, with the exponent $\alpha$ being in the range $0.3-0.4$. For small nonlinearities the distribution remains localized in a way similar to the linear case.

4 pages, 5 figs

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