# Destruction of Anderson localization by a weak nonlinearity - Condensed Matter > Disordered Systems and Neural Networks

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Abstract: We study numerically a spreading of an initially localized wave packet in aone-dimensional discrete nonlinear Schr\-odinger lattice with disorder. Wedemonstrate that above a certain critical strength of nonlinearity the Andersonlocalization is destroyed and an unlimited subdiffusive spreading of the fieldalong the lattice occurs. The second moment grows with time $\proptot^\alpha$, with the exponent $\alpha$ being in the range $0.3 - 0.4$. For smallnonlinearities the distribution remains localized in a way similar to thelinear case.

Autor: A. S. Pikovsky, D. L. Shepelyansky

Fuente: https://arxiv.org/