Destruction of Anderson Localization by a Weak Nonlinearity

2007/08/24 by Arkady Pikovsky, A. S. Pikovsky, Dima L. Shepelyansky +1 · 8 citations
Computer Science · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #cond-mat.dis-nn #nlin.CD

paper · pdf · doi:10.1103/physrevlett.100.094101

published as Phys. Rev. Lett. v.100, p.094101 (2008) · 4 pages, 5 figs

arxiv created 2007/08/24 · openalex publication_date 2008/03/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study numerically the 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 proportional, variant 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.

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