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DY: Fachverband Dynamik und Statistische Physik
DY 15: ISPS Intersectional Poster Session
DY 15.1: Poster
Tuesday, March 15, 2011, 18:00–20:00, P1
Wave packet spreading in strongly disordered nonlinear lattices — Mikhail Ivanchenko1,2, •Tetyana Laptyeva2, and Sergej Flach2 — 1Theory of Oscillations Department, University of Nizhniy Novgorod, Russia — 2Max Planck Institute for the Physics of Complex Systems, Noethnitzer Str. 38, 01187 Dresden, Germany
Localization of eigenmodes and halt of wave propagation in linear lattices by disorder, the famous Anderson localization, underpins a set of fundamental physical phenomena. To mention are electrical and thermal conductivities, localization of light and matter waves in optical lattices. Nonlinearity induces interaction between eigenmodes and the question of whether it destroys Anderson localization or not is under hot debate in the fields of nonlinear science and condensed matter.
We achieve a progress there by studying analytically and computationally the limit of strongly disordered nonlinear lattices characterized by compactly localized eigenmodes. Employing perturbation theory techniques we demonstrate that even in this case there is always a finite probability for a wave packet to spread that decreases linearly with the energy. Moreover, we show that the same holds in the limit of infinitely small energy density too, the full energy being the only control parameter. Above a certain threshold in energy finite-size excitations will spread with probability 1. Infinitely small energy density limit gives an exponentially small probability of localization in this case. Numerics confirm the predictions above, revealing, in addition, intermittent and not diffusive type of spreading in this strong disorder limit.