Delocalization induced by nonlinearity in systems with disorder

Details Delocalization induced by nonlinearity in systems with disorder Delocalization induced by nonlinearity in systems with disorder

2008-05-05

arxiv.org/abs/0805.0539v2

Phys. Rev. E 79, 026205 (2009)

Physics

Condensed Matter

Disordered Systems and Neural Networks

8 pages, 13 figures. New data and references added. Research at http://www.quantware.ups-tlse.fr/

Scientific paper

10.1103/PhysRevE.79.026205

We study numerically the effects of nonlinearity on the Anderson localization in lattices with disorder in one and two dimensions. The obtained results show that at moderate strength of nonlinearity an unlimited spreading over the lattice in time takes place with an algebraic growth of number of populated sites $\Delta n \propto t^{\nu}$. The numerical values of $\nu$ are found to be approximately $0.15 - 0.2$ and 0.25 for the dimension $d=1$ and 2 respectively being in a satisfactory agreement with the theoretical value $d/(3d+2)$. The localization is preserved below a certain critical value of nonlinearity. We also discuss the properties of the fidelity decay induced by a perturbation of nonlinear field.

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