title: Delocalization induced by nonlinearity in systems with disorder.
abstract: 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 a spreading over the lattice in time takes place with an algebraic growth of number of populated sites Deltan proportional to tnu. This spreading continues up to a maximal dimensionless time scale t=10(9) reached in the numerical simulations. 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). During the computational times t<or=10(9) 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.
authors.affiliation: Laboratoire de Physique Théorique, UMR 5152 du CNRS, Université Toulouse III, 31062 Toulouse, France.
authors.forename: Ignacio
authors.initials: I
authors.lastname: García-Mata
authors.forename: Dima L
authors.initials: DL
authors.lastname: Shepelyansky