Delocalization induced by nonlinearity in systems with disorder.
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.
García-Mata
Ignacio
I
Laboratoire de Physique Théorique, UMR 5152 du CNRS, Université Toulouse III, 31062 Toulouse, France.
Shepelyansky
Dima L
DL