Delocalization induced by nonlinearity in systems with disorder

I. GARCÍA-MATA; D.L. SHEPELYANSKY

PHYSICAL REVIEW E

AMER PHYSICAL SOC

Año: 2009 vol. 79 p. 26205 - 26213

1539-3755

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 Δn∝tν. This spreading continues up to a maximal dimensionless time scale t=109 reached in the numerical simulations. The numerical values of ν 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⩽109 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.