Journal
PHYSICAL REVIEW E
Volume 79, Issue 2, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.79.026205
Keywords
Anderson model
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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 Delta n proportional to t(nu). 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 <= 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.
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