Delocalization and ballistic dynamics in the two-dimensional Anderson model with long-range correlated disorder

We study the nature of one-electron eigenstates in a two-dimensional (2d) Anderson model with long-range correlated disorder. Long-range correlations are introduced by using a 2d discrete Fourier method which generates an appropriated disorder distribution with spectral density S(k) proportional to 1/k(alpha2d). Our numerical data suggest that the exponents governing the collapse of the participation function for low energies (xi proportional to N (D2)) and the long time decay of the autocorrelation function (C(t) proportional to t(-beta)) satisfy the scaling relation D-2 = betad. They also imply that the system exhibits a crossover from a diffusive spread for weakly correlated disorder to a ballistic dynamics associated with the emergence of extended states in the strongly correlated disorder regime (alpha(2d) > 2).