Diffusion in the Anderson model in higher dimensions

We present an extended microcanonical Lanczos method (MCLM) for a direct evaluation of the diffusion constant and its frequency dependence within the disordered Anderson model of noninteracting particles. The method allows to study systems beyond $10^6$ sites of hypercubic lattices in $ d = 3- 7$ dimensions. Below the transition to localization, where we confirm dynamical scaling behavour, of interest is a wide region of incoherent diffusion, similar to percolating phenomena and to interacting many-body localized systems.