Diffusion in the Anderson model of a disordered system: A numerical study

Abstract

Anderson's model for a disordered system is studied numerically by a direct simulation of the particle diffusion on the two-dimensional square lattice. The energy-dependent diffusivity and the participation ratio are evaluated in extended regime for various sets of band energies and disorder parameters. Far from the mobility edges our results are qualitatively consistent with the coherent-potential approximation, which is shown to generally overestimate the diffusivity. In the critical regime, our data indicate a continuous nearly linear variation of the diffusivity and thus contradict the concept of minimum metallic conductivity. The participation ratio also reveals a critical dependence. The results are interpreted in terms of classical percolation character of the particle diffusion near the mobility edges.