Transport in the three-dimensional Anderson model: an analysis of the dynamics at scales below the localization length

Abstract

Single-particle transport in disordered potentials is investigated at scales below the localization length. The dynamics at those scales is concretely analyzed for the three-dimensional Anderson model with Gaussian on-site disorder. This analysis particularly includes the dependence of characteristic transport quantities on the amount of disorder and the energy interval, e. g. the mean free path that separates ballistic and diffusive transport regimes. For these regimes mean velocities and diffusion constants are quantitatively given. Using the Boltzmann equation in the limit of weak disorder, we reveal the known energy dependences of transport quantities. By the application of the time-convolutionless projection operator technique in the limit of strong disorder, we obtain evidence for much less pronounced energy dependences. All our results are partially confirmed by the numerically exact solution of the time-dependent Schrodinger equation or by approximative numerical integrators. A comparison with other findings in the literature is also provided.