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Single-particle transport in disordered potentials is investigated on scalesbelow the localization length. The dynamics on those scales is concretelyanalyzed for the 3-dimensional Anderson model with Gaussian on-site disorder.This analysis particularly includes the dependence of characteristic transportquantities on the amount of disorder and the energy interval, e.g., the meanfree path which separates ballistic and diffusive transport regimes. For theseregimes mean velocities, respectively diffusion constants are quantitativelygiven. By the use of the Boltzmann equation in the limit of weak disorder wereveal the known energy-dependencies of transport quantities. By an applicationof the time-convolutionless (TCL) projection operator technique in the limit ofstrong disorder we find evidence for much less pronounced energy dependencies.All our results are partially confirmed by the numerically exact solution ofthe time-dependent Schroedinger equation or by approximative numericalintegrators. A comparison with other findings in the literature is additionallyprovided.

Transport in the 3-dimensional Anderson model: an analysis of the dynamics on scales below the localization length