  Single-particle transport in disordered potentials is investigated on scales
below the localization length. The dynamics on those scales is concretely
analyzed for the 3-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 which separates ballistic and diffusive transport regimes. For these
regimes mean velocities, respectively diffusion constants are quantitatively
given. By the use of the Boltzmann equation in the limit of weak disorder we
reveal the known energy-dependencies of transport quantities. By an application
of the time-convolutionless (TCL) projection operator technique in the limit of
strong disorder we find evidence for much less pronounced energy dependencies.
All our results are partially confirmed by the numerically exact solution of
the time-dependent Schroedinger equation or by approximative numerical
integrators. A comparison with other findings in the literature is additionally
provided.
