Character of eigenstates of the 3D disordered Anderson Hamiltonian

We study numerically the character of electron eigenstates of the three dimensional disordered Anderson model. Analysis of the statistics of inverse participation ratio as well as numerical evaluation of the electron-hole correlation function confirm that there are no localized states below the mobility edge, as well as no metallic state in the tail of the conductive band. We discuss also finite size effects observed in the analysis of all the discussed quantities.Comment: 7 pages, 9 figures, resubmitted to Physical Review

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

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.Comment: 23 pages, 10 figure