# Regensburg 2013 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 31: Anomalous Diffusion

### DY 31.1: Vortrag

### Donnerstag, 14. März 2013, 15:00–15:15, H48

**A self-consistent theory for the localization transition in the Lorentz model** — •Simon Lang^{1}, Teresa Behl^{2}, Felix Höfling^{3}, and Thomas Franosch^{1} — ^{1}Institut für Theoretische Physik, Erlangen-Nürnberg — ^{2}Fakultät für Physik, LMU München — ^{3}Institut für Theoretische Physik IV, Universität Stuttgart; MPI für Intelligente Systeme, Stuttgart

The reference system for transport in porous media is the Lorentz model, which mimics the dynamics of a particle in a heterogeneous environment of obstacles randomly distributed in space. For a tracer particle obeying brownian repeated collisions with a single obstacle is sufficient to explain the persistent correlations. Therefore for brownian motion the low-density expansion already reveals the onset of long-time tails for the velocity-auto-correlation function (VACF) in next to leading order in density [1]. Here, we use the results of the low-density approximation to formulate a self-consistent theory for the VACF for brownian dynamics of a tracer particle in two dimensions. For low densities, the theory reduces to the exact expansion of Ref. [1], for higher density a consistent diffusion-localization transition is predicted at an obstacle density, which is close to the percolation threshold found for simulations in two dimensions. We find asymptotic scaling laws in the VACF, which are persistent as one approaches the localization transition, as well as long-time tails within the diffusive regime originating from repeated scattering processes.

[1] T. Franosch, F. Höfling, T. Bauer and E. Frey J. Chem. Phys. 375 (2010).