Regensburg 2013 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
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 Lang1, Teresa Behl2, Felix Höfling3, and Thomas Franosch1 — 1Institut für Theoretische Physik, Erlangen-Nürnberg — 2Fakultät für Physik, LMU München — 3Institut 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).