Dresden 2006 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 24: Brownian Motion and Kinetic Theory I
DY 24.7: Vortrag
Dienstag, 28. März 2006, 16:00–16:15, H\"UL 186
Localization Transition of the 3D Lorentz Model and Continuum Percolation — •Thomas Franosch1,2, Felix Höfling1, and Erwin Frey2 — 1Hahn-Meitner-Institut, Abteilung Theorie, Glienicker St. 100, D-14109 Berlin — 2Arnold Sommerfeld Center and CeNS, Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München
The Lorentz model has served as a paradigm for transport in disordered media. It describes a structureless test particle moving in a random array of identical obstacles which interact with the test particle via a hard-sphere repulsion. At high densities, the model exhibits a localization transition, i. e., above a critical density, the test particle is always trapped by the obstacles.
It has been a longstanding open question whether the dynamics close to the critical density can be mapped to the transport properties of continuum percolation (“Swiss cheese model”). The fractal nature of the void space between the overlapping spheres in the Lorentz model suggested to use a description in terms of an equivalent random resistor network model.
We present extensive Molecular Dynamics simulations and provide the first unambiguous evidence for an intimate connection between the Lorentz model and continuum percolation [1]. In particular, we show the validity of a generalized dynamic scaling theory employing two divergent length scales, and discuss corrections to scaling. The non-Gaussian parameter is predicted to diverge close to the transition.
[1] F. Höfling, T. Franosch, and E. Frey, cond-mat/0510442.