Berlin 2005 – scientific programme

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DY: Dynamik und Statistische Physik

DY 34: Poster

DY 34.60: Poster

Monday, March 7, 2005, 15:30–18:00, Poster TU D

Simulation of the localisation transition of the Lorentz gas — •Felix Höfling, Erwin Frey, and Thomas Franosch — Hahn-Meitner-Institut, Glienicker Str. 100, 14109 Berlin

The Lorentz model for transport in disordered media describes a structureless, classical particle moving through a random array of fixed spherical obstacles. It exhibits a localisation transition, i.e. above a certain density, the particle is trapped in the medium and the system becomes non-ergodic. Although this transition is related to the liquid-glass transition, a divergent length scale is present in the Lorentz model. This transition has been characterised theoretically by mode-coupling theory (MCT).

We have carried out computer simulations of the Lorentz gas at obstacle densities close to the critical point, such that the diffusion coefficient is suppressed by five orders of magnitude. Therefore, it becomes possible to determine the critical density and critical exponents. Our results indicate that the transition is compatible with the underlying problem of continuum percolation as conjectured in the literature. Furthermore, when approaching the critical point, we observe the opening of a time window where the particle shows subdiffusive behaviour—in agreement with the theoretical predictions of MCT.