4 research outputs found
The Localization Transition of the Two-Dimensional Lorentz Model
We investigate the dynamics of a single tracer particle performing Brownian
motion in a two-dimensional course of randomly distributed hard obstacles. At a
certain critical obstacle density, the motion of the tracer becomes anomalous
over many decades in time, which is rationalized in terms of an underlying
percolation transition of the void space. In the vicinity of this critical
density the dynamics follows the anomalous one up to a crossover time scale
where the motion becomes either diffusive or localized. We analyze the scaling
behavior of the time-dependent diffusion coefficient D(t) including corrections
to scaling. Away from the critical density, D(t) exhibits universal
hydrodynamic long-time tails both in the diffusive as well as in the localized
phase.Comment: 13 pages, 7 figures