The localization transition of the two-dimensional Lorentz model |
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Authors: | T?Bauer F?H?fling T?Munk E?Frey T?Franosch |
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Institution: | (2) Department of Chemistry and Chemical Biology, Cornell University, Ithaca, USA;(3) School of Chemistry and Chemical Biology, University College Dublin, Dublin, Ireland; |
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Abstract: | 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. |
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