Dresden 2011 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 41: Brownian Motion, Stochastic Processes, Transport II
DY 41.2: Talk
Friday, March 18, 2011, 10:30–10:45, HÜL 186
Exact low-density expansion of the dynamics in the Lorentz gas — •Thomas Franosch1, Felix Höfling2, Teresa Bauer3, and Erwin Frey3 — 1Institut für Theoretische Physik, FAU Erlangen, Erlangen, Germany — 2Max-Planck-Institut für Metallforschung, Stuttgart, and Institut für Theoretische und Angewandte Physik, Universität Stuttgart, Stuttgart, Germany — 3Arnold Sommerfeld Center for Theoretical Physics, LMU München, München, Germany
We provide an analytic solution for the dynamics of a tracer for a dilute planar Lorentz gas [1] employing the many-body T-matrix formalism. In particular, we show that for particles performing Brownian motion in a frozen array of obstacles long-time correlations emerge in the mean-square displacement. Defining the velocity autocorrelation function (VACF) via the second time-derivative of the mean-square displacement, power-law tails govern the long-time dynamics similar to the case of ballistic motion. The physical origin of the persistent memory is due to repeated encounters with the same obstacle which occurs naturally in Brownian dynamics without involving other scattering centers. This observation suggests that in this case the VACF exhibits these anomalies already at first order in the scattering density.
Our result support the idea that quenched disorder provides a generic mechanism for persistent correlations irrespective of the microdynamics of the tracer particle. Our analytic approach is corroborated by computer simulations with a surprisingly large range of validity.
[1] T. Franosch, F. Höfling, T. Bauer, and E. Frey, Chem. Phys. 375 (2010) 540