Dresden 2014 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 36: Brownian Motion and Transport
DY 36.5: Talk
Thursday, April 3, 2014, 16:00–16:15, ZEU 160
Calculation of the waiting time distribution with a Fokker Planck equation: hopping in a one-dimensional periodic potential — •Robert Gernert1, Clive Emary2, and Sabine H.L. Klapp1 — 1Institut für theoretische Physik, Technische Universität Berlin — 2Department of Physics and Mathematics, University of Hull, United Kingdom
``How long will a complex stochastic process take?'' The waiting time distribution (WTD) gives us the answer. The question is important in Brownian as well as in quantum transport [1,2], because it allows to identify the, possibly several, relevant time scales of non-equilibrium motion and to get these single-particle resolved.
Recent developments in quantum transport[2] have shown that the WTD is (especially for short times) more detailed than full counting statistics, i.e. than the cumulants of motion like mean position, mean squared displacement or non-Gaussian parameter.
A way to calculate the WTD directly with a Fokker-Planck equation is presented. As an example the one-dimensional overdamped motion of one Brownian particle in a washboard potential is investigated.
We also present a Master equation approach, based on [3], which gives analytic access to the WTD. Both approaches are verified by comparison to Brownian dynamics simulations.
[1] R.D.L. Hanes, C. Dalle-Ferrier, M. Schmiedeberg, M.C. Jenkins, S.U. Egelhaaf, Soft Matter 8, 2714 (2012)
[2] M. Albert, C. Flindt, M. Büttiker, PRL 107, 086805 (2011)
[3] C. Emary, R. Gernert, S.H.L. Klapp, PRE 86, 061153 (2012)