Dresden 2006 – scientific programme

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DY: Dynamik und Statistische Physik

DY 26: Brownian Motion and Kinetic Theory II

DY 26.8: Talk

Tuesday, March 28, 2006, 18:00–18:15, H\"UL 186

On a Non-Markovian Fokker-Planck equation — •Knud Zabrocki and Steffen Trimper — Martin-Luther-University Fachbereich Physik, 06099 Halle,

We consider a model for a probability distribution function p(x,t) which is subjected to the distribution function at a former time via a feedback coupling. As a consequence the behaviour of p(x,t) is changed drastically. Whereas for a long range feedback coupling, i.e. a coupling to the initial distribution function, the system offers non-trivial stationary solution, in case of a short time coupling this stationary distribution disappears. We demonstrate that this non-Markovian Fokker-Planck equation without a drift term is equivalent to a Fokker-Planck-equation with a drift term. Different initial distributions and their influence on the stationary solution in one dimension are analysed in detail. The investigation can be extended to higher dimensions. Depending on the initial condition and the dimension, the system reveals different drift terms and entirely different potentials. A further generalization is given by a kind of co-moving frame. In that case a particle, performing a random walk, is affected at a given time t by all processes taking place within a sphere of radius R = v t. For a non-zero velocity v the system exhibits three distinguished time regimes with complete different behaviour. The model could be applied for glasses and strongly inhomogeneous systems.