Regensburg 2010 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 17: Anomalous Transport II (talks contributed by DY)

DY 17.2: Talk

Wednesday, March 24, 2010, 11:30–11:45, H38

From Anomalous Deterministic Diffusion to the Continuous-Time Random Walk — •Markus Niemann and Holger Kantz — Max-Planck-Institut für Physik komplexer Systeme, Dresden

There are several stochastic models describing anomalous diffusion. The most common are the fractional Brownian motion and the Continuous-Time Random Walk (CTRW). The question arises how to choose the correct model for a given process. Our approach is to look for deterministic foundations of these models. We present a method how to derive a CTRW as asymptotic description of a deterministic diffusion process.

We have introduced a diagrammatic method to determine the joint probability distributions of CTRWs. This method is extended to allow couplings between steps. These couplings may arise from deterministic maps, thereby allowing a unified treatment of stochastic and deterministic systems. Often, these processes converge in the scaling limit to a CTRW without coupling between steps. We apply the theory to a diffusion process driven by a deterministic map of Manneville-Pomeau type. Depending on the parameter, one gets a transition from an uncoupled to a coupled CTRW and a transition from sub- to superdiffusion. These findings are well supported by numerical simulations.