Dresden 2011 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 41: Brownian Motion, Stochastic Processes, Transport II

DY 41.5: Talk

Friday, March 18, 2011, 11:15–11:30, HÜL 186

Markovian embedding and origin of hyperdiffusion in generalized Brownian motion — Peter Siegle, •Igor Goychuk, and Peter Hänggi — University of Augsburg

The Fractional Langevin Equation (FLE) describes a non-Markovian Generalized Brownian Motion with long time persistence (superdiffusion), or anti-persistence (subdiffusion) of both velocity-velocity correlations, and position increments. It presents a case of the Generalized Langevin Equation (GLE) with a singular power law memory kernel. We propose and numerically realize a numerically efficient and reliable Markovian embedding of this superdiffusive GLE [1], which accurately approximates the FLE over many, about r=N lg b -2, time decades, where N denotes the number of exponentials used to approximate the power law kernel, and b>1 is a scaling parameter for the hierarchy of relaxation constants leading to this power law. Besides its relation to the FLE, our approach presents an independent and very flexible route to model anomalous diffusion. In particular, it contains as a special case the minimal three-dimensional embedding of ballistic superdiffusion [2]. Studying such a superdiffusion in tilted washboard potentials, we demonstrate the phenomenon of transient hyperdiffusion which emerges due to transient kinetic heating effects.

[1] P. Siegle, I. Goychuk, P. Hänggi, arXiv:1011.2848 [cond-mat.stat-mech] (2010).

[2] P. Siegle, I. Goychuk, P. Hänggi, Phys. Rev. Lett. 105, 100602 (2010).