Berlin 2008 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 17: Poster I

DY 17.17: Poster

Dienstag, 26. Februar 2008, 16:00–18:00, Poster C

Anomalous transport in disordered iterated systems — •Andreas Fichtner and Günter Radons — TU Chemnitz, D-09107 Chemnitz

Diffusive transport is not only a phenomenon arising from stochastic environmental forces, which act e.g. on a heavy particle. While this picture requires many degrees of freedom, one can find normal and, more interestingly, anomalous diffusion already in low dimensional systems such as random walks in quenched random environments. A class of recurrent random walks, for which properties of the so called Golosov-phenomenon had been proven, is known under the heading of Sinai diffusion. In our work we extend the discrete Sinai model to random walks with next-nearest neighbour transitions. Thereby a generalization of binary disorder guarantees recurrence [1].

For Sinai disorder the known results concern quantities such as the disorder averaged mean square displacement, the density of states of the propagator, and the size-dependence of the escape rate. For each of them one can define a characteristic exponent. We show numerically for our generalized model that these exponents exist likewise and seem to coincide [2]. Perturbation theory, which is exact in the Sinai case, enables calculating escape rates for significant larger systems. For our model we find as function of system size a transition from a large preasymptotic regime to the asymptotic behaviour in dependence on the system parameters.

[1] G. Radons Physica D 187 (2004) 3.

[2] A. Fichtner, G. Radons New J. Phys. 7 (2005) 30.