Regensburg 2007 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 30: Poster II

DY 30.9: Poster

Donnerstag, 29. März 2007, 16:00–18:00, Poster D

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

Anomalous transport is not only a phenomenon of systems with stochastic environmental forces. Also random walks in random environments can show such a behaviour. Sinai diffusion [1] characterises a class of random walks for which the so called Golosov phenomenon [2] was proven rigorously. We extend the Sinai model to random walks whose transitions are not restricted to nearest-neighbours. Thereby a vanishing global bias is guaranteed by a generalisation of binary disorder. [3,4]

For Sinai disorder exact results exist for the disorder averaged mean square displacement, the density of states of the propagator, and the size-dependence of the escape rate, or, the mean first passage time, respectively. For each of these quantities a characteristic exponent can be definded. We could show numerically that the characteristic exponents also exist for our extended model. At least for relatively small systems the characteristic exponents show a non-trivial dependence on system size and coincide. Perturbation theory, which is exact in the Sinai case, enables us to calculate escape rates for significantly larger systems. For our model we find as function of system size a transition from a large preasymptotic regime to the asymptotic behaviour.

[1] Ya.G.Sinai, Theor. Prob. Appl. 27 (1982) 247.

[2] A.Golosov, Commun. Math. Phys. 92 (1984) 491.

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

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