Deterministic Walks in Quenched Random Environments of Chaotic Maps

Abstract

This paper concerns the propagation of particles through a quenched random medium. In the one- and two-dimensional models considered, the local dynamics is given by expanding circle maps and hyperbolic toral automorphisms, respectively. The particle motion in both models is chaotic and found to fluctuate about a linear drift. In the proper scaling limit, the cumulative distribution function of the fluctuations converges to a Gaussian one with system dependent variance while the density function shows no convergence to any function. We have verified our analytical results using extreme precision numerical computations.

18 pages, 9 figures

References in corpus (2)

• Quenched CLT for random toral automorphism
• Exponential Decay of Correlations for Randomly Chosen Hyperbolic Toral Automorphisms

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• Suppression of Quasiperiodicity in Circle Maps with Quenched Disorder