Dynamical crossover in deterministic diffusion

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Abstract
We study diffusion in a one-dimensional periodic array of scatterers modeled by a simple map. The chaotic scattering process of the map can be changed by a control parameter and exhibits a dynamics analogous to a crisis in chaotic scattering. We show that the associated strong backscattering induces a crossover between different asymptotic laws for the parameter-dependent diffusion coefficient. These laws are obtained from exact diffusion coefficient results and are supported by simple random walk models. We conjecture that the main physical feature of this crossover is present in many other dynamical systems exhibiting nonequilibrium transport.

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