Understanding Anomalous Transport in Intermittent Maps: From Continuous Time Random Walks to Fractals

Abstract

We show that the generalized diffusion coefficient of a subdiffusive intermittent map is a fractal function of control parameters. A modified continuous time random walk theory yields its coarse functional form and correctly describes a dynamical phase transition from normal to anomalous diffusion marked by strong suppression of diffusion. Similarly, the probability density of moving particles is governed by a time-fractional diffusion equation on coarse scales while exhibiting a specific fine structure. Approximations beyond stochastic theory are derived from a generalized Taylor-Green-Kubo formula.

4 pages, 3 eps figures

References in corpus (3)

• Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics
• Exact Solution for the Influence of Spectral Diffusion on Single-Molecule Photon-Statistics
• Anomalous transport: a deterministic approach

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• Singularity of Levy walks in the lifted Pomeau-Manneville map
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• Does an intermittent dynamical system remain (weakly) chaotic after drilling in a hole?