V-Langevin Equations, Continuous Time Random Walks and Fractional Diffusion

Details V-Langevin Equations, Continuous Time Random Walks and Fractional Diffusion V-Langevin Equations, Continuous Time Random Walks and Fractional Diffusion

2007-04-19

arxiv.org/abs/0704.2517v1

Physics

Plasma Physics

Latex 69 pages including 23 EPS figures

Scientific paper

The following question is addressed: under what conditions can a strange diffusive process, defined by a semi-dynamical V-Langevin equation or its associated Hybrid kinetic equation (HKE), be described by an equivalent purely stochastic process, defined by a Continuous Time Random Walk (CTRW) or by a Fractional Differential Equation (FDE)? More specifically, does there exist a class of V-Langevin equations with long-range (algebraic) velocity temporal correlation, that leads to a time-fractional superdiffusive process? The answer is always affirmative in one dimension. It is always negative in two dimensions: any algebraically decaying temporal velocity correlation (with a Gaussian spatial correlation) produces a normal diffusive process. General conditions relating the diffusive nature of the process to the temporal exponent of the Lagrangian velocity correlation (in Corrsin approximation) are derived.

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