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Anomalous Diffusion of Inertial, Weakly Damped Particles

R. Friedrich·F. Jenko·A. Baule·S. Eule
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Abstract

The anomalous (i.e. non-Gaussian) dynamics of particles subject to a deterministic acceleration and a series of 'random kicks' is studied. Based on an extension of the concept of continuous time random walks to position-velocity space, a new fractional equation of the Kramers-Fokker-Planck type is derived. The associated collision operator necessarily involves a fractional substantial derivative, representing important nonlocal couplings in time and space. For the force-free case, a closed solution is found and discussed.

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R. Friedrich, F. Jenko, A. Baule, S. Eule. 2006-04-10. Anomalous Diffusion of Inertial, Weakly Damped Particles. https://doi.org/10.1103/physrevlett.96.230601

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