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arXiv · 1203.1354

Universal anomalous diffusion of weakly damped particles

Vlad Bezuglyy·Michael Wilkinson·Bernhard Mehlig
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Abstract

We show that anomalous diffusion arises in two different models for the motion of randomly forced and weakly damped particles: one is a generalisation of the Ornstein-Uhlenbeck process with a random force which depends on position as well as time, the other is a generalisation of the Chandrasekhar-Rosenbluth model of stellar dynamics, encompassing non-Coulombic potentials. We show that both models exhibit anomalous diffusion of position $x$ and momentum $p$ with the same exponents: $ \sim C_x t^2$ and $ \sim C_p t^{2/5}$. We are able to determine the prefactors $C_x$, $C_p$ analytically.

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Vlad Bezuglyy, Michael Wilkinson, Bernhard Mehlig. 2012-03-06. Universal anomalous diffusion of weakly damped particles. https://doi.org/10.1103/physreve.85.061128

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