Universal anomalous diffusion of weakly damped particles

Bezuglyy, V.; Wilkinson, M. and Mehlig, B. (2012). Universal anomalous diffusion of weakly damped particles. Physical Review E, 85 061128.

DOI: https://doi.org/10.1103/PhysRevE.85.061128

Abstract

We show that anomalous diffusion arises in two different models for the motion of randomly forced and weakly damped particles: one is a generalization of the Ornstein-Uhlenbeck process with a random force, which depends on position as well as time, the other is a generalization 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: (x²) ~ C_x t² and (p²) ~ C_p t^2/5. We are able to determine the prefactors C_x , C_p analytically.

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