Universal anomalous diffusion of weakly damped particles

Details Universal anomalous diffusion of weakly damped particles Universal anomalous diffusion of weakly damped particles

2012-03-06

arxiv.org/abs/1203.1354v1

Nonlinear Sciences

Chaotic Dynamics

7 pages, 4 figures

Scientific paper

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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