Universal anomalous diffusion of weakly damped particles

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: $<x^2>\sim C_x{t}^2$ and $<p^2>\sim C_p{t}^{2/5}$. We are able to determine the prefactors $C_x$, $C_p$ analytically.

7 pages, 4 figures

References in corpus (3)

• Generalised Ornstein-Uhlenbeck processes
• Super-diffusion in optical realizations of Anderson localization
• Enhanced transport when Anderson localization is destroyed

Cited by in corpus (2)

• Is transport in time-dependent random potentials universal ?
• Transport in time-dependent random potentials