Bezuglyy, V.; Wilkinson, M. and Mehlig, B.
Universal anomalous diffusion of weakly damped particles.
Physical Review E, 85
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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) ~ Cx t2 and (p2) ~ Cp t2/5. We are able to determine the prefactors Cx , Cp analytically.
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