Bezuglyy V, Wilkinson M, Mehlig B
Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 1):061128. doi: 10.1103/PhysRevE.85.061128. Epub 2012 Jun 26.
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: (x{2})∼C{x}t{2} and (p{2})∼C{p}t{2/5}. We are able to determine the prefactors C{x}, C{p} analytically.
