Classical Motion in Force Fields with Short Range Correlations

We study the long time motion of fast particles moving through time-dependent random force fields with correlations that decay rapidly in space, but not necessarily in time. The time dependence of the averaged kinetic energy aOE (c) p (2)(t)>/2 and mean-squared displacement aOE (c) q (2)(t)> is shown to exhibit a large degree of universality; it depends only on whether the force is, or is not, a gradient vector field. When it is, aOE (c) p (2)(t)> a1/4t (2/5) independently of the details of the potential and of the space dimension. The stochastically accelerated particle motion is then superballistic in one dimension, with aOE (c) q (2)(t)> a1/4t (12/5), and ballistic in higher dimensions, with aOE (c) q (2)(t)> a1/4t (2). These predictions are supported by numerical results in one and two dimensions. For force fields not obtained from a potential field, the power laws are different: aOE (c) p (2)(t)> a1/4t (2/3) and aOE (c) q (2)(t)> a1/4t (8/3) in all dimensions da parts per thousand yen1.