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 〈p2(t)〉/2 and mean-squared displacement 〈q2(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, 〈p2(t)〉~t2/5 independently of the details of the potential and of the space dimension. The stochastically accelerated particle motion is then superballistic in one dimension, with 〈q2(t)〉~t12/5, and ballistic in higher dimensions, with 〈q2(t)〉~t2. 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: 〈p2(t)〉~t2/3 and 〈q2(t)〉~t8/3 in all dimensions d≥1.
B. Aguer et al., "Classical Motion in Force Fields with Short Range Correlations," Journal of Statistical Physics, Springer Verlag, Feb 2010.
The definitive version is available at http://dx.doi.org/10.1007/s10955-009-9898-7
Keywords and Phrases
Random Potential; Stochastic Acceleration; Diffusion
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