Classical Motion in Force Fields with Short Range Correlations |
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Authors: | B Aguer S De Bièvre P Lafitte P E Parris |
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Institution: | 1. Laboratoire Paul Painlevé, CNRS, UMR 8524 et UFR de Mathématiques, Université des Sciences et Technologies de Lille, 59655, Villeneuve d’Ascq Cedex, France 2. Equipe-Projet SIMPAF, Centre de Recherche INRIA Futurs, Parc Scientifique de la Haute Borne, 40, avenue Halley, B.P. 70478, 59658, Villeneuve d’Ascq Cedex, France 3. Department of Physics, Missouri University of Science & Technology, Rolla, MO, 65409, USA
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Abstract: | 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 〈p 2(t)〉/2 and mean-squared displacement 〈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, 〈p 2(t)〉~t 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 〈q 2(t)〉~t 12/5, and ballistic in higher dimensions, with 〈q 2(t)〉~t 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: 〈p 2(t)〉~t 2/3 and 〈q 2(t)〉~t 8/3 in all dimensions d≥1. |
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