Long time tails in stationary random media II: Applications |
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Authors: | J Machta M H Ernst H van Beijeren J R Dorfman |
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Institution: | (1) Department of Physics and Astronomy, University of Massachusetts, 01003 Amherst, Massachusetts;(2) Institute for Theoretical Physics, State University, P.O.B. 80.006, 2508 TA Utrecht, The Netherlands;(3) Institute for Theoretical Physics, Rhein-Westf. Techn. Hochschule, 5100 Aachen, West Germany;(4) Institute for Physical Science and Technology and Department of Physics and Astronomy, University of Maryland, 20742 College Park, Maryland |
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Abstract: | In a previous paper we developed a mode-coupling theory to describe the long time properties of diffusion in stationary, statistically homogeneous, random media. Here the general theory is applied to deterministic and stochastic Lorentz models and several hopping models. The mode-coupling theory predicts that the amplitudes of the long time tails for these systems are determined by spatial fluctuations in a coarse-grained diffusion coefficient and a coarse-grained free volume. For one-dimensional models these amplitudes can be evaluated, and the mode-coupling theory is shown to agree with exact solutions obtained for these models. For higher-dimensional Lorentz models the formal theory yields expressions which are difficult to evaluate. For these models we develop an approximation scheme based upon projecting fluctuations in the diffusion coefficient and free volume onto fluctuations in the density of scatterers.Work supported by grant No. CHE 77-16308 from the National Science Foundation and by a Nato Travel Grant. |
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Keywords: | Long time tails random media mode-coupling theory Lorentz models random walks |
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