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Long time tails in stationary random media. I. Theory

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Abstract

Diffusion of moving particles in stationary disordered media is studied using a phenomenological mode-coupling theory. The presence of disorder leads to a generalized diffusion equation, with memory kernels having power law long time tails. The velocity autocorrelation function is found to decay like t−(d/2+1), while the time correlation function associated with the super-Burnett coefficient decays liket −d/2 for long times. The theory is applicable to a wide variety of dynamical and stochastic systems including the Lorentz gas and hopping models. We find new, general expressions for the coefficients of the long time tails which agree with previous results for exactly solvable hopping models and with the low-density results obtained for the Lorentz gas. Finally we mention that if the moving particles are charged, then the long time tails imply that there is an ωd/2 contribution to the low-frequency part of the frequency-dependent electrical conductivity.

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Authors and Affiliations

  1. Institute for Theoretical Physics, State University, 3508, TA Utrecht, The Netherlands

    M. H. Ernst

  2. Department of Physics and Astronomy, University of Massachusetts, 01003, Amherst, Massachusetts

    J. Machta

  3. Institute for Physical Science and Technology and Department of Physics and Astronomy, University of Maryland, 20742, College Park, Maryland

    J. R. Dorfman

  4. Institute for Theoretical Physics, Rhein-Westf. Techn. Hochschule, 5100, Aachen, West Germany

    H. van Beijeren

Authors
  1. M. H. Ernst
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  2. J. Machta
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  3. J. R. Dorfman
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  4. H. van Beijeren
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Ernst, M.H., Machta, J., Dorfman, J.R. et al. Long time tails in stationary random media. I. Theory. J Stat Phys 34, 477–495 (1984). https://doi.org/10.1007/BF01018555

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