Long time tails in stationary random media. I: Theory
type: Item
instance of: scholarly article
title: Long time tails in stationary random media. I: Theory
zbMATH Open document ID: 0588.60084
DOI: 10.1007/BF01018555
author: M. H. Ernst
author: J. Machta
author: J. R. Dorfman
author: Henk van Beijeren
published in: Journal of Statistical Physics
publication date: 1984-01-01T00:00:00Z
review text: 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 like \(t^{-d/2}\) 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 \(\omega^{d/2}\) contribution to the low-frequency part of the frequency-dependent electrical conductivity.
Mathematics Subject Classification ID: 60J70
Mathematics Subject Classification ID: 82B05
zbMATH DE Number: 3945010
zbMATH Keywords: moving particles in stationary disordered media
zbMATH Keywords: mode-coupling theory
zbMATH Keywords: Lorentz gas
zbMATH Keywords: long time tails
zbMATH Keywords: hopping models
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01018555
OpenAlex ID: W2077732449
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description: scientific article; zbMATH DE number 3945010