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Density-Dependent Diffusion in the Periodic Lorentz Gas

Authors
  • Klages, R.1
  • Dellago, Christoph2
  • 1 Université Libre de Bruxelles, Campus Plaine, Center for Nonlinear Phenomena and Complex Systems, Blvd du Triomphe, Brussels, B-1050, Belgium , Brussels
  • 2 University of Rochester, Department of Chemistry, Rochester, New York, 14627 , Rochester
Type
Published Article
Journal
Journal of Statistical Physics
Publisher
Springer-Verlag
Publication Date
Oct 01, 2000
Volume
101
Issue
1-2
Pages
145–159
Identifiers
DOI: 10.1023/A:1026445601619
Source
Springer Nature
Keywords
License
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Abstract

We study the deterministic diffusion coefficient of the two-dimensional periodic Lorentz gas as a function of the density of scatterers. Based on computer simulations, and by applying straightforward analytical arguments, we systematically improve the Machta–Zwanzig random walk approximation [Phys. Rev. Lett.50:1959 (1983)] by including microscopic correlations. We furthermore, show that, on a fine scale, the diffusion coefficient is a non-trivial function of the density. On a coarse scale and for lower densities, the diffusion coefficient exhibits a Boltzmann-like behavior, whereas for very high densities it crosses over to a regime which can be understood qualitatively by the Machta–Zwanzig approximation.

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