Density-Dependent Diffusion in the Periodic Lorentz Gas |
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Authors: | R Klages Christoph Dellago |
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Institution: | (1) Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Campus Plaine, CP 231, Blvd du Triomphe, B-1050 Brussels, Belgium;(2) Department of Chemistry, University of Rochester, Rochester, New York, 14627 |
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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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Keywords: | deterministic diffusion periodic Lorentz gas computer simulations random walk chaotic scattering Boltzmann approximation |
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