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Density-dependent diffusion in the periodic Lorentz gas

par Klagers, Rainer ;Dellago, Christoph
Référence Journal of statistical physics, 101, 1-2, page (145-159)
Publication Publié, 2000-10

Article révisé par les pairs

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Résumé :

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 lor 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.