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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Klages, R., Dellago, C. Density-Dependent Diffusion in the Periodic Lorentz Gas. Journal of Statistical Physics 101, 145–159 (2000). https://doi.org/10.1023/A:1026445601619
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DOI: https://doi.org/10.1023/A:1026445601619