Random walk approach to the d-dimensional disordered Lorentz gas

Details Random walk approach to the d-dimensional disordered Lorentz gas Random walk approach to the d-dimensional disordered Lorentz gas

2007-11-12

arxiv.org/abs/0711.1875v2

Phys. Rev. E 77, 021118 (2008)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 5 figures

Scientific paper

10.1103/PhysRevE.77.021118

A correlated random walk approach to diffusion is applied to the disordered nonoverlapping Lorentz gas. By invoking the Lu-Torquato theory for chord-length distributions in random media [J. Chem. Phys. 98, 6472 (1993)], an analytic expression for the diffusion constant in arbitrary number of dimensions d is obtained. The result corresponds to an Enskog-like correction to the Boltzmann prediction, being exact in the dilute limit, and better or nearly exact in comparison to renormalized kinetic theory predictions for all allowed densities in d=2,3. Extensive numerical simulations were also performed to elucidate the role of the approximations involved.

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