Diffusive properties of persistent walks on cubic lattices with application to periodic Lorentz gases

Details Diffusive properties of persistent walks on cubic lattices with application to periodic Lorentz gases Diffusive properties of persistent walks on cubic lattices with application to periodic Lorentz gases

2010-09-20

arxiv.org/abs/1009.3922v1

Physics

Condensed Matter

Statistical Mechanics

17 pages, 10 figures

Scientific paper

We calculate the diffusion coefficients of persistent random walks on cubic and hypercubic lattices, where the direction of a walker at a given step depends on the memory of one or two previous steps. These results are then applied to study a billiard model, namely a three-dimensional periodic Lorentz gas. The geometry of the model is studied in order to find the regimes in which it exhibits normal diffusion. In this regime, we calculate numerically the transition probabilities between cells to compare the persistent random-walk approximation with simulation results for the diffusion coefficient.

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