Transmission and Scattering of a Lorentz Gas on a Slab

TL;DR

This paper investigates the transmission and reflection properties of a Lorentz gas on a triangular lattice through numerical experiments, comparing finite and infinite horizon cases with random walk and Levy walk models.

Contribution

It provides a detailed numerical analysis of scattering in Lorentz gases, highlighting differences between finite and infinite horizon regimes and validating theoretical models.

Findings

Transmission and reflection coefficients scale as predicted in finite horizon case.

In infinite horizon case, results align with Levy walk models showing logarithmic corrections.

Symmetry properties of scattering are characterized and discussed.

Abstract

We perform numerical scattering experiments on a Lorentz array of disks centered on a triangular lattice with L columns and study its transmission and reflection properties. In the finite horizon case, the motion of the particles may be modeled as simple one dimensional random walks with absorbing walls for which the scaling of the transmission and reflection coefficients are known, and agree with those found numerically. In the infinite horizon case the analogy with a simple diffusive process is no longer valid. In this case we compare our results with those expected for a one dimensional Levy walk, again with absorbing walls, for which logarithmic corrections to the scaling relations appear. The scaling with L and the symmetry properties of the forward and the backward are also studied, and some of their salient features are discussed.