Transmission and scattering of a Lorentz gas on a slab

摘要

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 In the infinite horizon case the analogy with a simple diffusive process is no longer valid.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 to those expected for a one-dimensional Levy walk, again with absorbing walls, for which logarithmic corrections to the scaling relations appear. These corrections an consistent with the numerical results. The scaling with L and the symmetry properties of the forward sigma(T)(phi) and backward sigma(R)(phi) differential cross sections are also studied, and some of their salient features are discussed. [S1063-651X(98)05310-0]. [References: 19]