Diffusion in Lorentz Lattice Gas Cellular Automata: the honeycomb and quasi-lattices compared with the square and triangular lattices

摘要

We study numerically the nature of the diffusion process on a honeycomb and aquasi-lattice, where a point particle, moving along the bonds of the lattice,scatters from randomly placed scatterers on the lattice sites according tostrictly deterministic rules. For the honeycomb lattice fully occupied by fixedrotators two (symmetric) isolated critical points appear to be present, withthe same hyperscaling relation as for the square and the triangular lattices.No such points appear to exist for the quasi-lattice. A comprehensivecomparison is made with the behavior on the previously studied square andtriangular lattices. A great variety of diffusive behavior is found rangingfrom propagation, super-diffusion, normal, quasi-normal, anomalous to absenceof diffusion. The influence of the scattering rules as well as of the latticestructure on the diffusive behavior of a point particle moving on the alllattices studied so far, is summarized.