DETERMINISTIC LATTICE LORENTZ GAS .1. CHIRAL MODEL

We study diffusion by using a specific type of cellular automaton, where particles move in a random environment of scatterers. The deterministic collision rules, used in the model, give rise to certain difficulties related to non-ergodicity. The class of models, introduced by Gunn and Ortuno, also contains the model studied by Gates. Previously developed theory, including the Boltzmann approximation, the ring and repeated-ring approximations and the effective medium approximation (EMA), is generalized for this model. The validity is further investigated using computer simulations. In the presence of reflecting scatterers EMA yields low-density results that show the breakdown of the Boltzman equation, while they agree quantitatively with the low-density simulations. EMA also agrees with a phase transition that occurs for some parameter choices.