Journal of Statistical Physics, Vol. 51, Nos. 5/6, 1988. p. 981-990.
We present several ballistic models of the Lorentz gas in two-dimensional lattices with deterministic and stochastic deflection rules, and their corresponding Liouville equations. Boltzmann-level-equation results are obtained for the diffusion coefficient and velocity autocorrelation function for models with stochastic deflection rules, The long-time behavior of the mean square displacement is briefly discussed and the possibility of abnormal diffusion indicated. Even if the diffusion coefficient exists, its low-density limit may not be given correctly by the Boltzmann equation.