THERE IS MORE TO BE LEARNED FROM THE LORENTZ MODEL

The classical Lorentz model for charged noninteracting point particles in a perpendicular magnetic field is reconsidered in 2D. We show thai the standard Boltzmann equation is not valid for this model, even in the Grad limit. We construct a generalized Boltzmann equation which is , and solve the corresponding initial value problem exactly. By an ind ependent calculation, we find the same solution by directly constructi ng the Green Function from the dynamics of the model in the Grad limit . From this solution an expression for the diffusion tensor, valid for arbitrary short-range forces, is derived. For hard disks we calculate the diffusion tensor explicitly. Away from the Grad limit a percolati on problem arises. We determine numerically the percolation threshold and the corresponding geometric critical exponents. The numerical evid ence strongly suggests that this continuum percolation model is in the universality class of 2D lattice percolation. Although we have explic itly determined a number of limiting properties of the model, several intriguing open problems remain.