Two-Dimensional Magnetotransport According to the Classical Lorentz Model

The classical Lorentz model for charged noninteracting point particles in a perpendicular magnetic field is reconsidered in 2D. We show that 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. The diffusion tensor follows. Away from the Grad limit a percolation problem arises. We study numerically its critical properties.