Magneto-Transport in the Two-Dimensional Lorentz Gas

Abstract

We consider the two-dimensional Lorentz gas with Poisson distributed hard disk scatterers and a constant magnetic field perpendicular to the plane of motion. The velocity autocorrelation is computed numerically over the full range of densities and magnetic fields with particular attention to the percolation threshold between hopping transport and pure edge currents. The Ohmic and Hall conductance are compared with mode-coupling theory and a recent generalized kinetic equation valid for low densities and small fields. We argue that the long time tail as $t^{-2}$ persists for non-zero magnetic field.