Magnetotransport in the two-dimensional Lorentz gas

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 corresponding Ohmic and Hall conductances are compared with (i) an exact expression in the percolating regime, (ii) mode-coupling theory, and (iii) a recent generalized kinetic equation valid for low densities and small fields. We argue that the long-time tail as [Formula Presented] persists for a nonzero magnetic field.