MAGNETOTRANSPORT IN THE 2D LORENTZ MODEL - LINEAR AND NONLINEAR EFFECTS OF A WEAK ELECTRIC-FIELD

We study the two-dimensional (2D) classical Lorentz model in a transve rse magnetic and an in-plane electric field, in the regime where the d imensionless electric field is smaller than all other parameters. Sinc e, therefore, the dimensionless density must be kept finite, we start from the Liouville equation and derive, by the multiple time scale met hod, the equations governing nonlinear as well as linear transport. Th e same diffusion tensor, formally rederived as the Kubo expression is, surprisingly, found to govern both regimes, albeit in different manne r. Subsequently, explicit asymptotic results for the two components of the current density are calculated in the low-density regime.