Magneto-transport in the two dimensional Lorentz model

A recently developed theory for the motion of a classical particle in a random array of scatterers is improved and extended to discuss the effects of weak and intermediate magnetic fields. By deriving expressions for the general relaxation kernels it is shown that only the current relaxation kernel is the physical relevant one diverging at the percolation edge. The percolation density and localization length turn out to be independent of the magnetic field. A negative magneto resistance at low scatterer density, a positive magneto resistance at larger density and a non classical Hall coefficient are obtained. For the velocity correlation spectrum a shift of the cyclotron resonance to higher frequency and a new low frequency side peak is predicted.