From the Liouville Equation to the Generalized Boltzmann Equation for Magnetotransport in the 2D Lorentz Model
A. V. Bobylev, Alex Hansen, J. Piasecki, E. H. Hauge
Abstract
We consider a system of non-interacting charged particles moving in two dimensions among fixed hard scatterers, and acted upon by a perpendicular magnetic field. Recollisions between charged particles and scatterers are unavoidable in this case. We derive from the Liouville equation for this system a generalized Boltzmann equation with infinitely long memory, but which still is analytically solvable. This kinetic equation has been earlier written down from intuitive arguments.
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