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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Bobylev, A.V., Hansen, A., Piasecki, J. et al. From the Liouville Equation to the Generalized Boltzmann Equation for Magnetotransport in the 2D Lorentz Model. Journal of Statistical Physics 102, 1133–1150 (2001). https://doi.org/10.1023/A:1004880010020
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DOI: https://doi.org/10.1023/A:1004880010020