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

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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

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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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A. V. Bobylev, Alex Hansen, J. Piasecki, E. H. Hauge. 1999-03-15. From the Liouville Equation to the Generalized Boltzmann Equation for Magnetotransport in the 2D Lorentz Model. https://arxiv.org/abs/cond-mat/9903235

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