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Abstract
A quantum theory of electrical conduction in crosfsed electric and magnetic fields is given for the limit of very weak scattering. A density matrix formulation of the problem is used, and an arbitrary scattering mechanism is considered. The theory is found to be completely equivalent to theories given earlier by Titeica and by Davydov and Pomeranchuk. Formulae are given for the resistivity in the quantum limit for both longitudinal and transverse orientations of electric field, for degenerate and non-degenerate statistics, and for several different scattering mechanisms. The oscillatory conductivity is calculated for acoustical and ionized-impurity scattering mechanisms. Formulae obtained for the quantum transport effects are in disagreement with the formulae of Lifshitz and of Argyres. The discrepancy is attributed to unwarranted approximations in those authors' treatments of scattering.
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