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A quantum-mechanical theory using a density matrix for electrical conductivity in the presence of a magnetic field is described. The conventional methods using the Boltzmann transport equation are not satisfactory because the magnetic field introduces a curvature in the free path of an electron. The expectation value of the current density and the components of the conductivity tensor in a magnetic field are obtained. The advantages of the density matrix in electric transport problems with a magnetic field are discussed.
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Vikas Arora (1976) studied this question.
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