Quantum Theory of Galvanomagnetic Effect. I. Basic Considerations

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Abstract
A quantummechanical theory of galvanomagnetic effect is developed on the basis of the general theory of irreversible processes previously reported by Kubo (J. Phys. Soc. Japan 12 (1957) 570). The present theory applies to arbitrary shape of Fermi surface, as far as it makes a closed surface in the momentum space. Complications due to the interband effect and Harper's broadening effect are neglected here. On these assumptions it is proved that the static conductivity can be expressed generally in terms of the migration process of the center coordinate of the cyclotron motion. This is based on the assumption that the relative coordinates to describe the cyclotron motion are essentially bounded quantities in classical and also in quantummechanical sense. Without referring to any dubious use of transport theory, a very satisfactory logical basis is thus obtained for treating galvanomagnetic effect. This method is particularly useful for strong field. Applications will be reported in a subsequent paper.

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