On Quantum Theory of Transport Phenomena Steady Diffusion

A general formulation is given to the quantum theory of steady diffusion. In seeking for a steady solution of Liouville's equation, the boundary condition is taken into account by requiring that the solution should lead to a given distribution of average density. The distribution is to be determin­ ed by macroscopic law of diffusion and macroscopic boundary condition. The basic equation thus obtained has a form similar to Bloch's kinetic equation and reduces to the latter in the limit of a system of weakly interacting particles. This is shown by generalizing a damping theoretical expansion of Kohn and Luttinger. It is found that the Einstein relation is valid only for the symmetric part of diffusion- and electric conductivity tensors, in agreement with Kasuya's suggestion.