Theoretical Study of Transport Phenomena based on Mori Formula

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Very recently we have found that the ordinary perturbation technique based on the Feynrnan's diagram can be applied to calculate the Mori formura for electrical resistivity. (J.Phys. Soc. Japan 64 No.11 (1995) 4092-4096) The aim of the present project was to utilize the new expression of the Mori formura for examining the traditional understanding of the Mori formula itself and searching possibility of its extensive application, e.g., for calculation of the transport coefficients in many electron systems.As it should be, the Mori formula must be equivalent to the Kubo formula. In fact, we have confirmed the equivalence explicitly for resitivity due to impurity scattering and optical conductivity in 2 band systems. (J.Phys. Soc. Japan 65 No.2 (1996) 525-528) Moreover, with the help of some identities which hold among dynamical correlation functions, it. has been shown that the both formulae are equivalent to each other rigorously. (J.Phys. Soc. Japan 65 No.2 (1996) 342-344)However, in real systems we must rely upon the some approximation procedure and it may happen that there occurs some discrepancy between results obtained through the two formulae. In fact, it has been widely believed that when we calculate electrical resistivity the memory function approximation based on the Mori formula is more convinient to he used. Then, in order to check whether it. is really so or not, we have calculated electrical resistivity clue to the impurity scattering and also that clue to the d-p hybridization term by applying the same approximation procedure to the two formulae and shown that the both results are identical and the memory function approximation is justified at high frequency limit, which invalidiate the traditional way of its application. (J.Phys. Soc. Japan 66 No.9 (1997) 2790-2797)。In conclusion, we argue that the Mori formula and the Kubo formula are identical to each other as far as the same approximation procedure are applied.