Theoretical Study of Transport Phenomena based on Mori Formula

最近我们发现，基于费恩南图的普通微扰法可以用来计算电阻率的森公式。（J.Phys.Soc.Japan64No.11（1995）4092-4096）本课题的目的是利用Mori公式的新表达式来检验对Mori公式本身的传统理解，并寻找其广泛应用的可能性，例如，Mori公式与Kubo公式是等价的。事实上，我们已经明确地证实了两带系统中杂质散射引起的电阻率和光学电导率的等价性。（J.Phys.Soc.Japan65No.2（1996）525-528）此外，借助于动力学关联函数之间的一些恒等式，证明了这两个公式是严格等价的。（J.Phys.Soc.Japan65No.2（1996）342-344）然而，在真实的系统中，我们必须依赖某种近似过程，并且可能发生的是，在通过两个公式获得的结果之间出现某种差异。事实上，人们普遍认为，在计算电阻率时，基于Mori公式的记忆函数近似法更便于使用。然后，为了验证这一点，我们用同样的近似方法计算了杂质散射项下的电阻率和d-p杂化项下的电阻率，结果表明，两个公式的结果是一致的，记忆函数近似在高频极限是合理的，从而使传统的应用方法失效。（J. Phys. Soc. Japan 66 No.9（1997）2790-2797）。最后，我们认为，森公式和久保公式是彼此相同的，只要相同的近似程序被应用。

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.