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Theoretical Study of Transport Phenomena based on Mori Formula

基于Mori公式的输运现象理论研究

基本信息

批准号：
08640483
负责人：
KURODA Yoshihiro
金额：
$ 1.34万
依托单位：
Nagoya University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1996
资助国家：
日本
起止时间：
1996 至 1998
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-08640483/
关键词：
transport phenomena Mori formula Kubo formula

项目摘要

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.

最近，我们发现基于费南图解的普通摄动法可以用来计算电阻率的Mori公式。(J.Phys.SoC。本项目的目的是利用森公式的新表达式来检验对森公式本身的传统理解，并探索其广泛应用的可能性，例如，用于计算许多电子系统中的输运系数。事实上，我们已经明确地证实了双波段系统中杂质散射引起的电阻率与光学导电性的等价性。(J.Phys.SoC。日本65 No.2(1996)525-528)，并借助于动力关联函数之间的一些恒等式，进一步证明了该方法的有效性。证明了这两个公式严格等价。(J.Phys.SoC。日本65 No.2(1996)342-344)然而，在实际系统中，我们必须依靠某种近似过程，通过这两个公式得到的结果可能会出现一些差异。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更便于使用。然后，为了检查它是否。无论是真是假，我们通过对两个公式应用相同的近似过程，计算了杂质散射的电阻率线索和d-p杂化项的线索，结果表明，这两个结果是一致的，并且记忆函数近似在高频下是合理的，这使得它的传统应用方式失效。(J.Phys.SoC。日本66号9(1997)2790-2797)。总之，我们认为，只要应用相同的近似过程，Mori公式和Kubo公式是彼此相同的。