1999 Fiscal Year Final Research Report Summary
New Developments in the Green's-Function Method and Construction of the Strong-Coupling Theory for Superconductivity with Vertex Corrections
| Project/Area Number |
10640363
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
物性一般(含基礎論)
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| Research Institution | The University of Tokyo |
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Principal Investigator |
TAKADA Yasutami The Univ. of Tokyo, ISSP, Associate Professor, 物性研究所, 助教授 (00126103)
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| Project Period (FY) |
1998 – 1999
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| Keywords | Strong Electron Correlation / Superconductivity / Green's Function / Vertex Correction / Electron-Gas Model / Excitonic Scattering between Electron and Hole / Gauge-Invariant Self-Consistent Method / Self-Energy Revision Operator Theory |
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| Research Abstract |
In order to illuminate fundamental physics in dynamical processes in a strongly-correlated system, I propose a theory of twofold hierarchy The first stage is to set up a firm framework to provide exact results without attention to feasibility of computation and the second one is to introduce a relevant approximation to the key quantity in the framework with taking full account of available resources of computation. Since I have already established the theory of the self-energy revision operator F for the first stage, the main objective of this study is the second stage, namely, to obtain a good approximation to F.
The simplest approximation is the gauge-invariant self-consistent (GISC) method in which I neglect the vector vertex function ΓィイD2νィエD2 in relating the scalar vertex function Γ with the self-energy Σ through the Ward identity. I have improved on this GISC systematically by introducing the ratio function R, defined as the ratio between Γ and the longitudinal part of ΓィイD2νィエD2. I exploit its asymptotic properties in various limits to construct a good approximate form for R.
For its illustration, I apply this algorithm to the electron gas and find the following : (i) Near the Fermi surface, RPA is found to provide rather accurate results because of the strong cancellation between Γ and Σ due to the Panli principle; (ii) it is not the case for the processes far from the Fermi surface; and (iii) a strong lower-energy shift is observed in the dynamic structure factor owing to the attractive electron-hole excitonic multiple scatterings. I shall apply the same method to real crystals.
As for superconductivity, I develop a theory on the GISC level and investigated the validity of the conventional Eliashberg theory in various aspects. I shall extend the theory so as to provide more accurate results with full attention to the role of Nambu-Goldstone modes in Γ.
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Research Products
(13 results)
