An Expansion Theorem for the Electric Conductivity of Metals. I : Electric Conductivity for Longitudinal Electric Field
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概要
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A systematic diagram representation in a composite 4-dimensional space is developed for Kubo's response function which describes the electric response currents of metals for longitudinal electric fields. Proper diagrams are defined as the Feynman type linked diagrams which cannot be decomposed into simpler diagrams connected only by one Coulomb line. The greatest care is exercised with reference to the fact that Kubo's formula for the conduction phenomena gives the transport coefficient χ(q, ω) defined as the ratio of the electric current vector to the electric displacement vector D(q, ω), while the electric conductivity σ(q, ω) of a metal is defined as the electric current vector divided by the electric field vector E(q, ω) in the metal. Thus σ(q, ω) is written as the product of σ(q, ω) and the dielectric constant of the metal. It is shown that, the product is reduced to a simple form. In the reduced form, χ(q, ω) is expressed as the sum of the proper diagrams. In this expression the lowest order term in respect to the Coulomb interaction includes the usual sum on ring diagrams and, moreover, constitutes a much better approximation than the ring approximation.
- 理論物理学刊行会の論文
- 1961-06-25
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