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Properties and Use of the Green’s Functionsnctions like the conductivity. The poles of an appropriate analytic continuation of . in the complex .-plane can be interpreted as the energy (the real part of the pole) and the inverse lifetime (the imaginary part of the pole) of quasiparticles. The latter are entities that allow us to map an interacting system to a noninteracting one.

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evaculate

Electrical Conductivity and Green’s Functionsfunctions have played a central role as a theoretical tool. In this chapter, we shall introduce several transport quantities, such as electrical conductivity, and present several schemes for their calculation.

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Green’s Functions and Perturbation Theory .(.) corresponding to ℌ.. 2) Express .(.) as a perturbation series in terms of .(.) and ℌ., where .(.) is the Green’s function associated with ℌ. 3) Extract from .(.) information about the eigenvalues and eigenfunctions of ℌ.

难解

Green’s Functions for Tight-Binding Hamiltoniansι; the sites {ι} form a lattice. Such Hamiltonians are very important in solid-state physics. Here we calculate the Green’s functions associated with the TBH for various simple lattices. We also review briefly some applications in solid-state physics.

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Single Impurity Scatteringty in a perfect periodic lattice. We obtain explicit results for bound and scattering states. Certain important applications, such as gap levels in solids, Cooper pairs in superconductivity, resonance and bound states producing the Kondo effect, and impurity lattice vibrations, are presented.

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摘要

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