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arXiv:chem-ph/9605003 · Annals of Physics

Extended Two-Particle Green's Functions and Optical Potentials for Two-Particle Scattering by Many-Body Targets

Joachim Brand, Lorenz S. Cederbaum

Published Dec 1, 1996• 13 citations
arXivHTMLPDF
DOI
10.1006/aphy.1996.0132

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An extension of the fermionic particleparticle propagator is presented that possesses similar algebraic properties to the single-particle Green’s function. In particular, this extended two-particle Green’s function satisfies Dyson’s equation and its self energy has the same analytic structure as the the self energy of the single-particle Green’s function. For the case of a system interacting with one-particle potentials only, the two-particle self energy takes on a particularly simple form, just like the common self energy does. The new two-particle self energy also serves as a well behaved optical potential for the elastic scattering of a two-particle projectile by a many-body target. Due to its analytic structure, the two-particle self energy avoids divergences that appear with effective potentials derived by other means. 1996 Academic Press, Inc. I.

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I review the quantum theory of the electron moving in a random environment. First, the quantum mechanics of individual particles scattered on a random potential is discussed. The quantum-mechanical description is extended to many-body systems by using many-body Green functions. The many-body approach is used to derive the coherent-potential approximation and to show how it fits into the dynamical mean-field theory. The generating functional of the coherent-potential approximation is obtained in an analytic form from the limit to infinite dimensions of the general many-body description of non-interacting electrons in random lattices. The analytic generating functional of the mean-field description of random systems is extended to the Falicov-Kimball model with thermally equilibrated scattering lattice potential. The many-body Green functions are then used to calculate transport properties. The electrical conductivity of the coherent-potential approximation is derived from the two-particle Green function calculated in infinite spatial dimensions. Finally, a perturbation theory for the vertex corrections to the mean-field conductivity is introduced. In particular, it is shown how to make the expansion beyond the local approximations conserving.

arXiv:2109.04723•Sep 10, 2021•1 citation
An extension of the fermionic particleparticle propagator is presented that possesses similar algebraic properties to the single-particle Green’s function. In particular, this extended two-particle Green’s function satisfies Dyson’s equation and its self energy has the same analytic structure as the the self energy of the single-particle Green’s function. For the case of a system interacting with one-particle potentials only, the two-particle self energy takes on a particularly simple form, just like the common self energy does. The new two-particle self energy also serves as a well behaved optical potential for the elastic scattering of a two-particle projectile by a many-body target. Due to its analytic structure, the two-particle self energy avoids divergences that appear with effective potentials derived by other means. 1996 Academic Press, Inc. I.
The standard text book Green's function possesses a self-energy that is known to be an optical potential for elastic scattering. The introduction of an optical potential reduces the complex many-body scattering problem into a tractable one-body problem. In this paper inelastic Green's functions are introduced and discussed which possess self-energies that are optical potentials for inelastic scattering. If the projectile is indistinguishable from particles comprising the target, intriguing aspects arise even for noninteracting particles.
I review the quantum theory of the electron moving in a random environment. First, the quantum mechanics of individual particles scattered on a random potential is discussed. The quantum-mechanical description is extended to many-body systems by using many-body Green functions. The many-body approach is used to derive the coherent-potential approximation and to show how it fits into the dynamical mean-field theory. The generating functional of the coherent-potential approximation is obtained in an analytic form from the limit to infinite dimensions of the general many-body description of non-interacting electrons in random lattices. The analytic generating functional of the mean-field description of random systems is extended to the Falicov-Kimball model with thermally equilibrated scattering lattice potential. The many-body Green functions are then used to calculate transport properties. The electrical conductivity of the coherent-potential approximation is derived from the two-particle Green function calculated in infinite spatial dimensions. Finally, a perturbation theory for the vertex corrections to the mean-field conductivity is introduced. In particular, it is shown how to make the expansion beyond the local approximations conserving.