Theory of Disordered Systems.II. Functional Equation of tho Self‐Energy

1977

The diagonal vertex approximation for Gaussian random systems is defined. It can considered to be the best c-number approximation of the self-energy of such systems. Numerical computations of the density of states of the 1D Anderson model in this approximation agree within about one per thousand with the CPA.Die Diagonal-Vertex-Approximation fur Systeme mit GauDscher Unordnung wird definiert. Sie kann als die beste c-Zahl-Approximation der Selbstenergie solcher Systeme angesehen werden. Numerische Berechnungen der Zustandsdichte des 1 -dimensionalen Anderson-Modells in dieser Approximation stimmen innerhalb von etwa einem Promille mit CPA uberein.

Section: The Diagonal Vertex Approximation In Gaussian Random Systemsmentioning

confidence: 89%

The diagonal vertex approximation for gaussian random systems as a further test of the CPA

1977

“…so t h a t in our model (3.7) is an algebraic equation for ~( x : 2). (3.6) and (4.2) imply that where Ti = n E' is the "linear" density of the %potentials (4.1), which provides us with the natural energy unit .cO = 2 h2 9 / m .…”

Section: (42)mentioning

confidence: 91%

Theory of Disordered Systems III. Single‐Site Theory of Transport in Systems with Randomly Distributed Scatterers

1972

Jn case of systems with randomly distributed scatterers the self-consistent, single-site approximation of Schwartz and Ehrenreich [l] leads to a simple expression for the kernel of the Rethe-Salpeter equation in terms of the local self-energies. Thus, a consistent singlesite theory of linear response of such systems is given. It is applied to the disordered KronigPenney model which permits exact solutions of the Schwartz-Ehrenreich and the corresponding Bethe-Salpeter equation. Numerical results of the density of states and the mobility of the electrons are given. The existence of a mobility edge is established. I m Falle von Systemen mit willkiirlich verteilten Streuern fiihrt die selbstkonsistciite Einzentren-Approximation von Schwartz und Ehrenreich [l] zu einem einfachen Ausdruck fur den Kern derBethe-Salpeter-Gleichung in den loknlen Sclbstenergien. Uadurch ist eine konsistente Einzentren-Theorie der linearen Responsion solcher Systeme gegeben. Sie wird auf das ungeordnete KronigPenney-Model1 angewendet, das exakt,e Losungen dcr Schwartz-Ehrenreich-und der entsprochenden Bethe-Salpeter-Gleichung erlaubt. Kumerische Resultate der Zustandsdichte und der Beweglichkeit der Elektronen werden angegeben. Die Existenz einer BeTveglichkeitskante wird nachgewiesen.

“…is the mean Hartree-Pock energy of the system. Equation (4.2) is the generalization of Puff's functional equation [6] to interacting disordered systems. The novel aspect of this functional equation is that it comprises functional derivatives like (3.6) which bring charge transfer phenomena into play.…”

Section: Density Response and Screeningmentioning

confidence: 99%

Theory of disordered systems. IV. Coulomb interaction and screening

1975

The formal theory of interacting disordered systems is developed. Its main characteristic is that an external potential to which the system responds is coupled not only to the electronic but also to the disordered ionic charge density. This allows to describe the screening of individual potentials and potential fluctuations by the response properties of the averaged system. Electron-electron and electron-ion correlations constitute an effective screened interaction function from which the "screened" single-site approximation is derived.Die formale Theorie wechselwirkender ungeordneter Systeme wird entwickelt. Ihr Hauptmerkmal ist, daD ein LuDeres Potential, auf das das System reagiert, nicht nur an die Elektronen-sondern auch an die ungeordnete Ionenladungsdichte gekoppelt wird. Das erlaubt die Beschreibung der Abschirmung von individuellen Potentialen und Potentialfluktuationen durch die Responsionseigenschaften des gemittelten Systems. Elektron-Elektron-und Elektron-Ion-Korrelationen konstituieren eine effektive, abgeschirmte Wechselwirkungsfunktion, aus der die ,,abgeschirmte" Einzentren-Approximation abgeleitet wird.