Spectra of Random and Almost-Periodic Operators. (= Grundlehren der mathematischen Wissenschaften, Band 297).

Pastur, Leonid and Alexander Figotin:

ISBN 10: 3540506225 / ISBN 13: 9783540506225

Editore: Berlin, Springer, 1991

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VIII, 587 Seiten Einband etwas berieben, Bibl.Ex., innen guter und sauberer Zustand 9783540506225 Sprache: Englisch Gewicht in Gramm: 1004 8° , Leinen- Hardcover/Pappeinband, Codice articolo 143978

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Titolo: Spectra of Random and Almost-Periodic ...

Casa editrice: Berlin, Springer

Data di pubblicazione: 1991

Legatura: Rilegato

Edizione: 1.Auflage,.

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Riassunto:

In the last fifteen years the spectral properties of the Schrodinger equation and of other differential and finite-difference operators with random and almost-periodic coefficients have attracted considerable and ever increasing interest. This is so not only because of the subject's position at the in- tersection of operator spectral theory, probability theory and mathematical physics, but also because of its importance to theoretical physics, and par- ticularly to the theory of disordered condensed systems. It was the requirements of this theory that motivated the initial study of differential operators with random coefficients in the fifties and sixties, by the physicists Anderson, 1. Lifshitz and Mott; and today the same theory still exerts a strong influence on the discipline into which this study has evolved, and which will occupy us here. The theory of disordered condensed systems tries to describe, in the so-called one-particle approximation, the properties of condensed media whose atomic structure exhibits no long-range order. Examples of such media are crystals with chaotically distributed impurities, amorphous substances, biopolymers, and so on. It is natural to describe the location of atoms and other characteristics of such media probabilistically, in such a way that the characteristics of a region do not depend on the region's position, and the characteristics of regions far apart are correlated only very weakly. An appropriate model for such a medium is a homogeneous and ergodic, that is, metrically transitive, random field.