Spectra of Random and Almost-periodic Operators: Part 297 (Die Grundlehren der Mathematischen Wissenschaften) [Hardcover] Pastur, Leonid and Figotin, Alexander

Pastur, Leonid; Figotin, Alexander

ISBN 10: 3540506225 / ISBN 13: 9783540506225

Editore: Springer, 1991

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Some outer edges have minor scuffs. Cover has light scratches/marks. Textblock has shelf wear. Content is in very good readable condition.

Codice articolo 074215-9

Dati bibliografici

• Titolo: Spectra of Random and Almost-periodic Operators: Part 297 (Die Grundlehren der Mathematischen Wissenschaften) [Hardcover] Pastur, Leonid and Figotin, Alexander
• Editore: Springer
• Data di pubblicazione: 1991
• Lingua: Inglese
• ISBN 10: 3540506225
• ISBN 13: 9783540506225
• Rilegatura: Rilegato
• Condizione: Poor

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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.