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Spectra of Random and Almost-Periodic Operators: 297 (Grundlehren der mathematischen Wissenschaften) - Softcover
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Book by Pastur Leonid Figotin Alexander
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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.
Reseña del editor
The study of the spectra and related characteristics of random and almost periodic operators of various types (Schrödinger, continuous, discrete and more general) is a lively and fascinating field of research lying at the intersection of mathematical physics, spectral theory of operators and probability theory. A widespread interest in the domain and a vast amount of mathematical activity have led to many remarkable new results and viewpoints yielding insight even into traditional questions. This book by two of the leading researchers having contributed to this field is the first systematic treatment of the fundamental problems and the large body of mathematical results known, and thus fills the gap in the reference literature. Not content to highlight the important ideas and recently developed concepts and methods, it also provides a large number of exercises illustrating these, to guide the reader towards improvements and generalizations. This long-awaited book is a welcome addition to the literature both for specialists in the field and for graduate students moving into research, as well as for all interested in the major problems of mathematical physics today.
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- VerlagSpringer
- Erscheinungsdatum2011
- ISBN 10 364274348X
- ISBN 13 9783642743481
- EinbandTapa blanda
- SpracheEnglisch
- Anzahl der Seiten600
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Spectra of Random and Almost-Periodic Operators (Grundlehren der mathematischen Wissenschaften)
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Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Artikel-Nr. 9783642743481
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