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

Pastur, Leonid and Alexander Figotin:

ISBN 10: 3540506225 / ISBN 13: 9783540506225

Published by Berlin, Springer, 1991

About this Item

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

Bibliographic Details

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

Publisher: Berlin, Springer

Publication Date: 1991

Binding: Hardcover

Edition: 1.Auflage,.

About this title

Synopsis:

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.

Synopsis:

The study of the spectra and related characteristics of random and almost periodic operators of various types (Schrodinger, continuous, discrete and more general) is a lively 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 considerable amount of mathematical activity have led to many new results and viewpoints yielding insight even into traditional questions. This book by two of the leading researchers is a systematic treatment of the fundamental problems and the large body of mathematical results known. The book also provides a number of exercises illustrating these results to guide the reader towards improvements and generalizations.