Grundlehren der mathematischen Wissenschaften

Spectra of Random and Almost-Periodic Operators

Authors: Pastur, Leonid, Figotin, Alexander

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About this book

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.

Buy this book

Softcover $119.99
price for USA in USD
  • ISBN 978-3-642-74348-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.

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Bibliographic Information

Bibliographic Information
Book Title
Spectra of Random and Almost-Periodic Operators
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
297
Copyright
1992
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
Softcover ISBN
978-3-642-74348-1
Series ISSN
0072-7830
Edition Number
1
Number of Pages
VIII, 587
Topics