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Spectra of Random and Almost-Periodic Operators by Leonid Pastur (English) Paper

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Specificaties

Objectstaat
Nieuw: Een nieuw, ongelezen en ongebruikt boek in perfecte staat waarin geen bladzijden ontbreken of ...
ISBN-13
9783642743481
Book Title
Spectra of Random and Almost-Periodic Operators
ISBN
9783642743481
Publication Name
Spectra of Random and Almost-Periodic Operators
Item Length
9.3in
Publisher
Springer Berlin / Heidelberg
Publication Year
2011
Series
Grundlehren Der Mathematischen Wissenschaften Ser.
Type
Textbook
Format
Trade Paperback
Language
English
Item Height
0.5in
Author
Alexander Figotin, Leonid Pastur
Item Width
6.1in
Item Weight
31.6 Oz
Number of Pages
VIII, 587 Pages

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Product Information

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.

Product Identifiers

Publisher
Springer Berlin / Heidelberg
ISBN-10
364274348x
ISBN-13
9783642743481
eBay Product ID (ePID)
6038701249

Product Key Features

Author
Alexander Figotin, Leonid Pastur
Publication Name
Spectra of Random and Almost-Periodic Operators
Format
Trade Paperback
Language
English
Publication Year
2011
Series
Grundlehren Der Mathematischen Wissenschaften Ser.
Type
Textbook
Number of Pages
VIII, 587 Pages

Dimensions

Item Length
9.3in
Item Height
0.5in
Item Width
6.1in
Item Weight
31.6 Oz

Additional Product Features

Series Volume Number
297
Number of Volumes
1 Vol.
Lc Classification Number
Qc19.2-20.85
Table of Content
I. Metrically Transitive Operators.- 1 Basic Definitions and Examples.- 2 Simple Spectral Properties of Metrically Transitive Operators.- Problems.- II. Asymptotic Properties of Metrically Transitive Matrix and Differential Operators.- 3 Review of Basic Results.- 4 Matrix Operators on ?2 (Zd).- 5 Schrödinger Operators and Elliptic Differential Operators on L2(Rd).- Problems.- III. Integrated Density of States in One-Dimensional Problems of Second Order.- 6 The Oscillation Theorem and the Integrated Density of States.- 7 Examples of Calculation of the Integrated Density of States.- Problems.- IV. Asymptotic Behavior of the Integrated Density of States at Spectral Boundaries in Multidimensional Problems.- 8 Stable Boundaries.- 9 Fluctuation Boundaries: General Discussion and Classical Asymptotics.- 10 Fluctuation Boundaries: Quantum Asymptotics.- Problems.- V. Lyapunov Exponents and the Spectrum in One Dimension.- 11 Existence and Properties of Lyapunov Exponents.- 12 Lyapunov Exponents and the Absolutely Continuous Spectrum.- 13 Lyapunov Exponents and the Point Spectrum.- Problems.- VI. Random Operators.- 14 The Lyapunov Exponent of Random Operators in One Dimension.- 15 The Point Spectrum of Random Operators.- Problems.- VII. Almost-Periodic Operators.- 16 Smooth Quasi-Periodic Potentials.- 17 Limit-Periodic Potentials.- 18 Unbounded Quasiperiodic Potentials.- Problems.- Appendix A: Nevanlinna Functions.- Appendix B: Distribution of Eigenvalues of Large Random Matrices.- List of Symbols.
Copyright Date
1992
Topic
Functional Analysis, Probability & Statistics / General, Physics / Mathematical & Computational, Mathematical Analysis
Intended Audience
Scholarly & Professional
Illustrated
Yes
Genre
Science, Mathematics

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