Spectra of Random and Almost-Periodic Operators

Alexander Figotin

ISBN 10: 364274348X / ISBN 13: 9783642743481

Published by Springer Berlin Heidelberg, 2011

About this Item

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.

Seller Inventory # 9783642743481

Bibliographic Details

• Title: Spectra of Random and Almost-Periodic Operators
• Publisher: Springer Berlin Heidelberg
• Publication Date: 2011
• Language: English
• ISBN 10: 364274348X
• ISBN 13: 9783642743481
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 33D millimeters 235 millimeters width by 155 millimeters height by 33 millimeters depth
• Weight: 896 grams

About this title

Synopsis

This is the first research-level monograph to be written on this vast and multi-faceted subject on the interface of mathematics and theoretical physics. The book gives a unified account of what is known, established theory and a state-of-the-art account of what is still developing. The mathematical content is not easy, but the results are nevertheless in demand, not only from physicists, but from engineers working for example in semi-conductors and composite materials and other branches of chemical engineering. The book contains many concrete examples, for such applications.