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Caught by disorder
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Caught by disorder

Caught by disorder

Bound States in Random Media

Peter Stollmann

166 pages, parution le 04/12/2001

Résumé

Disorder is one of the central topics in science today. Over the past 15 years various aspects of the effects of disorder have changed a number of paradigms in mathematics and physics. One such effect is a phenomenon called localization, which describes the very strange behavior of waves in random media. Instead of traveling through space as they do in ordered environments, localized waves stay in a confined region and are caught by disorder. This work is the first treatment of the subject in monograph or textbook form.
The study of disorder has generated enormous research activity in mathematics and physics. Over the past 15 years various aspects of the subject have changed a number of paradigms and have inspired the discovery of deep mathematical techniques to deal with complex problems arising from the effects of disorder. One important effect is a phenomenon called localization, which describes the very strange behavior of waves in random media – the fact that waves, instead of traveling through space as they do in ordered environments, stay in a confined region (caught by disorder). To date, there is no treatment of this subject in monograph or textbook form. This book fills that gap.

'Caught by Disorder' presents:

  • an introduction to disorder that can be grasped by graduate students in a hands-on way
  • a concise, mathematically rigorous examination of some particular models of disordered systems
  • a detailed application of the localization phenomenon, worked out in two typical model classes that keep the technicalities at a reasonable level
  • a thorough examination of new mathematical machinery, in particular, the method of multi-scale analysis
  • a number of key unsolved problems
  • an appendix containing the prerequisites of operator theory, as well as other proofs
  • examples, illustrations, comprehensive bibliography, author and keyword index.

Mathematical background for this book requires only a knowledge of pdes, functional analysis – mainly operator theory and spectral theory – and elementary probability theory. The work will be an excellent text for a graduate course or seminar in mathematical physics or will serve as a standard reference for specialists.

Table of Contents:

Introduction
1. Bound States versus Extended States
2. Ergodic Operator Families: Definition and Abstract Theory
3. Some Important Examples
4. Our Basic Models (P + A) and (DIV)
5. Localization and Lifshitz Tails: The Heuristic Picture
6. Lifshitz Tails for (P + A)
7. Initial Length Tail Estimates
8. Wegener Estimates
9. Combes--Thomas Estimates
10. Changing Cubes
11. Idea of the Proof of Localization and Historical Notes
12. Multi-scale Analysis
13. Exponential Localization
14. Dynamical Localization
15. More Models
16. Appendix: A Short Story of Selfadjoint Operators
17. Aftermath
Bibliography
Index

Caractéristiques techniques

  PAPIER
Éditeur(s) Birkhäuser
Auteur(s) Peter Stollmann
Parution 04/12/2001
Nb. de pages 166
Format 16 x 24
Couverture Relié
Poids 341g
Intérieur Noir et Blanc
EAN13 9780817642105
ISBN13 978-0-8176-4210-5

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