Caught by Disorder: Bound States in Random Media

ISBN-13: 9780817642105 / Angielski / Twarda / 2001 / 166 str.

Peter Stollmann

Opis

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 behaviour of waves in random media. Instead of travelling 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.

Spis treści

Introduction 1. Getting Started 1.1. Bound States versus Extended States 1.2. Ergodic Operator Families 1.3. Some Important Examples 1.4. Our Basic Models (P + A) and (DIV) 1.5. Localization and Lifshitz Tails: The Heuristic Picture 2. Analysis of Anderson-type Models 2.1. Lifshitz Tails for (P + A) 2.2. Initial Length Scale Estimates 2.3. Wegner Estimates 2.4. Combes--Thomas Estimates 2.5. Changing Cubes 3. Multiscale Analysis 3.1. Idea of the Proof of Localization and Historical Notes 3.2. Multiscale Analysis 3.3. Exponential Localization 3.4. Dynamical Localization 3.5. More Models 4. Appendix 4.1. A Short Story of Selfadjoint Operators 4.2. Some Basics from Probability Theory 5. Aftermath References Index

O autorze

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 introducing readers to disorder in a hands-on way.