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Multi-scale Analysis for Random Quantum Systems with Interaction

  • Victor Chulaevsky
  • Yuri Suhov

Part of the Progress in Mathematical Physics book series (PMP, volume 65)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Single-Particle Localization

    1. Front Matter
      Pages 1-1
    2. Victor Chulaevsky, Yuri Suhov
      Pages 3-26
    3. Victor Chulaevsky, Yuri Suhov
      Pages 27-133
  3. Multi-particle Localization

    1. Front Matter
      Pages 135-135
    2. Victor Chulaevsky, Yuri Suhov
      Pages 137-170
    3. Victor Chulaevsky, Yuri Suhov
      Pages 171-228
  4. Back Matter
    Pages 229-238

About this book

Introduction

The study of quantum disorder has generated considerable research activity in mathematics and physics over past 40 years. While single-particle models have been extensively studied at a rigorous mathematical level, little was known about systems of several interacting particles, let alone systems with positive spatial particle density. Creating a consistent theory of disorder in multi-particle quantum systems is an important and challenging problem that largely remains open. Multi-scale Analysis for Random Quantum Systems with Interaction  presents the progress that had been recently achieved in this area.

 

The main focus of the book is on a rigorous derivation of the multi-particle localization in a strong random external potential field. To make the presentation accessible to a wider audience, the authors restrict attention to a relatively simple tight-binding Anderson model on a cubic lattice Zd.

 

This book includes the following cutting-edge features:

* an introduction to the state-of-the-art single-particle localization theory

* an extensive discussion of relevant technical aspects of the localization theory

* a thorough comparison of the multi-particle model with its single-particle counterpart

* a self-contained rigorous derivation of both spectral and dynamical localization in the multi-particle tight-binding Anderson model.

 

Required mathematical background for the book includes a knowledge of functional calculus, spectral theory (essentially reduced to the case of finite matrices) and basic probability theory. This is an excellent text for a year-long graduate course or seminar in mathematical physics. It also can serve as a standard reference for specialists.

Keywords

Anderson localization Stolmann’s estimate Wegner’s estimate delocalization dynamical localization multi-particle MSA multi-scale analysis spectral localization

Authors and affiliations

  • Victor Chulaevsky
    • 1
  • Yuri Suhov
    • 2
  1. 1.Département de MathématiquesUniversité de Reims Champagne-ArdenneReimsFrance
  2. 2.Statistical Laboratory, DPMMSUniversity of CambridgeCambridgeUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-8226-0
  • Copyright Information Springer Science+Business Media New York 2014
  • Publisher Name Birkhäuser, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-8225-3
  • Online ISBN 978-1-4614-8226-0
  • Series Print ISSN 1544-9998
  • Series Online ISSN 2197-1846
  • Buy this book on publisher's site