Progress in Mathematical Physics

Multi-scale Analysis for Random Quantum Systems with Interaction

Authors: Chulaevsky, Victor, Suhov, Yuri

  • Introduces the reader to recent progress in this field
  • Attracts attention to possible directions for future research
  • Presents new and exciting research the first time in the literature and includes all necessary background material
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About this Textbook

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.

Table of contents (4 chapters)

  • A Brief History of Anderson Localization

    Chulaevsky, Victor (et al.)

    Pages 3-26

  • Single-Particle MSA Techniques

    Chulaevsky, Victor (et al.)

    Pages 27-133

  • Multi-particle Eigenvalue Concentration Bounds

    Chulaevsky, Victor (et al.)

    Pages 137-170

  • Multi-particle MSA Techniques

    Chulaevsky, Victor (et al.)

    Pages 171-228

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-1-4614-8226-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA
  • ISBN 978-1-4614-8225-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA
  • ISBN 978-1-4939-3952-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Multi-scale Analysis for Random Quantum Systems with Interaction
Authors
Series Title
Progress in Mathematical Physics
Series Volume
65
Copyright
2014
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-8226-0
DOI
10.1007/978-1-4614-8226-0
Hardcover ISBN
978-1-4614-8225-3
Softcover ISBN
978-1-4939-3952-7
Series ISSN
1544-9998
Edition Number
1
Number of Pages
XI, 238
Number of Illustrations and Tables
5 b/w illustrations
Topics