Overview
- 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
Part of the book series: Progress in Mathematical Physics (PMP, volume 65)
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About this book
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.
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Table of contents (4 chapters)
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Front Matter
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Single-Particle Localization
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Front Matter
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Multi-particle Localization
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Front Matter
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Back Matter
Authors and Affiliations
Bibliographic Information
Book Title: Multi-scale Analysis for Random Quantum Systems with Interaction
Authors: Victor Chulaevsky, Yuri Suhov
Series Title: Progress in Mathematical Physics
DOI: https://doi.org/10.1007/978-1-4614-8226-0
Publisher: Birkhäuser New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2014
Hardcover ISBN: 978-1-4614-8225-3Published: 20 September 2013
Softcover ISBN: 978-1-4939-3952-7Published: 23 August 2016
eBook ISBN: 978-1-4614-8226-0Published: 20 September 2013
Series ISSN: 1544-9998
Series E-ISSN: 2197-1846
Edition Number: 1
Number of Pages: XI, 238
Number of Illustrations: 5 b/w illustrations
Topics: Functional Analysis, Mathematical Methods in Physics, Probability Theory and Stochastic Processes, Applications of Mathematics, Solid State Physics, Spectroscopy and Microscopy