Multi-Scale Analysis for Random Quantum Systems with Interaction 2014 Edition Contributor(s): Chulaevsky, Victor (Author), Suhov, Yuri (Author) |
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ISBN: 1461482259 ISBN-13: 9781461482253 Publisher: Birkhauser OUR PRICE: $94.99 Product Type: Hardcover - Other Formats Published: September 2013 |
Additional Information |
BISAC Categories: - Mathematics | Functional Analysis - Mathematics | Applied - Science | Physics - Mathematical & Computational |
Dewey: 515.7 |
LCCN: 2013950173 |
Series: Progress in Mathematical Physics |
Physical Information: 0.63" H x 6.14" W x 9.21" (1.17 lbs) 238 pages |
Descriptions, Reviews, Etc. |
Publisher Description: 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. |