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.
- Book Title Multi-scale Analysis for Random Quantum Systems with Interaction
- Series Title Progress in Mathematical Physics
- Series Abbreviated Title Progress Mathemat.Physics(formerly:Progress in Physics)
- 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 Mathematics and Statistics (R0)
- Hardcover ISBN 978-1-4614-8225-3
- Softcover ISBN 978-1-4939-3952-7
- eBook ISBN 978-1-4614-8226-0
- Series ISSN 1544-9998
- Series E-ISSN 2197-1846
- Edition Number 1
- Number of Pages XI, 238
- Number of Illustrations 5 b/w illustrations, 0 illustrations in colour
Mathematical Methods in Physics
Probability Theory and Stochastic Processes
Applications of Mathematics
Solid State Physics
Spectroscopy and Microscopy
- Buy this book on publisher's site
- Industry Sectors
- Finance, Business & Banking