Multi-scale Analysis for Random Quantum Systems with Interaction
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Multi-scale Analysis for Random Quantum Systems with Interaction
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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.
Product details
- Type:
- Book
- Edition:
- 1
- Languages:
-
Original:
English
- Number of Pages:
-
252
- Publisher:
-
Birkhäuser
- Publication Date:
-
2013-09-20
- ISBN / EAN:
-
9781461482253
- Weight:
-
547 g
- Dimensions:
-
16/24/2 cm
- GPSR Manufacturer Reference:
-
[email protected]
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