Multi-Scale Analysis for Random Quantum Systems with Interaction (BOK)

Yuri Suhov, V.A. Chulaevsky

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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.

Produktfakta

Språk Engelsk Engelsk Innbinding Innbundet
Utgitt 2013 Forfatter V.A. Chulaevsky, Yuri Suhov
Forlag
Springer
ISBN 9781461482253
Antall sider 226 Dimensjoner 15,5cm x 23,5cm x 1,6cm
Vekt 543 gram Leverandør Bertram Trading Ltd
Emner og form Applied mathematics, Probability & statistics, Functional analysis & transforms, Mathematical physics, Spectrum analysis, spectrochemistry, mass spectrometry