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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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Multi-scale Analysis for Random Quantum Systems with Interaction (Hardcover, 2014 ed.)
Loot Price: R3,216
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Multi-scale Analysis for Random Quantum Systems with Interaction (Hardcover, 2014 ed.)
Series: Progress in Mathematical Physics, 65
Expected to ship within 10 - 15 working days
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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.
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