Multi-scale Analysis for Random Quantum Systems with Interaction (Progress in Mathematical Physics, Band 65) - Softcover

Chulaevsky, Victor; Suhov, Yuri

Softcover

ISBN 10: 1493939521 ISBN 13: 9781493939527

Verlag: Birkhäuser, 2016

Inhaltsangabe

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 Z^d.

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.

Über diesen Titel

Über die Autorin bzw. den Autor

Prof Chulaevsky teaches at the Univ. of Riems

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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 Z^d.

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.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 2016
• Sprache: Englisch
• ISBN 10: 1493939521
• ISBN 13: 9781493939527
• Einband: Taschenbuch
• Anzahl der Seiten: 252
• Kontakt zum Hersteller: Nicht verfügbar
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