Multi-scale Analysis for Random Quantum Systems with Interaction
Seiten
2016
|
Softcover reprint of the original 1st ed. 2014
Birkhauser Boston Inc (Verlag)
978-1-4939-3952-7 (ISBN)
Birkhauser Boston Inc (Verlag)
978-1-4939-3952-7 (ISBN)
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.
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.
Prof Chulaevsky teaches at the Univ. of Riems
Preface.- Part I Single-particle Localisation.- A Brief History of Anderson Localization.- Single-Particle MSA Techniques.- Part II Multi-particle Localization.- Multi-particle Eigenvalue Concentration Bounds.- Multi-particle MSA Techniques.- References.- Index.
| Erscheinungsdatum | 04.10.2016 |
|---|---|
| Reihe/Serie | Progress in Mathematical Physics ; 65 |
| Zusatzinfo | 5 Illustrations, black and white; XI, 238 p. 5 illus. |
| Verlagsort | Secaucus |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Naturwissenschaften ► Chemie ► Analytische Chemie | |
| Naturwissenschaften ► Physik / Astronomie | |
| Schlagworte | Anderson localization • delocalization • dynamical localization • multi-particle MSA • multi-scale analysis • spectral localization • Stolmann’s estimate • Wegner’s estimate |
| ISBN-10 | 1-4939-3952-1 / 1493939521 |
| ISBN-13 | 978-1-4939-3952-7 / 9781493939527 |
| Zustand | Neuware |
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