Multi-scale Analysis for Random Quantum Systems with Interaction (eBook)

Victor Chulaevsky, Yuri Suhov (Autoren)

eBook Download: PDF

2013 | 2014
XI, 238 Seiten
Springer New York (Verlag)
978-1-4614-8226-0 (ISBN)

Infos

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 theorya 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.

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 20.9.2013
• Reihe/Serie: Progress in Mathematical Physics
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Chemie ► Analytische Chemie
• Themenwelt: 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: 1-4614-8226-7 / 1461482267
• ISBN-13: 978-1-4614-8226-0 / 9781461482260