Multi-scale Analysis for Random Quantum Systems with Interaction / / by Victor Chulaevsky, Yuri Suhov

• Record Nr.: UNINA9910299975403321
• Autore: Chulaevsky Victor
• Pubbl/distr/stampa: New York, NY : , : Springer New York : , : Imprint : Birkhäuser, , 2014
• ISBN: 1-4614-8226-7
• Edizione: [1st ed. 2014.]
• Descrizione fisica: 1 online resource (XI, 238 p. 5 illus.) : online resource
• Collana: Progress in Mathematical Physics, , 1544-9998 ; ; 65
• Disciplina: 515.7
• Soggetti: Functional analysis; Physics; Probabilities; Applied mathematics; Engineering mathematics; Solid state physics; Spectrum analysis; Microscopy; Functional Analysis; Mathematical Methods in Physics; Probability Theory and Stochastic Processes; Applications of Mathematics; Solid State Physics; Spectroscopy and Microscopy
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references (pages [229]-235) and index.
• Nota di contenuto: 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.
• Sommario/riassunto: 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.