TY  - BOOK
AU  - Chulaevsky,Victor
AU  - Suhov,Yuri
ED  - SpringerLink (Online service)
TI  - Multi-scale Analysis for Random Quantum Systems with Interaction
T2  - Progress in Mathematical Physics,
SN  - 9781461482260
AV  - QA319-329.9 
U1  - 515.7 23
PY  - 2014///
CY  - New York, NY
PB  - Springer New York, Imprint: Birkhäuser
KW  - Mathematics
KW  - Functional analysis
KW  - Applied mathematics
KW  - Engineering mathematics
KW  - Probabilities
KW  - Physics
KW  - Solid state physics
KW  - Spectroscopy
KW  - Microscopy
KW  - Functional Analysis
KW  - Mathematical Methods in Physics
KW  - Probability Theory and Stochastic Processes
KW  - Applications of Mathematics
KW  - Solid State Physics
KW  - Spectroscopy and Microscopy
KW  - Electronic books
KW  - local
N1  - 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
N2  - 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
UR  - http://ezproxy.alfaisal.edu/login?url=http://dx.doi.org/10.1007/978-1-4614-8226-0
ER  -