Multi-scale Analysis for Random Quantum Systems with Interactio
General Material Designation
[Book]
First Statement of Responsibility
/ electronic resource
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
New York, NY
Name of Publisher, Distributor, etc.
: Springer New York :Imprint: Birkh?user,
Date of Publication, Distribution, etc.
, 2014.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
XI, 238 s. 5 illus. , online resource..
SERIES
Series Title
(Progress in Mathematical Physics
Volume Designation
; 65,1544-9998)
GENERAL NOTES
Text of Note
9781461482253.
NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
Text of Note
Electronic
CONTENTS NOTE
Text of Note
Summary: 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 apresents the progress that had been recently achieved in this area. a 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. a 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. a 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.
Text of Note
Preface -- Part I Single-particle Localisation -- A Brief History of Anderson Localization.-aSingle-Particle MSA Techniques -- Part II Multi-particle Localization -- Multi-particle Eigenvalue Concentration Bounds -- Multi-particle MSA Techniques -- References -- Index.