Multi-scale analysis for random quantum systems with interaction
著者
書誌事項
Multi-scale analysis for random quantum systems with interaction
（Progress in mathematical physics / editors-in-chief, Anne Boutet de Monvel, Gerald Kaiser, v. 65）
Birkhäuser , Springer, c2014
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注記
Includes bibliographical references (p. 229-235) and index
内容説明・目次
内容説明
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.
目次
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.
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