EAN: 9781461482253

MULTI-SCALE ANALYSIS FOR RANDOM QUANTUM SYSTEMS...

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.

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