Summary:  The study of quantum disorder has generated considerable research activity in mathematics and physics over past 40 years. While singleparticle 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 multiparticle quantum systems is an important and challenging problem that largely remains open. Multiscale 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 multiparticle 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 tightbinding Anderson model on a cubic lattice Zd. This book includes the following cuttingedge features: * an introduction to the stateoftheart singleparticle localization theory * an extensive discussion of relevant technical aspects of the localization theory * a thorough comparison of the multiparticle model with its singleparticle counterpart * a selfcontained rigorous derivation of both spectral and dynamical localization in the multiparticle tightbinding 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 yearlong graduate course or seminar in mathematical physics. It also can serve as a standard reference for specialists
