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Propagation and localization phenomena in solid state physics and, more generally, in complex and disordered media, have attracted the attention of physicists and mathematicians for many years. One of the most powerful and rigorous methods of analysis of these phenomena is so-called multi-scale analysis.

This monograph gives a systematic exposition of this method for random lattice Schrodinger operators (LSO) with interaction. These results belong to the authors; many of them are presented for the first time in the literature. The authors focus on the Anderson tight binding model,...

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...