In this review recent investigations are summarized of many-body quantum systems with
long-range interactions, which are currently realized in Rydberg atom arrays, dipolar …

Experimental progress in atomic, molecular, and optical platforms in the last decade has
stimulated strong and broad interest in the quantum coherent dynamics of many long-range …

For a one-dimensional spin chain with random local interactions, we prove that many-body
localization follows from a physically reasonable assumption that limits the amount of level …

A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York
University This book is a concise and self-contained introduction of recent techniques to …

Our geometric concepts evolved first through the discovery of Non-Euclidean geometry. The
discovery of quantum mechanics in the form of the noncommuting coordinates on the phase …

We consider a weakly interacting quantum spin chain with random local interactions. We
prove that many-body localization follows from a physically reasonable assumption that …

The question whether Anderson insulators can persist to finite-strength interactions—a
scenario dubbed many-body localization—has recently received a great deal of interest. The …

We review the current (as of Fall 2016) status of the studies on the emergent integrability in
many‐body localized models. We start by explaining how the phenomenology of fully many …

A complete understanding of Schrödinger operators is a necessary prerequisite for unveiling
the physics of nonrelativistic quanturn mechanics. Furthermore recent research shows that it …

A mathematical framework based on noncommutative geometry is proposed to describe the
Integer Quantum Hall Effect (IQHE). It takes localization effects into account. It permits us to …