After many years of development of the basic tools, quantum simulation with ultracold atoms
has now reached the level of maturity at which it can be used to investigate complex …

This paper reviews recent experimental and theoretical progress concerning many-body
phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling …

Quantum computers, though not yet available on the market, will revolutionize the future of
information processing. Quantum computers for special purposes like quantum simulators …

In 1958, Anderson predicted the localization 1 of electronic wavefunctions in disordered
crystals and the resulting absence of diffusion. It is now recognized that Anderson …

In disordered media, quantum interference effects are expected to induce complete
suppression of electron conduction. The phenomenon, known as Anderson localization, has …

When attempting to understand the role of disorder in condensed-matter physics, we face
considerable experimental and theoretical difficulties, and many questions are still open …

We study numerically the spreading of an initially localized wave packet in a one-
dimensional discrete nonlinear Schrödinger lattice with disorder. We demonstrate that …

We experimentally probe the properties of the disordered Bose-Hubbard model using an
atomic Bose-Einstein condensate trapped in a 3D disordered optical lattice. Controllable …

The aim of this review is to introduce the reader to some of the physical notions and the
mathematical methods that are relevant to the study of nonlinear waves in Bose–Einstein …

The understanding of disordered quantum systems is still far from being complete, despite
many decades of research on a variety of physical systems. In this review we discuss how …