Time crystals are time-periodic self-organized structures postulated by Frank Wilczek in
2012. While the original concept was strongly criticized, it stimulated at the same time an …

This article reviews recent theoretical and experimental advances in the fundamental
understanding and active control of quantum fluids of light in nonlinear optical systems. In …

Despite enormous efforts devoted to the study of the many-body localization (MBL)
phenomenon, the nature of the high-energy behavior of the Heisenberg spin chain in a …

We present here various techniques to work with clean and disordered quantum Ising
chains, for the benefit of students and non-experts. Starting from the Jordan-Wigner …

At the quantum many-body level, atom-light interfaces generally remain challenging to solve
for or understand in a nonperturbative fashion. Here we consider a waveguide quantum …

The review deals with the physics of cold atomic gases in the presence of disorder. The
emphasis is on the theoretical developments, although several experiments are also briefly …

We show that one-dimensional lattice models exhibit superdiffusive transport in the
presence of random nodal impurities in the absence of interaction. Here a nodal impurity is …

Time crystals are quantum many-body systems which are able to self-organize their motion
in a periodic way in time. Discrete time crystals have been experimentally demonstrated in …

Entanglement in a pure state of a many-body system can be characterized by the R\'enyi
entropies $ S^{(\alpha)}=\ln\textrm {tr}(\rho^\alpha)/(1-\alpha) $ of the reduced density matrix …

Time crystals are quantum many-body systems that, due to interactions between particles,
are able to spontaneously self-organize their motion in a periodic way in time by analogy …