The spontaneous breaking of time-translation symmetry has led to the discovery of a new
phase of matter: the discrete time crystal. Discrete time crystals exhibit rigid subharmonic …

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 …

Quantum many-body systems display rich phase structure in their low-temperature
equilibrium states. However, much of nature is not in thermal equilibrium. Remarkably, it was …

The control of nonequilibrium quantum dynamics in many-body systems is challenging
because interactions typically lead to thermalization and a chaotic spreading throughout …

While Hermiticity lies at the heart of quantum mechanics, recent experimental advances in
controlling dissipation have brought about unprecedented flexibility in engineering non …

Spontaneous symmetry breaking is a fundamental concept in many areas of physics,
including cosmology, particle physics and condensed matter. An example is the breaking of …

Understanding quantum dynamics away from equilibrium is an outstanding challenge in the
modern physical sciences. Out-of-equilibrium systems can display a rich variety of …

Quantum many-body systems away from equilibrium host a rich variety of exotic phenomena
that are forbidden by equilibrium thermodynamics. A prominent example is that of discrete …

Time-periodic forcing in the form of coherent radiation is a standard tool for the coherent
manipulation of small quantum systems like single atoms. In the last years, periodic driving …

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 …