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 …

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 …

Time crystals are classified as discrete or continuous depending on whether they
spontaneously break discrete or continuous time translation symmetry. Although discrete …

The assumption that quantum systems relax to a stationary state in the long-time limit
underpins statistical physics and much of our intuitive understanding of scientific …

The permutational invariance of identical two-level systems allows for an exponential
reduction in the computational resources required to study the Lindblad dynamics of …

Time crystals are periodic states exhibiting spontaneous symmetry breaking in either time-
independent or periodically-driven quantum many-body systems. Spontaneous modification …

Explaining quantum many-body dynamics is a long-held goal of physics. A rigorous operator
algebraic theory of dynamics in locally interacting systems in any dimension is provided …

The Dicke model—a paradigmatic example of superradiance in quantum optics—describes
an ensemble of atoms which are collectively coupled to a leaky cavity mode. As a result of …

Synchronization is a phenomenon where interacting particles lock their motion and display
non-trivial dynamics. Despite intense efforts studying synchronization in systems without …

A class of systems exists in which dissipation, external drive and interactions compete and
give rise to non-equilibrium phases that would not exist without the drive. There, phase …