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 …

Experimental advances have allowed for the exploration of nearly isolated quantum many-
body systems whose coupling to an external bath is very weak. A particularly interesting …

Nascent platforms for programmable quantum simulation offer unprecedented access to
new regimes of far-from-equilibrium quantum many-body dynamics in almost isolated …

We report experimental realization of a quantum time quasicrystal and its transformation to a
quantum time crystal. We study Bose-Einstein condensation of magnons, associated with …

We show how a large family of interacting nonequilibrium phases of matter can arise from
the presence of multiple time-translation symmetries, which occur by quasiperiodically …

Ergodicity of quantum dynamics is often defined through statistical properties of energy
eigenstates, as exemplified by Berry's conjecture in single-particle quantum chaos and the …

Simulation of continuous-time evolution requires time discretization on both classical and
quantum computers. A finer time step improves simulation precision but it inevitably leads to …

Time-periodic (Floquet) driving is a powerful way to control the dynamics of complex
systems, which can be used to induce a plethora of new physical phenomena. However …

We present a brief overview of some of the analytic perturbative techniques for the
computation of the Floquet Hamiltonian for a periodically driven, or Floquet, quantum many …

Driven quantum systems may realize novel phenomena absent in static systems, but driving-
induced heating can limit the timescale on which these persist. We study heating in …