Related papers: A Brief History of Time Crystals
The conventional framework for defining and understanding phases of matter requires thermodynamic equilibrium. Extensions to non-equilibrium systems have led to surprising insights into the nature of many-body thermalization and the…
Crystals spontaneously break the continuous translation symmetry in space, despite the invariance of the underlying energy function. This has triggered suggestions of time crystals analogously lifting translational invariance in time.…
We present the theory of spontaneous symmetry breaking (SSB) of discrete time translations as recently realized in the space-time crystals of an atomic Bose-Einstein condensate. The non-equilibrium physics related to such a…
The public and scientists constantly have different perspectives. While on a time crystal, they stand in line and ask: What is a time crystal? Show me a material that is spontaneously crystalline in time? This study synthesizes a photonic…
We introduce a new class of out-of-equilibrium noninteracting topological phases, the topological space-time crystals. These are time-dependent quantum systems which do not have discrete spatial translation symmetries, but instead are…
Floquet (periodically driven) systems can give rise to unique non-equilibrium phases of matter without equilibrium analogs. The most prominent example is the realization of discrete time crystals. An intriguing question emerges: what other…
Discrete time crystals are periodically driven systems that display spontaneous symmetry breaking of time translation invariance in the form of indefinite subharmonic oscillations. We introduce a thermodynamically consistent model for a…
Periodically driven quantum systems host a range of non-equilibrium phenomena which are unrealizable at equilibrium. Discrete time-translational symmetry in a periodically driven many-body system can be spontaneously broken to form a…
Continuous time crystals (CTCs) are characterized by sustained oscillations that break the time translation symmetry. Since the ruling out of equilibrium CTCs by no-go theorems, the emergence of such dynamical phases has been observed in…
Time crystals appear when systems display a commensurate spontaneous breaking of the discrete time translational invariance imposed by an external periodic drive. No consensus on the definition has been reached as yet, but important aspects…
The notion of spontaneous symmetry breaking has been well established to characterize classical and quantum phase transitions of matter, such as in condensation, crystallization or quantum magnetism. Generalizations of this paradigm to the…
Discrete time crystals (DTCs) are new phases of matter characterized by the presence of an observable evolving with $nT$ periodicity under a $T$-periodic Hamiltonian, where $n>1$ is an integer insensitive to small parameter variations. In…
When the discrete time-translation symmetry of isolated, periodically driven systems is spontaneously broken, a new phase of matter can emerge. We review some recent developments on both the theoretical underpinnings and experimental…
A space-time crystal is defined as a quantum mechanical system with both spatial and temporal periodicity. Such a system can be described by the Floquet-Bloch (FB) theory. We first formulate a semiclassical theory by constructing a…
Discrete time crystals are a many-body state of matter where the extensive system's dynamics are slower than the forces acting on it. Nowadays, there is a growing debate regarding the specific properties required to demonstrate such a…
Time crystals are unexpected states of matter that spontaneously break time translation symmetry either in a discrete or continuous manner. However, spatially-mesoscale space-time crystals that break both the space and time symmetries have…
We investigate the emergence of a time crystal in a driven-dissipative many-body spin array. In this system the interplay between incoherent spin pumping and collective emission stabilizes a synchronized non-equilibrium steady state which…
Time crystals are quantum systems which are able to reveal condensed matter behavior in the time domain. It is known that crystalization in time can be observed in a periodically driven many-body system when interactions between particles…
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 driving an isolated quantum many-body system with two or more…
Recent works on observation of discrete time-crystalline signatures throw up major puzzles on the necessity of localization for stabilizing such out-of-equilibrium phases. Motivated by these studies, we delve into a clean interacting…