Related papers: Colloquium: Quantum and Classical Discrete Time Cr…

Time crystals are exotic phases of matter characterized by a broken time-translational symmetry, such that the ground state of the system evolves in time in a periodic fashion. Even though the time-crystal concept was introduced relatively…

Continuous time-translation symmetry is often spontaneously broken in open quantum systems, and the condition for their emergence has been actively investigated. However, there are only a few cases in which its condition for appearance has…

Discrete time quasicrystals (DTQC) constitute a class of non-equilibrium matter characterized by temporal order without strict periodicity, in contrast to conventional time crystals. Investigating these phenomena is essential for expanding…

In analogy with crystalline solids around us, Wilczek recently proposed the idea of "time crystals" as phases that spontaneously break the continuous time translation into a discrete subgroup. The proposal stimulated further studies and…

A rich variety of non-equilibrium dynamical phenomena and processes unambiguously calls for the development of general numerical techniques to probe and estimate a complex interplay between spatial and temporal degrees of freedom in…

It has been argued that the existence of time crystals requires a spontaneous breakdown of the continuous time translation symmetry so to account for the unexpected non-stationary behavior of quantum observables in the ground state. Our…

While a generic open quantum system decays to its steady state, continuous time crystals (CTCs) develop spontaneous oscillation and never converge to a stationary state. Just as crystals develop correlations in space, CTCs do so in time.…

Critical points and phase transitions are characterized by diverging susceptibilities, reflecting the tendency of the system toward spontaneous symmetry breaking. Equilibrium statistical mechanics bounds these instabilities to occur at zero…

We consider the possibility that classical dynamical systems display motion in their lowest energy state, forming a time analogue of crystalline spatial order. Challenges facing that idea are identified and overcome. We display arbitrary…

Time crystals, as temporal analogs of space crystals, manifest as stable and periodic behavior that breaks time translation symmetry. In an open quantum system, many-body interaction subjected to dissipation allows one to develop the time…

Time crystals are an enigmatic phase of matter in which a quantum mechanical system displays repetitive, observable motion - they spontaneously break the time translation symmetry. On the other hand optomechanical systems, where mechanical…

We discuss the emergence of non-stationarity in open quantum many-body systems. This leads us to the definition of dissipative time crystals which display experimentally observable, persistent, time-periodic oscillations induced by noisy…

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…

The exotic phenomenon of time translation symmetry breaking under periodic driving - the time crystal - has been shown to occur in many-body systems even in clean setups where disorder is absent. In this work, we propose the realization of…

Recent experiments with dense laser-driven atomic gases [G. Ferioli et al., arXiv:2207.10361 (2022)] have realized a many-body system which in the thermodynamic limit yields a so-called boundary time-crystal. This state of matter is…

Open many-body quantum systems can exhibit intriguing nonequilibrium phases of matter, such as time crystals. In these phases, the state of the system spontaneously breaks the time-translation symmetry of the dynamical generator, which…

Time crystals are a peculiar state of matter. Their emergence hinges on ergodicity breaking, which typically originates from many-body localization or Floquet prethermalization. Here we propose a novel scheme for devising robust dissipative…

A discrete time crystal (DTC) is a robust phase of driven systems that breaks the discrete time translation symmetry of the driving Hamiltonian. Recent experiments have observed DTC signatures in two distinct systems. Here we show nuclear…

Time crystals correspond to a phase of matter where time-translational symmetry (TTS) is broken. Up to date, they are well studied in open quantum systems, where external drive allows to break discrete TTS, ultimately leading to Floquet…

We define what it means for time translation symmetry to be spontaneously broken in a quantum system, and show with analytical arguments and numerical simulations that this occurs in a large class of many-body-localized driven systems with…