Related papers: Time Quasilattices in Dissipative Dynamical System…

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 class of such systems is those which do not thermalize under…

A discrete time crystal (DTC) is a remarkable non-equilibrium phase of matter characterized by the persistent sub-harmonic oscillations of physical observables in periodically driven many-body systems. Motivated by the question of whether…

Discrete time crystals (DTCs) are emergent non-equilibrium phases of periodically driven many-body systems, with potential applications ranging from quantum computing to sensing and metrology. There has been significant recent interest in…

It has been known that noise can suppress multistability by dynamically connecting coexisting attractors in the system which are otherwise in separate basins of attraction. The purpose of this mini-review is to argue that quasiperiodic…

We review recent results obtained for the dynamics of incipient chaos. These results suggest a common picture underlying the three universal routes to chaos displayed by the prototypical logistic and circle maps. Namely, the period…

Discrete time crystals (DTC) exhibit a special non-equilibrium phase of matter in periodically driven many-body systems with spontaneous breaking of time translational symmetry. The presence of decoherence generally enhances thermalization…

Solitons, defined as nonlinear waves which can reflect from boundaries or transmit through each other, are found in conservative, fully integrable systems. Similar phenomena, dubbed quasi-solitons, have been observed also in dissipative,…

Many-body quantum systems, under suitable conditions, exhibit time-translation symmetry breaking and settle in a discrete time crystalline (DTC) phase -- an out-of-equilibrium quantum phase of matter. The defining feature of DTC is a robust…

Discrete time crystals (DTCs) are nonequilibrium phases of matter with exotic observable dynamics. Among their remarkable features is their response to a periodic drive at a fraction of its frequency. Current successful experiments are…

Attempts to disentangle shear-flow turbulence often focus on identifying relatively simple solutions, such as travelling waves or periodic orbits. We show, however, that capturing multiscale features requires considering states at least as…

Time crystals are physical systems whose time translation symmetry is spontaneously broken. Although the spontaneous breaking of continuous time-translation symmetry in static systems is proved impossible for the equilibrium state, the…

We consider a dissipative version of the standard nontwist map. Nontwist systems present a robust transport barrier, called the shearless curve, that becomes the shearless attractor when dissipation is introduced. This attractor can be…

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…

Quasiperiodic mosaic systems with the quasiperiodic potential being added periodically with a fixed lattice interval have attracted significant attention due to their peculiar spectral properties with exactly known mobility edges, which…

Many-body quantum dynamics defined on a spatial lattice and in discrete time -- either as stroboscopic Floquet systems or quantum circuits -- has been an active area of research for several years. Being discrete in space and time, a natural…

We investigate the nonequilibrium dynamics of classical particles in a driven quasiperiodic lattice based on the Fibonacci sequence. An intricate transient dynamics of extraordinarily long ballistic flights at distinct velocities is found.…

We study the breaking of the discrete time-translation symmetry in small periodically driven quantum systems. Such systems are intermediate between large closed systems and small dissipative systems, which both display the symmetry…

We study systems that approach a state possessing discrete symmetry due to different degenerate realizations for the system. For concreteness, we consider fractionally filled systems where degeneracy comes from the presence of identical…

An infinite word x is said to be quasiperiodic if there exists a finite word q such that x is covered by occurrences of q (such a q is called a quasiperiod of x). Using the notion of derivation, we show that this definition is not…

A one-dimensional dynamical system with a marginal quasiperiodic gradient is presented as a mathematical extension of a nonuniform oscillator. The system exhibits a nonchaotic stagnant motion, which is reminiscent of intermittent chaos. In…