Related papers: Time Crystals and Phase-Space Noncommutative Quant…

Difficulties around the idea of spontaneous breaking of time translation symmetry in a closed quantum mechanical system are identified, and then overcome in a simple model. The possibility of ordering in imaginary time is also discussed.

We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…

Time crystals form when arbitrary physical states of a periodically driven system spontaneously break discrete time-translation symmetry. We introduce one-dimensional time-crystalline topological superconductors, for which time-translation…

I argue that a single driven quantum Van der Pol oscillator should not be considered a dissipative time crystal, contrary to previous claims. In particular, I show that its phase is prone to randomly drift when considering dephasing or…

Time crystals are classified into discrete time crystals and continuous time crystals based on whether they spontaneously break time-translation symmetry. Continuous-time crystals do not require external driving. By introducing AdS/CFT…

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…

By including appropriate Riemman cubic invariants, we find that the dynamics of classical time crystals can be straightforwardly realized in Einstein gravity on the FLRW metric. The time reflection symmetry is spontaneously broken in the…

In this paper, I present a mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, it is demonstrated that quantum tunneling can be…

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…

Discrete time crystals are a special phase of matter in which time translational symmetry is broken through a periodic driving pulse. Here, we first propose and characterize an effective mechanism to generate a stable discrete time crystal…

Crystals form regular and robust structures that under extreme conditions can melt and recrystallize into different arrangements in a process that is called crystal metamorphism. While crystals exist due to the breaking of a continuous…

We define topological time crystals, a dynamical phase of periodically driven quantum many-body systems capturing the coexistence of intrinsic topological order with the spontaneous breaking of discrete time-translation symmetry. We show…

A time crystal is an exotic phase of matter where time-translational symmetry is broken; this phase differs from the spatial symmetry breaking induced in crystals in space. Lots of experiments report the transition from a thermal…

The relation between the notion of crystalline symmetry and characteristic time intervals when this symmetry could be observed is analyzed. Several time scales are shown to exist for a system of interacting particles. It is only when the…

A time crystal is a time dependent physical system that does not reach a standstill, even in state of minimum energy. Here we show that the stability of a time crystal can be enhanced by its topology. For this we simulate time crystals made…

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…

Discrete time crystal is a class of nonequilibrium quantum systems exhibiting subharmonic responses to external periodic driving. Here we propose a class of discrete time crystals enforced by nonsymmorphic dynamical symmetry. We start with…

We solve explicitly the two-dimensional harmonic oscillator and the harmonic oscillator in a background magnetic field in noncommutative phase-space without making use of any type of representation. A key observation that we make is that…

Spontaneous symmetry breaking is responsible for rich quantum phenomena from crystalline structures to superconductivity. This concept was boldly extended to the breaking of time translation, opening an avenue to finding exotic phases of…

Continuous time crystals (CTCs) - media with broken continuous time translation symmetry - are an eagerly sought state of matter that spontaneously transition from a time-independent state to one of periodic motion in response to a small…