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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…

In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…

We describe a possible general and simple paradigm in a classical thermal setting for discrete time crystals (DTCs), systems with stable dynamics which is subharmonic to the driving frequency thus breaking discrete time-translational…

Investigation of states with a periodic time dependence of physical quantities attracts a considerable interest now. Although it has been proposed initially that such states (coined Quantum Time Crystals) might be macroscopic and…

Driven classical self-sustained oscillators have been studied extensively in the context of synchronization. Using the master equation, this work considers the classically driven generalized quantum Rayleigh-van der Pol oscillator, which is…

Time crystals are many-body systems that spontaneously break time-translation symmetry, and thus exhibit long-range spatiotemporal order and robust periodic motion. Recent results have demonstrated how to build time-crystal phases in driven…

The spontaneous breaking of time-translation symmetry in periodically driven quantum systems leads to a new phase of matter: discrete time crystals (DTC). This phase exhibits collective subharmonic oscillations that depend upon an interplay…

We consider a dissipative quantum Ising model periodically driven by a train of $\pi$-pulses and investigate dissipative discrete time crystals (DTCs) in solids. In this model, the interaction between the spins spontaneously breaks the…

We investigate the time-dependent, coherent, and dissipative dynamics of bound particles in single multilevel quantum dots in the presence of sequential tunnelling transport. We focus on the nonequilibrium regime where several channels are…

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…

Spontaneous symmetry breaking is one of the central organizing principles in physics. Time crystals have emerged as an exotic phase of matter, spontaneously breaking the time translational symmetry, and are mainly categorized as discrete or…

In a recent paper a slightly modified version of the Bateman system, originally proposed to describe a damped harmonic oscillator, was proposed. This system is really different from the Bateman's one, in the sense that this latter cannot be…

We present a quantum circuit with measurements and post-selection that exhibits a panoply of space- and/or time-ordered phases, from ferromagnetic order to spin-density waves to time crystals. Unlike the time crystals that have been found…

Time crystals are quantum many-body systems which are able to self-organize their motion in a periodic way in time. Discrete time crystals have been experimentally demonstrated in spin systems. However, the first idea of spontaneous…

Laser resonances play a crucial role in optical and quantum systems because the photons impact the stability and coherence of laser sources. While laser oscillations are typically stable and periodic, the presence of nonlinear effects can…

The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…

Spontaneous symmetry breaking is a fundamental concept in many areas of physics, ranging from cosmology and particle physics to condensed matter. A prime example is the breaking of spatial translation symmetry, which underlies the formation…

Unstable particles decay sooner or later, so they are not described by asymptotic one-particle states and they should not be included as independent states in unitarity relations such as the optical theorem. The same applies to any…

Discrete time-crystals are periodically driven quantum many-body systems with broken discrete-time translational symmetry, a non-equilibrium steady state representing self-organization of motion of quantum particles. Observations of…

We present fresh evidence for the presence of discrete quantum time crystals in two spatial dimensions. Discrete time crystals are intricate quantum systems that break discrete time translation symmetry in driven quantum many-body systems…