Related papers: Classical Time Crystals
We review a theoretical perspective of the dynamics of glass forming liquids and the glass transition. It is a perspective we have developed with our collaborators during this decade. It is based upon the structure of trajectory space. This…
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…
Magnetic emergent crystals are periodic alignment of "particle-like" spin textures that emerge in magnets. Instead of focusing on an individual spin or a macroscopic magnetization field, we analyze the dynamical behaviors of these novel…
Cosmological time crystals are created when a scalar field moves periodically through phase space in a spatially flat Friedmann-Robertson-Walker spacetime due to the presence of a limit cycle. All such cosmological time crystals in the…
Time crystals are proposed states of matter which spontaneously break time translation symmetry. There is no settled definition of such states. We offer a new definition which follows the traditional recipe for Wigner symmetries and order…
A one-dimensional long-range model of classical rotators with an extended degree of complexity, as compared to paradigmatic long-range systems, is introduced and studied. Working at constant density, in the thermodynamic limit one can prove…
In this PhD thesis, I investigate the properties of symmetry-breaking dynamical phase transitions that manifest in the fluctuations of time-integrated observables within classical systems. In particular, I analyze how these phase…
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 simulate the dynamics of paramagnetic colloidal particles that are placed above a magnetic hexagonal pattern and exposed to an external field periodically changing its direction along a control loop. The conformation of three colloidal…
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…
Between space crystals and amorphous materials there exists a third class of aperiodic structures which lack translational symmetry but reveal long-range order. They are dubbed quasi-crystals and their formation, similarly as the formation…
We consider crystal formation of particles with dipole-dipole interactions that are confined to move in a one-dimensional helical geometry with their dipole moments oriented along the symmetry axis of the confining helix. The stable…
Time crystals are genuinely non-equilibrium quantum phases of matter that break time-translational symmetry. While in non-equilibrium closed systems time crystals have been experimentally realized, it remains an open question whether or not…
It was recently discovered that a crystalline many-body state can exist in the phase space of a closed dynamical system. A phase space crystal can be an anomalous Chern insulator that supports chiral topological transport without breaking…
Recent work on the dynamics of triaxial stellar systems is reviewed. The motion of boxlike orbits in realistic triaxial potentials is generically stochastic. The degree to which the stochasticity manifests itself in the dynamics depends on…
We consider classical dynamics of a 1D system of $N$ particles bouncing on an oscillating mirror in the presence of gravitational field. The particles behave like hard balls and they are resonantly driven by the mirror. We identify the…
We demonstrate the emergence of a time crystal of atoms in a high-finesse optical cavity driven by a phase-modulated transverse pump field, resulting in a shaken lattice. This shaken system exhibits macroscopic oscillations in the number of…
We argue that time crystal properties naturally arise from phase-space noncommutative quantum mechanics. In order to exemplify our point we consider the 2-dimensional noncommutative quantum harmonic oscillator and show that it exibihits…
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…
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…