Related papers: Space-time crystal and space-time group
While numerous examples of fractal spaces may be found in various fields of science, the flow of time is typically assumed to be one-dimensional and smooth. Here we present a metamaterial-based physical system, which can be described by…
Spatial symmetries appearing in both real and momentum space are of fundamental significance to crystals. However, in the conventional framework, every space group in real space, either symmorphic or nonsymmorphic, corresponds to a…
A discrete time crystal is a phase unique to nonequilibrium systems, where discrete time translation symmetry is spontaneously broken. Most of conventional time crystals proposed so far rely on spontaneous breaking of on-site symmetries and…
We consider maximal globally hyperbolic flat (2+1) spacetimes with compact space S of genus g>1. For any spacetime M of this type, the length of time that the events have been in existence is M defines a global time, called the cosmological…
The relations between the hidden symmetries of the six-dimensional pseudo-Euclidean space with signature (+++ -- ) and the conserved quantum characteristics of elementary particles is established. The hidden symmetries are brought out by…
The wide-range application of photonic crystals and metamaterials benefits from the enormous design space of three-dimensional sub-wavelength structures. In this work, we study the space group constraints on photonic dispersions for all 230…
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…
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 spontaneous breaking of symmetries is a widespread phenomenon in physics. When time translational symmetry is spontaneously broken, an exotic nonequilibrium state of matter in which the same structures repeat themselves in time can…
We construct a natural and nonperturbative momentum space for quantum field theory on $(d+1)$-dimensional de Sitter (dS) spacetime in the Poincar\'e slicing, adapted to early Universe cosmology. In particular, we identify the dS frequency…
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…
Pair interaction potentials between atoms in a crystal are in general non-monotonic in distance, with a local minimum whose position gives the lattice constant of the crystal. A temporal analogue of this idea of crystal formation is still…
The behavior of identical particles interacting through the harmonic-repulsive pair potential has been studied in 3D using molecular dynamics simulations at a number of different densities. We found that at many densities, as the…
In this work we discuss the existence of time-translation symmetry breaking in a kicked infinite-range-interacting clean spin system described by the Lipkin-Meshkov-Glick model. This Floquet time crystal is robust under perturbations of the…
Discrete time crystals are periodically driven systems that display spontaneous symmetry breaking of time translation invariance in the form of indefinite subharmonic oscillations. We introduce a thermodynamically consistent model for a…
The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone--von Neumann theorem, the solutions of the dynamical equations, the Schr\"odinger equation (1) for states or the Heisenberg…
Quantum deformations of (anti-)de Sitter algebras in (2+1) dimensions are revisited, and several features of these quantum structures are reviewed. In particular, the classification problem of (2+1) (A)dS Lie bialgebras is presented and the…
It is well known that gravity in 2+1 dimensions can be recast as Chern-Simons theory, with the gauge group given by the local isometry group, depending on the metric signature and the cosmological constant. Point particles are added into…
Crystallographic groups are conventionally studied in real space to characterize crystal symmetries. Recent work has recognized that when these symmetries are realized projectively, momentum space inherently accommodates nonsymmorphic…
This perspective article elucidates both the importance and the implications of relativistic spacetime crystals as well as the renormalized blended coordinates transformation. It alludes to possible applications in materials science,…