Related papers: Six-dimensional time-space crystalline structures
Time crystals spontaneously break the time translation symmetry, as recently has been frequently reported in quantum systems. Here we describe the observation of classical analogues of both 1+1-dimensional and 2+1-dimensional discrete…
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…
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…
A spacetime crystal is a phase of matter that spontaneously develops periodic order in both space and time. Spacetime crystals have been experimentally observed in microscopic quantum many-body systems and, very recently, in a mesoscopic…
Time crystals are many-body systems whose ground state spontaneously breaks time-translation symmetry and thus exhibits long-range spatiotemporal order and robust periodic motion. Using hydrodynamics, we have recently shown how an…
With the theory of special relativity, time has been linked with space into a four-dimensional space-time from which a basic question must be asked: can space be really transformed into time and vice-versa? The response is affirmative if…
We examine a particular kind of six-dimensional Cremonian universe featuring one dimension of space, three dimensions of time and other two dimensions that can*not* be ranked as either time or space. One of these two, generated by a…
In this work we introduce {\it boundary time-crystals}. Here {\it continuous} time-translation symmetry breaking occurs only in a macroscopic fraction of a many-body quantum system. After introducing their definition and properties, we…
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 introduce a new class of out-of-equilibrium noninteracting topological phases, the topological space-time crystals. These are time-dependent quantum systems which do not have discrete spatial translation symmetries, but instead are…
Time crystals are many-body states that spontaneously break translation symmetry in time the way that ordinary crystals do in space. While experimental observations have confirmed the existence of discrete or continuous time crystals, these…
Periodic space crystals are well established and widely used in physical sciences. Time crystals have been increasingly explored more recently, where time is disconnected from space. Periodic relativistic spacetime crystals on the other…
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…
This Letter investigates the formation of quantum droplets in curved spacetime, highlighting the significant influence of curvature on the formation and properties of these objects. While our computations encompass various dimensions, we…
It is well-known that in two dimensions Turing systems produce spots, stripes and labyrinthine patterns, and in three dimensions lamellar and spherical structures or their combinations are observed. We study transitions between these states…
We explore the properties of physical theories in space-times with two time dimensions. We show that the common arguments used to rule such theories out do not apply if the dynamics associated with the additional time dimension is thermal…
Recently a stochastic underpinning for space time has been considered, what may be called Quantized Fractal Space Time. This leads us to a number of very interesting consequences which are testable, and also provides a rationale for several…
The absolute/relative debate on the nature of space and time is ongoing for thousands of years. Here we attempt to investigate space and time from the information theoretic point of view to understand spatial and temporal correlations under…
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…
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…