Localized solutions of the Dirac equation in free **space** and
electromagnetic space-**time** crystals

**space**-

**time**crystals and free space, defined by a given set of orthonormal complex scalar functions on a two-dimensional manifold, are obtained. Expand abstract.

**space**and electromagnetic field lattices with periodic dependence on

**space**-

**time**coordinates (electromagnetic

**space**-

**time**crystals) are treated using the expansions in basis wave functions. The techniques for calculating these functions with any prescribed accuracy are presented. It is shown that in the crystals created by two counterpropagating plane electromagnetic waves with the same or the opposite circular polarizations, the Dirac equation describing the basis functions reduces to matrix ordinary differential equations. These functions and the corresponding mean values of velocity, momentum, energy, and spin operators are found for the both types of crystals. Localized solutions describing the families of orthonormal beams in electromagnetic

**space**-

**time**crystals and free space, defined by a given set of orthonormal complex scalar functions on a two-dimensional manifold, are obtained. By way of illustration the orthonormal beams in free

**space**and various localized states with complex vortex structure of probability currents, defined by the spherical harmonics, are presented. The obtained solutions have high probability density only in very small core regions. The evolution of wave packets with one-dimensional localization in the both types of crystals created by two circularly polarized waves is described.

10/10 relevant

arXiv

ESA Voyage 2050 white paper -- GrailQuest: hunting for Atoms of Space
and **Time** hidden in the wrinkle of **Space**-Time

**space**-time granularity with a new concept of modular observatory of huge overall collecting area consisting in a fleet of small satellites in low orbits, with sub-microsecond

**time**... Expand abstract.

**Space**-Time) is an ambitious astrophysical mission concept that uses a fleet of small satellites, whose scientific objectives are discussed below. Within Quantum Gravity theories, different models for

**space**-

**time**quantisation predict an energy dependent speed for photons. Although the predicted discrepancies are minuscule, Gamma-Ray Bursts, occurring at cosmological distances, could be used to detect this signature of

**space**-

**time**granularity with a new concept of modular observatory of huge overall collecting area consisting in a fleet of small satellites in low orbits, with sub-microsecond

**time**resolution and wide energy band (keV-MeV). The enormous number of collected photons will allow to effectively search these energy dependent delays. Moreover, GrailQuest will allow to perform temporal triangulation of high signal-to-noise impulsive events with arc-second positional accuracies: an extraordinary sensitive X-ray/Gamma all-sky monitor crucial for hunting the elusive electromagnetic counterparts of Gravitational Waves. A pathfinder of GrailQuest is already under development through the HERMES (High Energy Rapid Modular Ensemble of Satellites) project: a fleet of six 3U cube-sats to be launched by the end of 2021.

10/10 relevant

arXiv

Waves of **space**-**time** from a collapsing compact object

**time**dependent collapse of a spherically symmetric compact object with initial mass $M_1+M_2$ and final mass $M_2$ and the waves of

**space**-

**time**emitted during the collapse via back-reaction effects. We obtain exact analytical solutions for the waves of

**space**-

**time**in an example in which $M_1=M_2=(M_1+M_2)/2$. The wavelengths of the

**space**-

**time**emitted waves during the collapse have the cut (we use natural units $c=\hbar=1$): $\lambda < (2/b)$, $(1/b)$-being the

**time**scale that describes the decay of the compact object.

10/10 relevant

arXiv

Tunable **space**-**time** crystal in room-temperature magnetodielectrics

**space**-

**time**crystals provide a new dimension for exploring dynamical phases of matter and can serve as a model nonlinear Floquet system, that brings in touch the rich fields of classical nonlinear waves, magnonics and periodically driven systems. Expand abstract.

**space**-

**time**crystal with tunable periodicity in

**time**and

**space**in the magnon Bose-Einstein Condensate (BEC), formed in a room-temperature Yttrium Iron Garnet (YIG) film by radio-frequency

**space**-homogeneous magnetic field. The magnon BEC is prepared to have a well defined frequency and non-zero wavevector. We demonstrate how the crystalline "density" as well as the

**time**and

**space**textures of the resulting crystal may be tuned by varying the experimental parameters: external static magnetic field, temperature, thickness of the YIG film and power of the radio-frequency field. The proposed

**space**-

**time**crystals provide a new dimension for exploring dynamical phases of matter and can serve as a model nonlinear Floquet system, that brings in touch the rich fields of classical nonlinear waves, magnonics and periodically driven systems.

10/10 relevant

arXiv

A **space**-**time** hybridizable discontinuous Galerkin method for linear
free-surface waves

**space**-

**time**HDG formulation makes use of weighted inner products. Expand abstract.

**space**-

**time**hybridizable discontinuous Galerkin (HDG) method for the linear free-surface problem on prismatic

**space**-

**time**meshes. We consider a mixed formulation which immediately allows us to compute the velocity of the fluid. In order to show well-posedness, our

**space**-

**time**HDG formulation makes use of weighted inner products. We perform an a priori error analysis in which the dependence on the

**time**step and spatial mesh size is explicit. We provide two numerical examples: one that verifies our analysis and a wave maker simulation.

10/10 relevant

arXiv

Transfer matrix method for the analysis of **space**-**time** modulated media
and systems

**space**-

**time**varying systems, which allows any number of time-modulated elements with arbitrary modulation profile, facilities the investigation of high order modes, and provides an interface between space-time modulated systems and other systems. Expand abstract.

**Space**-

**time**modulation adds another powerful degree of freedom to the manipulation of classical wave systems. It opens the door for complex control of wave behavior beyond the reach of stationary systems, such as nonreciprocal wave transport and realization of gain media. Here we generalize the transfer matrix method and use it to create a general framework to solve wave propagation problems in

**time**-varying acoustic, electromagnetic, and electric circuit systems. The proposed method provides a versatile approach for the study of general

**space**-

**time**varying systems, which allows any number of

**time**-modulated elements with arbitrary modulation profile, facilities the investigation of high order modes, and provides an interface between

**space**-

**time**modulated systems and other systems.

10/10 relevant

arXiv

Stochastic Local Interaction Model with Sparse Precision Matrix for
**Space**-**Time** Interpolation

**space**-

**time**lattices, the stochastic local interaction model is equivalent to a Gaussian Markov Random Field. Expand abstract.

**space**-

**time**data is beset by the requirement for storing and numerically inverting large and dense covariance matrices. Computationally efficient representations of

**space**-

**time**correlations can be constructed using local models of conditional dependence which can reduce the computational load. We formulate a stochastic local interaction model for regular and scattered

**space**-

**time**data that incorporates interactions within controlled

**space**-

**time**neighborhoods. The strength of the interaction and the size of the neighborhood are defined by means of kernel functions and adaptive local bandwidths. Compactly supported kernels lead to finite-size local neighborhoods and consequently to sparse precision matrices that admit explicit expression. Hence, the stochastic local interaction model's requirements for storage are modest and the costly covariance matrix inversion is not needed. We also derive a semi-explicit prediction equation and express the conditional variance of the prediction in terms of the diagonal of the precision matrix. For data on regular

**space**-

**time**lattices, the stochastic local interaction model is equivalent to a Gaussian Markov Random Field.

10/10 relevant

arXiv

Quantum thermodynamics in a static de Sitter **space**-**time** and initial
state of the universe

**space**-

**time**inside the causal horizon of a static de Sitter metric, in order to make a quantum thermodynamical description of

**space**-time. We found a finite number of discrete energy levels for a scalar field from a polynomial condition of the confluent hypergeometric functions expanded around $r=0$. As in the previous work, we obtain that the uncertainty principle is valid for each energy level on sub-horizon scales of

**space**-time. We found that temperature and entropy are dependent on the number of sub-states on each energy's level and the Bekenstein-Hawking temperature of each energy level is recovered when the number of sub-states of a given level tends to infinity. We propose that the primordial state of the universe could be described by a de Sitter metric with Planck energy $E_p=m_p\,c^2$, and a B-H temperature: $T_{BH}=\left(\frac{\hbar\,c}{2\pi\,l_p\,K_B}\right)$.

10/10 relevant

arXiv

Cosmic acceleration via **space**-time-matter theory

**space**-time, and also, obtain the observer area-distance as a measurable quantity to compare this theory with two other models. Expand abstract.

**space**-time-matter theory (STM) in a five-dimensional vacuum

**space**-

**time**with a generalized FLRW metric to investigate the late-

**time**acceleration of the universe. For this purpose, we derive the four-dimensional induced field equations and obtain the evolution of the state parameter with respect to the redshift. Then, we show that with consideration of the extra dimension scale factor to be a linear function of redshift, this leads to a model which gives an accelerating phase in the universe. Moreover, we derive the geodesic deviation equation in the STM theory to study the relative acceleration of the parallel geodesics of this

**space**-time, and also, obtain the observer area-distance as a measurable quantity to compare this theory with two other models.

10/10 relevant

arXiv

Space-**time** random walk loop measures

**space**-

**time**random walks and their loop measures and Poisson point loop processes. Interesting phenomena appear when the additional coordinate of the

**space**-

**time**process is on a discrete torus with non-symmetric jump rates. The projection of these

**space**-

**time**random walk loop measures onto the

**space**dimensions is loop measures on the spatial graph, and in the scaling limit of the discrete torus, these loop measures converge to the so-called [Bosonic loop measures]. This provides a natural probabilistic definition of [Bosonic loop measures]. These novel loop measures have similarities with the standard Markovian loop measures only that they give weights to loops of certain lengths, namely any length which is multiple of a given length $ \beta> 0 $ which serves as an additional parameter. We complement our study with generalised versions of Dynkin's isomorphism theorem (including a version for the whole complex field) as well as Symanzik's moment formulae for complex Gaussian measures. Due to the lacking symmetry of our

**space**-

**time**random walks, the distributions of the occupation

**time**fields are given in terms of complex Gaussian measures over complex-valued random fields ([B92,BIS09]. Our

**space**-

**time**setting allows obtaining quantum correlation functions as torus limits of

**space**-

**time**correlation functions.

10/10 relevant

arXiv