Nonzero Tensor Research Articles

Study of τ− → ωπ−ντ decay in resonance chiral theory with tensor sources

In this work, we make a study of the τ− → ωπ−ντ decay in the framework of low-energy effective field theory. The JPG\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {J}^{\\mathcal{P}G} $$\\end{document} decompositions of the quark currents and the ωπ final state show that, besides the Standard Model vector interaction, only the non-standard tensor interaction can have a non-zero contribution to the decay. To discuss its effect, a reliable calculation of the ωπ tensor form factors is necessary. After constructing the Lagrangian of resonance chiral theory with external tensor sources, we calculate both the vector and tensor form factors with the relevant resonance couplings determined by combining the QCD short-distance constraints, the fit to the spectral function of τ− → ωπ−ντ decay, as well as the matching between the Op4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({p}^4\\right) $$\\end{document} odd-intrinsic-parity operators after integrating out the vector resonances and the Op6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({p}^6\\right) $$\\end{document} operators of chiral perturbation theory. The new physics effect is then investigated in the distributions of the spectral function and the forward-backward asymmetry of τ− → ωπ−ντ decay. We find that the spectral function is dominated by the Standard Model, and the non-standard tensor contribution is negligible. However, since the forward-backward asymmetry can be only generated with a non-zero tensor interaction, the observable is quite sensitive to this kind of new physics. A future measurement of the observable at the Belle II experiment as well as at the proposed Tera-Z and STCF facilities is, therefore, strongly called for to check the existence of such a non-standard tensor interaction.

Hydrodynamical dual of the gravitational axial anomaly and the cosmological constant

We construct the hydrodynamic expansion for a rotating and accelerated medium in a curved space-time, and establish the relationship between the currents generated by the cosmological constant and the acceleration. Then we consider the more general case with a nonzero Weyl tensor, and show the duality between the current in flat space-time and the gravitational axial anomaly. This generalizes the previous derivation to the case with a nonzero Ricci tensor. Published by the American Physical Society 2024

Strong anisotropic third-harmonic generation in layered violet phosphorus.

We demonstrate that layered violet phosphorus, an emerging 2D semiconductor, undergoes strong anisotropic third-harmonic generation (THG). Polarization dependence of in-plane THG presents a cruciate-flower-shaped curve. Through theoretical modeling of the in-plane THG response, done by considering crystalline symmetry of violet phosphorus, we successfully quantify four non-zero third-order nonlinear optical susceptibility tensor elements. From control experiments, the magnitude of third-order nonlinear optical susceptibility |χ3| is calculated to be about 4.0 × 10-19 m2 V-2, which is comparable to those of conventional 2D layered semiconductors. These results indicate that the layered violet phosphorus can serve as an ideal building block for nonlinear optical applications.

Static spherically symmetric black holes of Brans–Dicke theory of gravity

This paper investigates the static spherically symmetric vacuum solutions of Brans–Dicke Theory of Gravity. In this paper, we systematically derive the static spherically symmetric solutions by starting with the general static spherically symmetric anzats, discovering the nonzero Christoffel symbols, nonzero Ricci tensor components and the Ricci Scalar. These results allow us to rewrite the four Brans–Dicke gravitational field equations explicitly in terms of the metric components, the scalar field and its scalar potential. This paper systematically explains and shows how to modify these linear second-order ordinary differential equations in order to be able to find the solution of the scalar field, the metric components and the scalar potential analytically. We successfully find the most general solution of the static spherically symmetric vacuum solutions of Brans–Dicke gravity and the well-known Schwarzschild solution is recovered as the simplest solution.

English

Using the mathematical aspects of the Schwarzschild metric, we present different variables transformation which proves that the central singularity hypothesis does not exist. The geometric interpretation of the black hole from the Schwarzschild metric is not mathematically convincing. The different mathematical approaches taken by many authors were viewed, such as the Painleve metric and its complex variant, and the Schwarzschild metric, to deduce a metric with a throat sphere which leads to a mirror space-time. Subsequently, the possibility of a bi-metric tangent to the Schwarzschild metric's throat sphere was deduced.  It was also shown that a false interpretation of the variables of the Schwarzschild metric can lead to false physical deductions and, in particular, to the concept of singularity. We computed the general solution of Einstein's equations in the presence of a non-zero energy tensor, that is, for a homogeneous fluid ball with energy conditions. This study method of resolution involves a reformulation of the Einstein equation and integration of the differential system. The metrics found are asymptotic to the Schwarzschild metric outside the fluid ball. Assumptions were presented for the pressure inside the fluid ball and the corresponding metrics were derived. Then, by solving the continuity equation of the energy-impulse tensor, we deduce an expression for the pressure inside the star that permits the express on of the interior and exterior metrics. Key words: Schwarzs child’s metric, black hole, singularity, gravity, bi-metric, internal metric.

Gravity from the determinant of the energy-momentum: Astrophysical implications

Determinants of the second rank tensors stand useful in forming generally invariant terms as in the case of the volume element of the gravitational actions. Here, we extend the action of the matter fields by an arbitrary function f(D) of the determinants of their energy-momentum, and the metric, D=|det.T|/|det.g|. We derive the gravitational field equations and examine the nonlinear terms induced by the determinant, specifically, the inverse of the energy-momentum tensor. We also show that these extensions require a nonzero stress-energy tensor for the vacuum. We propose a scale-free model, f(D)=λD1/4, and show how it induces the familiar invariant terms formed by the trace of the energy-momentum tensor by expanding the action around the stress-energy of the vacuum. We study the hydrostatic equilibrium equations for a neutron star by providing relevant values of the dimensionless constant λ. We show that the differences from the predictions of general relativity, in the mass-radius relations, which are sensitive to the equations of state, are conspicuous for λ∼−10−2. We also show that the model does not affect the predictions on the primordial nucleosynthesis when it is applied to the early radiation era. This novel and unfamiliar type of the gravity-matter coupling can lead to a rich phenomenology in gravitational physics.

Black hole solutions in scalar-tensor symmetric teleparallel gravity

Symmetric teleparallel gravity is constructed with a nonzero nonmetricity tensor while both torsion and curvature are vanishing. In this framework, we find exact scalarised spherically symmetric static solutions in scalar-tensor theories built with a nonminimal coupling between the nonmetricity scalar and a scalar field. It turns out that the Bocharova-Bronnikov-Melnikov-Bekenstein solution has a symmetric teleparallel analogue (in addition to the recently found metric teleparallel analogue), while some other of these solutions describe scalarised black hole configurations that are not known in the Riemannian or metric teleparallel scalar-tensor case. To aid the analysis we also derive no-hair theorems for the theory. Since the symmetric teleparallel scalar-tensor models also include f(Q) gravity, we shortly discuss this case and further prove a theorem which says that by imposing that the metric functions are the reciprocal of each other (grr = 1/gtt ), the f(Q) gravity theory reduces to the symmetric teleparallel equivalent of general relativity (plus a cosmological constant), and the metric takes the (Anti)de-Sitter-Schwarzschild form.

Photonic Assemblies of Randomly Oriented Nanocrystals for Engineered Nonlinear and Electro-Optic Effects.

Nonlinear crystals that have a noncentrosymmetric crystalline structure, such as lithium niobate (LiNbO3) and barium titanate (BaTiO3) exhibit nonzero second-order tensor susceptibilities (χ(2)) and linear electro-optic coefficients (r ij ). The constraints associated with top-down nanofabrication methods have led to bottom up approaches to harness the strong nonlinearities and electro-optical properties. Here, we present an overview of photonic assemblies made of randomly oriented noncentrosymmetric nanocrystals via bottom-up fabrication methods. In this configuration, nanocrystals can form objects with tunable dimensions, increased complexity, and a great span of symmetry level, ranging from thin layers to spheres. At the same time, according to their shape, photonic assemblies may support optical modes, that is, Mie or guided, which can tailor linear optical properties and enhance nonlinear and electro-optic responses. As a result, assemblies of noncentrosymmetric nanocrystals can form a disruptive platform to realize photonic integrated devices free of etching process and over large surface areas. Last, we foresee potential applications of noncentrosymmetric nanocrystals in various fields of nano-optics and sensing.

On the depth and reflexivity of tensor products

In this paper we study the depth of tensor products of homologically finite complexes over commutative Noetherian local rings. As an application of our main result, we determine new conditions under which the factors of a nonzero reflexive tensor product of finitely generated modules over hypersurface rings can be reflexive.A result of Asgharzadeh shows that nonzero symbolic powers of prime ideals in a local ring cannot have finite projective dimension, unless the ring in question is a domain. We make use of this fact in the appendix and consider the reflexivity of tensor products of prime ideals over hypersurface rings.

Observation of optical gyromagnetic properties in a magneto-plasmonic metamaterial

Metamaterials with artificial optical properties have attracted significant research interest. In particular, artificial magnetic resonances with non-unity permeability tensor at optical frequencies in metamaterials have been reported. However, only non-unity diagonal elements of the permeability tensor have been demonstrated to date. A gyromagnetic permeability tensor with non-zero off-diagonal elements has not been observed at the optical frequencies. Here we report the observation of gyromagnetic properties in the near-infrared wavelength range in a magneto-plasmonic metamaterial. The non-zero off-diagonal permeability tensor element causes the transverse magneto-optical Kerr effect under s-polarized incidence that otherwise vanishes if the permeability tensor is not gyromagnetic. By retrieving the permeability tensor elements from reflection, transmission, and transverse magneto-optical Kerr effect spectra, we show that the effective off-diagonal permeability tensor elements reach 10−3 level at the resonance wavelength (~900 nm) of the split-ring resonators, which is at least two orders of magnitude higher than magneto-optical materials at the same wavelength. The artificial gyromagnetic permeability is attributed to the change in the local electric field direction modulated by the split-ring resonators. Our study demonstrates the possibility of engineering the permeability and permittivity tensors in metamaterials at arbitrary frequencies, thereby promising a variety of applications of next-generation nonreciprocal photonic devices, magneto-plasmonic sensors, and active metamaterials.

Generalization of Kim's estimates in terms of the trace of divergence‐free symmetric tensor

In this paper, we generalized E.C. Kim's estimates by taking into account the trace of the divergence‐free symmetric nonzero tensor. We have also shown that E.C. Kim's estimates still valid in the case of the trace of the divergence‐free symmetric tensor vanished identically. In the equality case, we characterized eta–Killing spinor with Killing pair over Sasakian spin manifolds.

Stretch and stress distributions in the human artery based on two-layer model considering residual stresses.

The objective is to know the stress distributions in the arterial walls under residual stresses based on two-layer model. Human common carotid arteries were analysed to show stress distributions at physiological and supraphysiological intraluminal pressures. The analyses for the loaded states were performed with stretch ratios with reference to a Riemannian stress-free configuration which is a 3D non-Euclidean manifold due to the nonzero Riemann curvature tensor. The experimental data obtained by other literature were used for the common carotid arteries to analyse the stretch and stress distributions in the arterial wall although kinematics is different from the literature. The stretches and stresses were calculated for the unloaded state, i.e. the residual stretches and stresses. And those at the axial stretch ratio 1.1 with reference to the unloaded state were calculated at the intraluminal pressures 16, 50, and 100kPa. The stresses increased from the inner surface to the outer surface at all pressures analysed. These results suggest that in the human arteries the mechanical loads are mainly supported with the adventitia even though the media and intima play an important role to control of physiological functions.

Nonlinear transport in Weyl semimetals induced by Berry curvature dipole

Topological Weyl semimetals (WSMs) have been predicted to be excellent candidates for detecting Berry curvature dipole (BCD) and the related non-linear effects in electronics and optics due to the large Berry curvature concentrated around the Weyl nodes. And yet, linearized models of isolated tilted Weyl cones only realize a diagonal non-zero BCD tensor which sum to zero in the model of WSM with multiple Weyl nodes in the presence of mirror symmetry. On the other hand, recent \textit{ab initio} work has found that realistic WSMs like TaAs-type or MoTe$_2$-type compounds, which have mirror symmetry, indeed show an off-diagonal BCD tensor with an enhanced magnitude for its non-zero components. So far, there is a lack of theoretical work addressing this contradiction for 3D WSMs. In this paper, we systematically study the BCD in 3D WSMs using lattice Weyl Hamiltonians, which go beyond the linearized models. We find that the non-zero BCD and its related important features for these WSMs do not rely on the contribution from the Weyl nodes. Instead, they are dependent on the part of the Fermi surface that lies \textit{between} the Weyl nodes, in the region of the reciprocal space where neighboring Weyl cones overlap. For large enough chemical potential such Fermi surfaces are present in the lattice Weyl Hamiltonians as well as in the realistic WSMs. We also show that, a lattice Weyl Hamitonian with a non-zero chiral chemical potential for the Weyl cones can also support dips or peaks in the off-diagonal components of the BCD tensor near the Weyl nodes themselves, consistent with recent \textit{ab initio} work.

EPR Paradox, Einstein-Rosen bridges and teleportation

In this review, we go over the bases of quantum teleportation, ER bridges in General relativity, and the foundational work on the hypothesis ER=EPR and summarize the resulting wormhole teleportation protocol. We then discuss that − resulting from ER=EPR − certain wormholes have to be either traversable or at the very least let information permeate, resulting in the exploration of the possibility that incoming matter might change the metric outside of wormhole throats. In this study, made in the Schwarzschild metric with the original coordinate system, we managed to find a non-zero energy-momentum tensor produced by a particular solution of the electromagnetic wave equation in curved spacetime, implying a change in the overall metric by Einstein’s Equation.

Gravitational waves on Earth and their warming effects

The gravity or reactive bundle energy is the outlet of the morphogenetic impact, known as “BIG BANG”, creating a bounded ordered/structured universe along with the solar system, including the EARTH-world with its human race. Post-impact, the huge kinetic energy is spread into stellar bodies associated with the light flux under strong mutual connections or gravitational bundle. Einstein’s general relativity theory including the gravitational field can be expressed under a condensed tensor formulation as E  R − Rg =  T where E defines the geometry via a curved space-time structure (R) over the gravity field (1/2Rg), embedded in a matter distribution T The fundamental (ten non-linear partial differential) equations of the gravitational field are a kind of the space-time machine using the curvature of a four-dimensional space-time to engender the gravity field carrying away material structures. Gravity according to the curved space-time theory is not seen as a gravitational force, but it manifests itself in the relativistic form of the space-time curvature needing the constancy of the light speed. But the constant light velocity makes the tidal wave/pulsating energy, a characteristic of solar energy, impossible. The Einstein’s field equation, expressed in terms of tensor formulation along with the constant light speed postulate, needs two special space-time tensors (curvature and torsion) in 4 dimensions, where for the simplicity the torsion/twist tensor is less well approximated (Bianchi identity) leading to a constant/frozen gravity (twist-free gravity).The non-zero torsion tensor plays a significant physical role in the planetary dynamics as a finest gear of a planet, where its spinning rotation is directly connected to the own work and space-time structure (or clock), controlled by light fluctuations (or tidal effect of gravity). The spin correction of Einstein’s gravitational field refers to the curvature-torsion effect coupled with fluctuating light speed. The mutual curvature-torsion bundle self-sustained by the quantum fluctuations of light speed engenders helical gravitational wave fields of a quantum nature where bodies orbit freely in the light speed field (cosmic wind). In contrast to the Einstein’s field equation describing a gravitational frozen field, a quantum tidal gravity model is proposed in the paper.

Quantum Potentiality in Inhomogeneous Cosmology

For the Szekeres system which describes inhomogeneous and anisotropic spacetimes we make use of a point-like Lagrangian, which describes the evolution of the physical variables of the Szekeres model, in order to perform a canonical quantization and to study the quantum potentiality of the Szekeres system in the content of de Broglie–Bohm theory. We revise previous results on the subject and we find that for a specific family of trajectories with initial conditions which satisfy a constraint equation, there exists additional conservation laws for the classical Szekeres system which are used to define differential operators and to solve the Wheeler–DeWitt equation. From the new conservation laws we construct a wave function which provides a nonzero quantum potential term that modifies the Szekeres system. The quantum potential corresponds to new terms in the dynamical system such that new asymptotic solutions with a nonzero energy momentum tensor of an anisotropic fluid exist. Therefore, the silent property of the Szekeres spacetimes is violated by quantum correction terms, which results in the quantum potential adding pressure to the solution.

Polarized Raman scattering in micrometer-sized crystals of triclinic vanadium dioxide

Triclinic vanadium dioxide VO2 (T) films were produced using cathodic arc deposition. Under certain conditions, the film growth on sapphire substrates Al2O3 (001) is associated with the formation of triclinic monocrystals with lateral sizes of several tens of micrometers. Borders between different crystallites can be determined by Raman mapping analysis. X-ray diffraction measurements revealed that the micrometer-sized monocrystals had two different orientations—epitaxial (002) and non-epitaxial (201). The film was studied by polarized micro-Raman spectroscopy, which can be used to determine the orientation of any single crystallite. The Raman tensor elements of the VO2 (T) phase were determined, and it was shown that though crystallographically triclinic VO2 cell could be fitted by monoclinic one with a high degree of precision, such monoclinic approximation was not valid in terms of Raman spectroscopy. Contrary to the two types of phonons expected for the monoclinic crystal [having five nonzero (four independent) or four nonzero (two independent) Raman tensor elements], all phonons in VO2 (T) have nine (six independent) generally nonzero tensor components.

Алгебры Ли дифференцирований линейных алгебр над полем

In this paper, we study a system of linear equations that define the Lie algebra of differentiations DerA of an arbitrary finite-dimensional linear algebra over a field. A system of equations is obtained, which is satisfied by the components of an arbitrary differentiation with respect to a fixed basis of algebra A. This system is a system of linear homogeneous equa­tions. The law of transformation of the matrix of this system is proved. The invariance of the rank of the matrix of this system in the transition to a new basis in algebra is proved. Next, we consider the possibility of ap­plying the obtained results in differential geometry when estimating the dimensions of groups of affine transformations from above. As an exam­ple, the method of I. P. Egorov is given for studying the dimensions of Lie algebras of affine vector fields on smooth manifolds equipped with linear connections having non-zero torsion tensor fields.

Photophysical and theoretical investigations of diarylimidazole derivative with application as a fluorescence sensor for Fe(III)

A diarylimidazole derivative, 2-(2,4-difluorophenyl)-3-(3,5-dimethoxy phenyl)-4,5-diphenyl-1H-imidazole (DFMPI), comprising of electron withdrawing and electron donating substituents, has been designed and synthesized via a four component assembling of benzil, 2,4-difluorobenzaldehyde, 3,5-dimethoxybenzenamine and ammonium acetate in a medium of ethanol. The compound has been characterized by using FT-IR, 1H NMR, 13C-NMR spectral and single crystal XRD analyses. Single crystal X-ray analysis reveals that the compound crystallizes in a monoclinic P21/n space group. Absorption and emission spectral studies display its characteristic application as selective sensing of ferric ion. Theoretical calculations have been performed to calculate the electric dipole moment (μ) and hyperpolarizability (β) for the molecule and were correlated for NLO applications. The non-zero tensor components of the diarylimidazole derivative show that they possess prospective non-linear optical (NLO) behaviour. From the optimized geometry of DFMPI, HOMO-LUMO energies and potential (MEP) energy surfaces have been calculated, which shows the existence of intramolecular charge transfer. In addition, the reactivity of the synthesized molecule using various descriptors like Fukui functions, local softness, electrophilicity, electronegativity and hardness have been studied and discussed.

Tensor decompositions and rank increment conjecture

AbstractSome properties of tensor ranks and the non-closeness issue of sets with given restrictions on the rank of tensors entering those sets are studied. It is proved that the rank of the d-dimensional Laplacian equals d. The following conjecture is formulated: for any tensor of non-maximal rank there exists a nonzero decomposable tensor (tensor of rank 1) such that the rank increases by one after adding this tensor. In the general case, it is proved that this property holds algebraically almost everywhere for complex tensors of fixed size whose rank is strictly less than the generic rank.