Tensor Elements Research Articles

Estimating the Polytropic Indices of Plasmas with Partial Temperature Tensor Measurements: Application to Solar Wind Protons at ~1 au

We examine the relationships between temperature tensor elements and their connection to the polytropic equation, which describes the relationship between the plasma scalar temperature and density. We investigate the possibility to determine the plasma polytropic index by fitting the fluctuations of temperature either perpendicular or parallel to the magnetic field. Such an application is particularly useful when the full temperature tensor is not available from the observations. We use solar wind proton observations at ~1 au to calculate the correlations between the temperature tensor elements and the scalar temperature. Our analysis also derives the polytropic equation in selected streamlines of solar wind plasma proton observations that exhibit temperature anisotropies related to stream-interaction regions. We compare the polytropic indices derived by fitting fluctuations of the scalar, perpendicular, and parallel temperatures, respectively. We show that the use of the parallel or perpendicular temperature, instead of the scalar temperature, still accurately derives the true, average polytropic index value, but only for a certain level of temperature anisotropy variability within the analyzed streamlines. The use of the perpendicular temperature leads to more accurate calculations, because its correlation with the scalar temperature is less affected by the anisotropy fluctuations.

A Raman probe of phonons and electron\u2013phonon interactions in the Weyl semimetal NbIrTe4

There is tremendous interest in measuring the strong electron–phonon interactions seen in topological Weyl semimetals. The semimetal NbIrTe4 has been proposed to be a Type-II Weyl semimetal with 8 pairs of opposite Chirality Weyl nodes which are very close to the Fermi energy. We show using polarized angular-resolved micro-Raman scattering at two excitation energies that we can extract the phonon mode dependence of the Raman tensor elements from the shape of the scattering efficiency versus angle. This van der Waals semimetal with broken inversion symmetry and 24 atoms per unit cell has 69 possible phonon modes of which we measure 19 modes with frequencies and symmetries consistent with Density Functional Theory calculations. We show that these tensor elements vary substantially in a small energy range which reflects a strong variation of the electron–phonon coupling for these modes.

Few-nucleon matrix elements in pionless effective field theory in a finite volume

Pionless effective field theory in a finite volume (FVEFT$_{\pi\!/}$) is investigated as a framework for the analysis of multi-nucleon spectra and matrix elements calculated in lattice QCD (LQCD). By combining FVEFT$_{\pi\!/}$ with the stochastic variational method, the spectra of nuclei with atomic number $A\in\{2,3\}$ are matched to existing finite-volume LQCD calculations at heavier-than-physical quark masses corresponding to a pion mass $m_\pi=806$ MeV, thereby enabling infinite-volume binding energies to be determined using infinite-volume variational calculations. Based on the variational wavefunctions that are constructed in this approach, the finite-volume matrix elements of various local operators are computed in FVEFT$_{\pi\!/}$ and matched to LQCD calculations of the corresponding QCD operators in the same volume, thereby determining the relevant one and two-body EFT counterterms and enabling an extrapolation of the LQCD matrix elements to infinite volume. As examples, the scalar, tensor, and axial matrix elements are considered, as well as the magnetic moments and the isovector longitudinal momentum fraction.

Full optical rotation tensor at coupled cluster with single and double excitations level in the modified velocity gauge.

This work presents the first simulations of the full optical rotation (OR) tensor at coupled cluster with single and double excitations (CCSD) level in the modified velocity gauge (MVG) formalism. The CCSD-MVG OR tensor is origin independent, and each tensor element can in principle be related directly to experimental measurements on oriented systems. We compare the CCSD results with those from two density functionals, B3LYP and CAM-B3LYP, on a test set of 22 chiral molecules. The results show that the functionals consistently overestimate the CCSD results for the individual tensor components and for the trace (which is related to the isotropic OR), by 10%-20% with CAM-B3LYP and 20%-30% with B3LYP. The data show that the contribution of the electric dipole-magnetic dipole polarizability tensor to the OR tensor is on average twice as large as that of the electric dipole-electric quadrupole polarizability tensor. The difficult case of (1S,4S)-(-)-norbornenone also reveals that the evaluation of the former polarizability tensor is more sensitive than the latter. We attribute the better agreement of CAM-B3LYP with CCSD to the ability of this functional to better reproduce electron delocalization compared with B3LYP, consistent with previous reports on isotropic OR. The CCSD-MVG approach allows the computation of reference data of the full OR tensor, which may be used to test more computationally efficient approximate methods that can be employed to study realistic models of optically active materials.

Low-loss c-axis oriented Zn0.72Mg0.28O nonlinear planar optical waveguides on silicon.

A material platform of highly c-axis oriented Zn1-xMgxO thin films is developed for nonlinear planar waveguides and electro-optic modulators on Si. Mg content in the film greatly influences the quality of film growth. The second harmonic generation measurement and Maker-fringe analysis reveal that the second-order nonlinear susceptibility tensor element χ33 of the annealed Zn0.72Mg0.28O is approximately 4.2 times larger than that of ZnO. The propagation loss of 633 nm wavelength light in the annealed air/Zn0.72Mg0.28O/SiO2 slab waveguide is 0.68 ± 0.09 dB/cm and 0.48 ± 0.03 dB/cm for the TE0 and TM0 modes, respectively. These results suggest the great potential of the c-axis oriented Zn0.72Mg0.28O nonlinear planar waveguides for applications in on-chip optical interconnects.

Supervised learning with projected entangled pair states

Tensor networks, a model that originated from quantum physics, has been gradually generalized as efficient models in machine learning in recent years. However, in order to achieve exact contraction, only treelike tensor networks such as the matrix product states and tree tensor networks have been considered, even for modeling two-dimensional data such as images. In this work, we construct supervised learning models for images using the projected entangled pair states (PEPS), a two-dimensional tensor network having a similar structure prior to natural images. Our approach first performs a feature map, which transforms the image data to a product state on a grid, then contracts the product state to a PEPS with trainable parameters to predict image labels. The tensor elements of PEPS are trained by minimizing differences between training labels and predicted labels. The proposed model is evaluated on image classifications using the Modified National Institute of Standards and Technology database (MNIST) and the Fashion-MNIST datasets. We show that our model is significantly superior to existing models using treelike tensor networks. Moreover, using the same input features, our method performs as well as the multilayer perceptron classifier, but with much fewer parameters and is more stable. Our results shed light on potential applications of two-dimensional tensor network models in machine learning.

The ultrafast Kerr effect in anisotropic and dispersive media.

The ultrafast optical Kerr effect (OKE) is widely used to investigate the structural dynamics and interactions of liquids, solutions, and solids by observing their intrinsic nonlinear temporal responses through nearly collinear four-wave mixing. Non-degenerate mixing schemes allow for background free detection and can provide information on the interplay between a material's internal degrees of freedom. Here, we show a source of temporal dynamics in the OKE signal that is not reflective of the internal degrees of freedom but arises from a group index and momentum mismatch. It is observed in two-color experiments on condensed media with sizable spectral dispersion, a common property near an optical resonance. In particular, birefringence in crystalline solids is able to entirely change the character of the OKE signal via the off-diagonal tensor elements of the nonlinear susceptibility. We develop a detailed description of the phase-mismatched ultrafast OKE and show how to extract quantitative information on the spectrally resolved birefringence and group index from time-resolved experiments in one and two dimensions.

First-principles calculation of the Dzyaloshinskii-Moriya interaction: A Green's function approach

We present a Greens function approach to calculate the Dzyaloshinskii-Moriya interactions (DMI) from first principles electronic structure calculations, that is computationally more efficient and accurate than the most-commonly employed supercell and generalized Bloch-based approaches. The method is applied to the (111) Co/Pt bilayer where the Co- and/or Pt-thickness dependence of the DMI coefficients are calculated. Overall, the calculated DMI are in relatively good agreement with the corresponding values reported experimentally. Furthermore, we investigate the effect of strain in the DMI tensor elements and show that the isotropic N\'{e}el DMI can be significantly modulated by the normal strains, $\epsilon_{xx},\epsilon_{yy}$ and is relatively insensitive to the shear strain, $\epsilon_{xy}$. Moreover, we show that anisotropic strains, $(\epsilon_{xx}-\epsilon_{yy})$ and $\epsilon_{xy}$, result in the emergence of anisotropic N\'{e}el- and Bloch-type DMIs, respectively.

Determination of the Rashba and Dresselhaus Spin–Orbit Interaction Parameters and g‐Factor from the Critical Points of the Spectrum in a 2D Electron Gas in an In‐Plane Magnetic Field

A 2D electron gas with spin–orbit interaction (SOI) is known to form an anisotropic system with van Hove singularities controllable by a parallel magnetic field. The conductivity tensors of this system in the presence of both Rashba and Dresselhaus SOIs is studied. It is found that the diagonal elements of the conductivity tensor have sharp dips when the Fermi level passes through the singularity point of a spectrum. The energy position of these dips at different orientations of the magnetic field allows one to determine both SOI constants and the Landé g‐factor. The dependencies of the surface charge concentration on the Fermi level show a sharp change in the slope near the minimum of the spectrum due to the jumps of the density of states, while the van Hove singularities are not noticeable. In a zero magnetic field, the conductivity tensor has off‐diagonal terms which change the sign when the Fermi level passes the saddle points of the spectrum. The off‐diagonal terms evidence the appearance of the Hall voltage caused by the anisotropy of the Fermi surface and the scattering process.

A Learning-Based Optimization Algorithm: Image Registration Optimizer Network

Remote sensing image registration is valuable for image-based navigation system despite posing many challenges. As the search space of registration is usually non-convex, the optimization algorithm, which aims to search the best transformation parameters, is a challenging step. Conventional optimization algorithms can hardly reconcile the contradiction of simultaneous rapid convergence and the global optimization. In this paper, a novel learning-based optimization algorithm named Image Registration Optimizer Network (IRON) is proposed, which can predict the global optimum after single iteration. The IRON is trained by a 3D tensor (9x9x9), which consists of similar metric values. The elements of the 3D tensor correspond to the 9x9x9 neighbors of the initial parameters in the search space. Then, the tensor's label is a vector that points to the global optimal parameters from the initial parameters. Because of the special architecture, the IRON could predict the global optimum directly for any initialization. The experimental results demonstrate that the proposed algorithm performs better than other classical optimization algorithms as it has higher accuracy, lower root of mean square error (RMSE), and more efficiency. Our IRON codes are available for further study.https://www.github.com/jaxwangkd04/IRON

Exact Theory of Nonrelativistic Quadrupole Bremsstrahlung

Abstract The quantum mechanical treatment of quadrupole radiation due to bremsstrahlung exact to all orders in the Coulomb interaction of two nonrelativistically colliding charged spin-0 and unpolarized spin-1/2 particles is presented. We calculate the elements of the quadrupole tensor, and present analytical solutions for the double-differential photon emission cross section of identical and nonidentical particles. Contact is made to Born-level and quasi-classical results in the respective kinematic limits and effective energy loss rates are obtained. A generally valid formula for soft-photon emission is established and an approximate formula across the entire kinematic regime is constructed. The results apply to bremsstrahlung emission in the scattering of pairs of electrons and are hence relevant in the study of astrophysical phenomena. A definition of a Gaunt factor is proposed which should facilitate broad applicability of the results.

К РАСЧЕТУ МЕХАНИЧЕСКИХ ХАРАКТЕРИСТИК СОТОВЫХ ЗАПОЛНИТЕЛЕЙ, ИЗГОТОВЛЕННЫХ АДДИТИВНЫМИ ТЕХНОЛОГИЯМИ FDM

Honeycomb is described by orthotropic homogeneous media. The mechanical properties of the media are described by the simulation of the stress state honeycomb in commercial software ANSYS. The classical hexagonal honeycomb is analyzed numerically. The other types of the honeycomb are not considered in this paper. The media, which is obtained as a result of homogenization, has orthotropic mechanical properties. The honeycomb is produced from polycarbonate, which is orthotropic material. The suggested approach can be applied to other materials, which are used for 3D printing. The mechanical properties of this honeycomb material are determined experimentally for specimens, which are produced by FDM manufacturing. The matrix of the Hooke law is obtained in the result of six finite element calculations of the cell part of the honeycomb. To determine the different elements of this matrix, the cell part of the honeycomb undergoes different boundary conditions and different stressing. The fourth part of one cell is considered to calculate honeycomb mechanical properties. The software ANSYS is used to calculate the fourth part of the cell. The area near the cell part is filled up to cube using elastic air. The elastic air is isotropic material with a small Young modulus. The cube sides undergo constant displacements to perform numerical analysis. Such different displacements are equal to six. As a result of the numerical simulations, the elements of the stress tensor are determined by the stress averaging on the volume of the finite element. As a result of calculations, the set of nine engineering constants of orthotropic homogeneous media is obtained. Analysis of the convergence of the numerical simulation results is carried out for numerical simulations of the stress state by the concentration of the finite element mesh. As follows from the convergence analysis, 1745481 3D finite elements are enough for the discretization of the cube area.

Micromechanics-based rock-physics model for inorganic shale

The full set of transversely isotropic elastic stiffness constants of inorganic shale (mudrock with total organic carbon less than 1.5%) can be successfully modeled and, therefore, predicted based on the mineral composition, mineral stiffnesses, clay platelet orientation distribution function, and microgeometry of the pore space. A fundamentally novel concept drawing from the Maxwell homogenization scheme allows a zero-porosity mineral matrix of the mudrock to be expressed as a polycrystal of variable composition and clay mineral alignment. Introduction of the brine-saturated pore space allows us to account for realistic 3D pore types and their combinations as well as elastic interactions, opening the way for better integration of rock physics and geomechanics with modern petrographic investigations and better shale velocity/anisotropy prediction as a function of diagenetic porosity reduction. We were able to calibrate the model using a limited subset of high-quality ultrasonic measurements on shale and constrain main pore geometries such as tetrahedra and irregular spheroids, often reported in modern scanning electron microscopy images. The model is then used to constrain the anisotropy tensor elements of illite-dominated clay, impossible to measure directly, and explore the main compositional and microstructural controls on the anisotropic elasticity of inorganic shale, including the most troublesome [Formula: see text] stiffness and its derivative — the anisotropy parameter [Formula: see text], which is of paramount importance in quantitative seismic interpretation.

Measuring linear electric quadrupole susceptibility of non-centrosymmetric crystals with reflectivity difference.

I report experimental methods for measuring real and imaginary parts of the linear electric quadrupole susceptibility tensor of nonlinear optical crystals that lack inversion centers. The third-ranked tensor is related to the corresponding second-order nonlinear susceptibility tensor. For opaque materials such as GaAs, the methods involve normal-incidence reflectivity difference detection schemes. For transparent materials, quadrupole susceptibility tensor elements may be measured with similarly construed transmission difference detection schemes.

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.

Ground-state quantum geometry in superconductor–quantum dot chains

Multiterminal Josephson junctions constitute engineered topological systems in arbitrary synthetic dimensions defined by the superconducting phases. Microwave spectroscopy enables the measurement of the quantum geometric tensor, a fundamental quantity describing both the quantum geometry and the topology of the emergent Andreev bound states in a unified manner. In this work we propose an experimentally feasible multiterminal setup of $N$ quantum dots connected to $N+1$ superconducting leads to study nontrivial topology in terms of the many-body Chern number of the ground state. Moreover, we generalize the microwave spectroscopy scheme to the multiband case and show that the elements of the quantum geometric tensor of the noninteracting ground state can be experimentally accessed from the measurable oscillator strengths at low temperature.

ОЦЕНКА ГЕОДИНАМИЧЕСКОЙ СИТУАЦИИ ВОРОНЕЖСКОГО КРИСТАЛЛИЧЕСКОГО МАССИВА ПО ГЕОДЕЗИЧЕСКИМ ДАННЫМ

Repeated geodetic measurements allow you to evaluate such geodetic elements as coordinates, heights, and directions. And also represent discretely the field of displacement vectors of geodesic points. The obtained vectors allow us to determine the stress-strain state of the earth's surface according to the accepted model. There is a reasonable opinion about the significant presence of rotational (vortex) movements in geodynamic processes. Here, the corresponding algorithms are used for the territory of the Voronezh Crystal massif. Separately, it is possible to calculate the differential characteristics of the vector field, called divergence (div) and rotor (vortex, rot, curl). The article proposes to determine the rotor field from discrete geodetic observations of displacement vectors on the surface of the studied territory. The most important continuation of this research work is the method of mathe-matical modeling of geodynamic systems for predictive purposes. For the study of complex (nonlinear) geodynamic processes, an appropriate mathematical basis should be chosen. Here, attention is drawn to the involvement of the mathematical foundations of field theory. To evaluate the characteristics of vector fields when using repeated geodetic measurements, the method of finite elements can be used. Dividing the territory under study into triangles allows us to determine the deformation characteristics after calculating the elements of the strain tensor. In particular, the value of the angular velocity of the triangle rotation relative to its center of gravity is found. Next, it is easy to calculate the value of the rotor. The example given in the article of real geodetic observations on the Voronezh crystal massif confirms the possibility of predicting the location of an upcoming seismic event – an earth-quake.

Polarized Raman spectroscopy in low-symmetry 2D materials: angle-resolved experiments and complex number tensor elements.

In this perspective review, we discuss the power of polarized Raman spectroscopy to study optically anisotropic 2D materials, belonging to the orthorhombic, monoclinic and triclinic crystal families. We start by showing that the polarization dependence of the peak intensities is described by the Raman tensor that is unique for each phonon mode, and then we discuss how to determine the tensor elements from the angle-resolved polarized measurements by analyzing the intensities in both the parallel- and cross-polarized scattering configurations. We present specific examples of orthorhombic black phosphorus and monoclinic 1T'-MoTe2, where the Raman tensors have null elements and their principal axes coincide with the crystallographic ones, followed by a discussion on the results for triclinic ReS2 and ReSe2, where the axes of the Raman tensor do not coincide with the crystallographic axes and all elements are non-zero. We show that the Raman tensor elements are, in general, given by complex numbers and that phase differences between tensor elements are needed to describe the experimental results. We discuss the dependence of the Raman tensors on the excitation laser energy and thickness of the sample within the framework of the quantum model for the Raman intensities. We show that the wavevector dependence of the electron-phonon interaction is essential for explaining the distinct Raman tensor for each phonon mode. Finally, we close with our concluding remarks and perspectives to be explored using angle-resolved polarized Raman spectroscopy in optically anisotropic 2D materials.

The Bianisotropic Formulation of the Plane Wave Method from Faraday’s and Ampere’s Laws

The plane wave numerical technique is recast from Ampere’s and Faraday’s laws for materials that are characterized with a bianisotropic form of the constitutive relations. The populating expressions are provided for the eigenvalue matrix system that can be directly solved for the angular frequencies and field profiles when bianisotropy is included. To demonstrate the computation process and expected state diagrams and field profiles, numerical computation examples are provided for a bianisotropic Bragg Array with central defect. It is shown that the location of the magnetoelectric tensor elements has a significant effect on the eigenstates of an equivalent isotropic (anisotropic) structure. One form of the magnetoelectric tensor (diagonal elements only) leads to the observation of merging states and the formation of exceptional points. The numerical approach presented can be implemented as an add-on to the familiar plane wave numerical technique.

Origin of the complex Raman tensor elements in single-layer triclinic ReSe2

Low symmetry 2D materials offer an alternative for the fabrication of optoelectronic devices which are sensitive to light polarization. The investigation of electron–phonon interactions in these materials is essential since they affect the electrical conductivity. Raman scattering probes light–matter and electron–phonon interactions, and their anisotropies are described by the Raman tensor. The tensor elements can have complex values, but the origin of this behavior in 2D materials is not yet well established. In this work, we studied a single-layer triclinic ReSe2 by angle-dependent polarized Raman spectroscopy. The obtained values of the Raman tensor elements for each mode can be understood by considering a new coordinate system, which determines the physical origin of the complex nature of the Raman tensor elements. Our results are explained in terms of anisotropy of the electron–phonon coupling relevant to the engineering of new optoelectronic devices based on low-symmetry 2D materials.