Off-diagonal Components Research Articles

Large longitudinal magnetoresistance of multivalley systems

The longitudinal magnetoresistance (MR) is assumed to be hardly realized as the Lorentz force does not work on electrons when the magnetic field is parallel to the current. However, in some cases, longitudinal MR becomes large, which exceeds the transverse MR. To solve this problem, we have investigated the longitudinal MR considering multivalley contributions based on the classical MR theory. We have showed that the large longitudinal MR is caused by off-diagonal components of a mobility tensor. Our theoretical results agree with the experiments of large longitudinal MR in IV–VI semiconductors, especially in PbTe, for a wide range of temperatures, except for linear MR at low temperatures.

Induced energy-momentum tensor of a Dirac field in 2D de Sitter QED

We compute the expectation value of the energy-momentum tensor in the in-vacuum state of the quantized Dirac field coupled to a uniform electric field background on the Poincar$\rm\acute{e}$ path of the two dimensional de~Sitter spacetime ($\mathrm{dS}_{2}$). The adiabatic regularization scheme is applied to remove the ultraviolet divergencies from the expressions. We find, the off-diagonal components of the induced energy-momentum tensor vanishes and the absolute values of the diagonal components are increasing functions of the electric field which decrease as the Dirac field mass increases. We derive the trace anomaly of the induced energy-momentum tensor, which agrees precisely with the trace anomaly derived earlier in the literature. We have discusses the backreaction of the induced energy-momentum tensor on the gravitational field.

The Casimir Densities for a Sphere in the Milne Universe

The influence of a spherical boundary on the vacuum fluctuations of a massive scalar field is investigated in the background of a ( D + 1 ) -dimensional Milne universe, assuming that the field obeys Robin boundary conditions on the sphere. The normalized mode functions are derived for the regions inside and outside the sphere and different vacuum states are discussed. For the conformal vacuum, the Hadamard function is decomposed into boundary-free and sphere-induced contributions and an integral representation is obtained for the latter in both the interior and exterior regions. As important local characteristics of the vacuum state, the vacuum expectation values (VEVs) of the field squared and of the energy-momentum tensor are investigated. It is shown that the vacuum energy-momentum tensor has an off-diagonal component that corresponds to the energy flux along the radial direction. Depending on the coefficient in Robin boundary conditions, the sphere-induced contribution to the vacuum energy and the energy flux can be either positive or negative. At late stages of the expansion and for a massive field the decay of the sphere-induced VEVs, as functions of time, is damping oscillatory. The geometry under consideration is conformally related to that for a static spacetime with negative constant curvature space and the sphere-induced contributions in the corresponding VEVs are compared.

Density matrix formalism for femtosecond x-ray absorption and its excitonic enhancement

A reduced density matrix (RDM) formalism to simulate the dynamics of core-valence electronic excitation in a metal induced by a femtosecond x-ray laser pulse is presented. The theory is based on the time-dependent unrestricted Hartree–Fock (TDUHF) equation for a one-electron RDM combined with an off-diagonal collision term in the Born approximation (BA), where molecular orbitals (MOs) of a model cluster are used as a basis set. These MOs are calculated with a newly developed semiempirical method in the neglect of diatomic differential overlap approximation that takes into account atomic core structures and valence-orbital hybridization. The off-diagonal component of core-valence RDM is decomposed into a rapidly oscillating factor synchronizing with the x-ray field and a slowly varying envelope; time evolution of the latter yields induced electric polarization and complex electric susceptibility. As a numerical test, K-shell absorption near-edge spectra of copper are computed for a single-shot, weak femtosecond x-ray pulse. It is thereby shown that the attractive interaction between an excited electron and a core hole, described by the exchange part of the self-energy matrix, gives rise to excitonic enhancement of x-ray near-edge absorption. The TDUHF approximation significantly overestimates the excitonic enhancement; additional consideration of the screening of electron-hole interaction by valence electrons in BA leads to a prediction of absorption coefficients comparable to the existing experimental values.

Tracer-based estimates of eddy-induced diffusivities

This study provides estimates of the mean eddy-induced diffusivities of passive tracers in a three-layer, double-gyre quasigeostrophic (QG) simulation. A key aspect of this study is the use of a spatial filter to separate the flow and tracer fields into small-scale and large-scale components, and we compare results with those obtained using Reynolds temporal averaging. The eddy tracer flux is related to a rank-2 diffusivity tensor via the flux-gradient relation, which is solved for a pair of tracers with misaligned large-scale gradients. We concentrate on the symmetric part of the resulting diffusivity tensor which represents irreversible mixing processes. The eigenvalues of the symmetric tensor exhibit complicated behaviour, but a particularly dominant and robust feature is the positive/negative eigenvalue pairs, which physically represent filamentation of the tracer concentration. The large off-diagonal diffusivity tensor component is the primary contributor to the eigenvalue polarity, and since this is such a prevalent feature we argue that the (horizontal) eddy-induced diffusivity should always be treated as a full 2×2 tensor. Diffusivity magnitudes are largest in the upper layer and in the eastward jet region, where the eddying flow is strongest. After removing the rotational part of the eddy tracer flux, typical mean diffusivities (eigenvalues) in the upper-layer are on the order of 103 m2 s−1 in the jet region and 102 m2 s−1 elsewhere. We also confirm that the time-mean of the diffusivity calculated from instantaneous fluxes is not the same as the diffusivity associated with the time-mean fluxes.

Phonon-induced renormalization of electron wave functions

The Allen-Heine-Cardona theory allows us to calculate phonon-induced electron self-energies from first principles without resorting to the adiabatic approximation. However, this theory has not been able to account for the change of the electron wave function, which is crucial if interband energy differences are comparable to the phonon-induced electron self-energy as in temperature-driven topological transitions. Furthermore, for materials without inversion symmetry, even the existence of such topological transitions cannot be investigated using the Allen-Heine-Cardona theory. Here, we generalize this theory to the renormalization of both the electron energies and wave functions. Our theory can describe both the diagonal and off-diagonal components of the Debye-Waller self-energy in a simple, unified framework. For demonstration, we calculate the electron-phonon coupling contribution to the temperature-dependent band structure and hidden spin polarization of BiTlSe2 across a topological transition. These quantities can be directly measured. Our theory opens a door for studying temperature-induced topological phase transitions in materials both with and without inversion symmetry.

Analysis of the linear relationship between asymmetry and magnetic moment at the M edge of 3d transition metals

The magneto-optical response of Fe and Ni during ultrafast demagnetization is studied experimentally and theoretically. We have performed pump-probe experiments in the transverse magneto-optical Kerr effect (T-MOKE) geometry using photon energies that cover the M-absorption edges of Fe and Ni between 40 to 72 eV. The asymmetry was detected by measuring the reflection of light for two different orientations of the sample magnetization. Density functional theory (DFT) wasused to calculate the magneto-optical response of different magnetic configurations, representing different types of excitations: long-wavelength magnons, short wavelength magnons, and Stoner excitations. In the case of Fe, we find that the calculated asymmetry is strongly dependent on the specific type of magnetic excitation. Our modelling also reveals that during remagnetization Fe is, to a reasonable approximation, described by magnons, even though small non-linear contributions could indicate some degree of Stoner excitations as well. In contrast, we find that the calculated asymmetry in Ni is rather insensitive to the type of magnetic excitations. However, there is a weak non-linearity in the relation between asymmetry and the off-diagonal component of the dielectric tensor, which does not originate from the modifications of the electronic structure. Our experimental and theoretical results thus emphasize the need of considering a coupling between asymmetry and magnetization that may be more complex that a simple linear relationship. This insight is crucial for the microscopic interpretation of ultrafast magnetization experiments.

The grain boundary mobility tensor

The grain-boundary (GB) mobility relates the GB velocity to the driving force. While the GB velocity is normally associated with motion of the GB normal to the GB plane, there is often a tangential motion of one grain with respect to the other across a GB; i.e., the GB velocity is a vector. GB motion can be driven by a jump in chemical potential across a GB or by shear applied parallel to the GB plane; the driving force has three components. Hence, the GB mobility must be a tensor (the off-diagonal components indicate shear coupling). Performing molecular dynamics (MD) simulations on a symmetric-tilt GB in copper, we demonstrate that all six components of the GB mobility tensor are nonzero (the mobility tensor is symmetric, as required by Onsager). We demonstrate that some of these mobility components increase with temperature, while, surprisingly, others decrease. We develop a disconnection dynamics-based statistical model that suggests that GB mobilities follow an Arrhenius relation with respect to temperature T below a critical temperature [Formula: see text] and decrease as [Formula: see text] above it. [Formula: see text] is related to the operative disconnection mode(s) and its (their) energetics. For any GB, which disconnection modes dominate depends on the nature of the driving force and the mobility component of interest. Finally, we examine the impact of the generalization of the mobility for applications in classical capillarity-driven grain growth. We demonstrate that stress generation during GB migration (shear coupling) necessarily slows grain growth and reduces GB mobility in polycrystals.

Anisotropic RKKY interactions mediated by j=32 quasiparticles in half-Heusler topological semimetals

We theoretically explore the RKKY interaction mediated by spin-3/2 quasiparticles in half-Heusler topological semimetals in quasi-two-dimensional geometries. We find that while the Kohn-Luttinger terms gives rise to generalized Heisenberg coupling of the form ${\cal H}_{\rm RKKY} \propto {\sigma}_{1,i} {\cal I}_{ij} {\sigma}_{2,j}$ with a symmetric matrix ${\cal I}_{ij}$, addition of small antisymmetric linear spin-orbit coupling term leads to Dzyaloshinskii-Moriya (DM) coupling with an antisymmetric matrix ${\cal I}'_{ij}$. We demonstrate that besides the oscillatory dependence on the distance, all coupling strengths strongly depend on the relative orientation of the two impurities with respect to the lattice. This yields a strongly anisotropic behavior for ${\cal I}_{ij}$ such that by only rotating one impurity around another at a constant distance, we can see further oscillations of the RKKY couplings. This unprecedented effect is unique to our system which combines spin-orbit coupling with strongly anisotropic Fermi surfaces. We further find that all of the RKKY terms have two common features: a tetragonal warping in their map of spatial variations, and a complex beating pattern. Intriguingly, all these features survive in all dopings and we see them in both electron- and hole-doped cases. In addition, due to the lower dimensionality combined with the effects of different spin-orbit couplings, we see that only one symmetric off-diagonal term, ${\cal I}_{xy}$ and two DM components ${\cal I}'_{xz}$ and ${\cal I}'_{yz}$ are nonvanishing, while the remaining three off-diagonal components are identically zero. This manifests another drastic difference of RKKY interaction in half-Heusler topological semimetals compared to the electronic systems with spin-1/2 effective description.

Spinor fields in spherical symmetry: Einstein–Dirac and other space-times

We discuss the static spherically symmetric Einstein-spinor field system in the possible presence of various spinor field nonlinearities. We take into account that the spinor field energy-momentum tensor (EMT) has in general some off-diagonal components, whose vanishing due to the Einstein equations substantially affects the form of the spinor field itself and the space-time geometry. In particular, the EMT structure with any spinor field nonlinearities turns out to be the same as that of the EMT of a minimally coupled scalar field with a self-interaction potential. Therefore many results previously obtained for systems with such scalar fields are directly extended to the Einstein-spinor field system. Some special solutions are obtained and discussed, in particular, a solution for the Einstein-Dirac system (which lack asymptotic flatness) and some examples with spinor field nonlinearities.

New Perspectives on Stability Analysis of Three-Phase Grid-Connected Inverter Considering System Couplings

This paper considers the three-phase grid-connected inverter (GCI) as a MIMO system, and presents some new perspectives on the stability of GCI. It is found that with traditional Nyquist criterion (NC)-based method which ignores the off-diagonal components of impedance or admittance matrix, the stability results of impedance and admittance models are different. To make up this disadvantage, a simple stability analysis method based on system feedback ratio matrix (SFRM) is proposed. Instead of ignoring the couplings of impedance or admittance, the SFRM in the proposed method can be equivalent to diagonal matrix by adding a perturbation matrix into the system model, so identical results of stability analysis under impedance and admittance models are attained. Furthermore, to ensure the correctness of stability result, the boundary conditions of the proposed method are also provided. Theoretical analysis, simulation and experimental results show that compared with the state of art methods, the proposed SFRM-based method is of low computational complexity and high accuracy, and is more suitable for engineering application.

System identification method by using inverse solution of equations of motion in time domain and noisy condition

In direct system identification (DSI) method, inverse solution of the equations of motion is applied to obtain physical parameters of a linear system (structural mass, damping, and stiffness matrices). With the small error in measurement, caused by sensor drift or signal noise, these physical parameters are identified with a significant drift. In this paper, a new simple post-processing method is proposed, for error reduction in DSI in the time domain in a manner that structural properties are identified without applying the optimization process. In noisy condition, baseline correction is applied through a nonic curve-fitting approach. The modified signals are partitioned into a number of sub-signals, and their mean is applied for system identification. The number of sub-signals is optimized so that the root mean square (RMS) of off-diagonal components of the mass matrix becomes near zero. Seeking more precision, the residual force in every time step at all degrees of freedom (DOFs) is minimized. The validity of the proposed method is tested on a multistory structure, subjected to a random force at the foundation level. In terms of incomplete measurement and 5% noise, identified parameters including mass, stiffness and damping matrices, have satisfying mean errors of 0.094%, 0.545%, and 4.42% with the coefficient of variations of 0.35%, 1.38% and 6.98%, respectively. The sensitivity of the proposed method to the noise level is also investigated. It is observed that the baseline slop of velocity and displacement signals are sharply increased when the noise level goes beyond 3%.

Testing for the Diffusion Matrix in a Continuous-Time Markov Process Model with Applications to the Term Structure of Interest Rates

Abstract For each component in the diffusion matrix of a d-dimensional diffusion process, we propose a test for the parametric specification of this component. Overall, d(d−1)/2 test statistics are constructed for the off-diagonal components, while d test statistics being for the main diagonal components. Using theories of degenerate U-statistics, each of all these test statistics is shown to follow an asymptotic standard normal distribution under null hypothesis, while diverging to infinity if the component is misspecified over a significant range. We obtain new empirical findings by applying our tests to evaluate a variety of three-factor affine term structure models in modeling the volatility dynamics of monthly U.S. Treasury yields.

On the replica structure of Sachdev-Ye-Kitaev model

We investigate existence of replica off-diagonal solutions in the field-theoretical description of Sachdev-Ye-Kitaev model. To this end we evaluate a set of local and non-local dynamic correlation functions in the long time limit. We argue that the structure of the soft-mode Schwarzian action is qualitatively different in replica-diagonal vs. replica-off-diagonal scenarios, leading to distinct long-time predictions for the correlation functions. We then evaluate the corresponding correlation functions numerically and compare the simulations with analytical predictions of replica-diagonal and replica-off-diagonal calculations. We conclude that all our numerical results are in a quantitative agreement with the theory based on the replica-diagonal saddle point plus Schwarzian and massive Gaussian fluctuations (the latter do contain replica off-diagonal components). This seems to exclude any contributions from replica-off-diagonal saddle points, at least on the time scales shorter than the inverse many-body level spacing.

Effective medium theory with closed-form expressions for bi-anisotropic optical metamaterials.

Bi-anisotropic optical metamaterials are playing an increasingly important role in current wave-functional metamaterials and topological photonics due to their extra degree of freedom in addition to the permittivity and permeability. In this work, we derived the closed-form expressions for effective constitutive parameters of 2-dimensional (2D) bi-anisotropic metamaterials whose chirality tensors can possess both diagonal and off-diagonal components in the long-wavelength limit based on the Mie theory. Our formulas can be regarded as an extension of the Maxwell-Garnet formula to 2D bi-anisotriopic metamaterials and are verified through full wave numerical simulations. These closed-form formulas will benefit the design and analysis of the optical properties of 2D bi-anisotriopic metamaterials.

A Full-Tensor Superconducting Gravity Gradiometer System Composed of Levitation-Type Accelerometers

In this paper, a superconducting gravity gradiometer system that is designed to measure full-tensor gravity gradients based on levitation-type component accelerometers without using mechanical springs is presented. All components of the gradiometer system are made of a superconducting material, niobium. Working principles are the flux quantization and the perfect diamagnetism of the superconductor. Each component of the gravity gradient tensor is obtained from the differential gravity measured by using two accelerometers, each of which is composed of a cubic test mass, a flat sensing coil, and a flat counter coil to balance the repulsive force of the sensing coil and ambient gravity. The measured signals are amplified by using superconducting quantum interference devices. The full-tensor gradiometer system consists of three perpendicularly aligned sets of gradiometers, each of which measures one diagonal and two off-diagonal components. The details of the structure of the system, the dynamics of the gradiometer, the transfer function, the common mode rejection, and the optimum conditions are discussed.

Experimental and Theoretical In Situ Spectral Magneto-Ellipsometry Study of Layered Ferromagnetic Structures

A method for processing of in situ spectral magneto-ellipsometry data has been developed to analyze planar ferromagnetic nanostructures. A multilayer model containing a ferromagnetic layer with two interfaces, a nonferromagnetic buffer layer, and a nonferromagnetic substrate has been tested within a new approach to the interpretation of magnetic-field-modulated spectral ellipsometric measurements involving the magnetooptical Kerr effect in the transverse configuration. In particular, the effect of the thickness of the ferromagnetic layer on the results of magneto-ellipsometric measurements has been analyzed. The measurements have been performed with polycrystalline Fe films with different thicknesses on a nonferromagnetic SiO2/Si(100) surface. The diagonal and off-diagonal components of the complex dielectric tensor in the spectral range of 1.38–3.45 eV have been determined by processing spectral magneto-ellipsometric data. The results have been compared to the available data obtained by other authors and to the calculation of the dielectric tensor of Fe within the density functional theory.

Anomalous optical forces in PT-symmetric waveguides.

Evanescently coupled passive waveguides experience optical forces of attractive or repulsive nature, depending on the mode of operation. Here we explore the optical forces between parity-time-symmetric coupled waveguides, with balanced levels of gain and loss. We find that, besides the diagonal stress components that result in a pressure normal to the surface of the waveguides, this system exhibits an off-diagonal stress component that creates a shear along the propagation direction. In addition, for a critical value of balanced gain and loss, the normal pressure can be reduced to zero. These anomalous optical forces are related to the unusual power flow in coupled active-passive channels, and open interesting opportunities for microfluidics and micro-optomechanical systems.

Dielectric Tensor of a Metal Nanowire with an Elliptical Cross Section

The influence of the cross-section geometry of metal nanowires on the dielectric tensor has been examined. Diagonal and off-diagonal components of the dielectric tensor were calculated taking the size dependence of the Fermi energy into account within the free-electron model using the boundary-shape perturbation method. The effect of variation of the eccentricity of the cross section, the effective radius, and the composition of nanowires on frequency dependences of the real and imaginary parts of components of the dielectric tensor was studied. Calculations were performed for Ag, Cu, and Al.

Co-rich Amorphous Microwires with Improved Giant Magnetoimpedance Characteristics Due to Glass Coating Etching

Glass-coated Co-rich amorphous microwires are very promising for the development of tiny magnetic sensors that can be used in portable electronic devises. In this study, a substantial decrease in the residual quenching stress in Co-rich microwires is achieved by reducing the thickness of the glass coating by means of precise etching of the wire in a specially designed gel. This effect is confirmed experimentally by means of the small-angle magnetization rotation method as well as by direct measurement of the off-diagonal component of the giant magnetoimpedance (GMI) tensor of wires with different thicknesses of glass coating as a function of the applied magnetic field. A reduction in the thickness of the glass coating to the range of 0.5–2.0 µm resulted in a nearly twofold increase in the steepness of the off-diagonal GMI component of the studied Co-rich microwires. Therefore, this method can be used to improve the sensitivity of miniature magnetic sensors to weak external magnetic fields.