Nonzero Tensor Research Articles

Terahertz generation by optical rectification in uniaxial birefringent crystals

The angular dependence of terahertz (THz) emission from birefringent crystals can differ significantly from that of cubic crystals. Here we consider optical rectification in uniaxial birefringent materials, such as chalcopyrite crystals. The analysis is verified in (110)-cut ZnGeP_2 and compared to (zincblende) GaP. Although the crystals share the same nonzero second-order tensor elements, the birefringence in chalcopyrite crystals cause the pump pulse polarization to evolve as it propagates through the crystal, resulting in a drastically different angular dependence in chalcopyrite crystals. The analysis is extended to {012}- and {114}-cut chalcopyrite crystals and predicts more efficient conversion for the {114} crystal cut over the {012}- and {110}-cuts.

3D, 9C seismic modeling and inversion of Weyburn Field data

Inversion of 3D, 9C wide azimuth vertical seismic profiling (VSP) data from the Weyburn Field for 21 independent elastic tensor elements was performed based on the Christoffel equation, using slowness and polarization vectors measured from field data. To check the ability of the resulting elastic tensor to account for the observed data, simulation of the 3C particle velocity seismograms was done using eighth-order, staggered-grid, finite-differencing with the elastic tensor as input. The inversion and forward modeling results were consistent with the anisotropic symmetry of the Weyburn Field being orthorhombic. It was dominated by a very strong, tranverse isotropy with a vertical symmetry axis, superimposed with minor near-vertical fractures with azimuth [Formula: see text] from the inline direction. The predicted synthetic seismograms were very similar to the field VSP data. The examples defined and provided a validation of a complete workflow to recover an elastic tensor from 9C data. The number and values of the nonzero tensor elements identified the anisotropic symmetry present in the neighborhood of a 3C borehole geophone. Computation of parameter correlation matrices allowed evaluation of solution quality through relative parameter independence.

Magnetization dynamics, gyromagnetic relation, and inertial effects

The gyromagnetic relation—that is, the proportionality between the angular momentum L→ and the magnetization M→—is evidence of the intimate connections between the magnetic properties and the inertial properties of ferromagnetic bodies. However, inertia is absent from the dynamics of a magnetic dipole: The Landau–Lifshitz equation, the Gilbert equation, and the Bloch equation contain only the first derivative of the magnetization with respect to time. In order to investigate this paradoxical situation, the Lagrangian approach, proposed originally by Gilbert, is revisited keeping an arbitrary nonzero inertia tensor. The corresponding physical picture is a generalization to three dimensions of Ampère’s hypothesis of molecular currents. A dynamic equation generalized to the inertial regime is obtained. It is shown how both the usual gyromagnetic relation and the well-known Landau–Lifshitz–Gilbert equation are recovered in the kinetic limit, that is, for time scales longer than the relaxation time of the angular momentum.

Photophysical studies of fused phenanthrimidazole derivatives as versatile π-conjugated systems for potential NLO applications

Two new heterocyclic imidazole derivatives consists of π-conjugated system attached to a phenanthrimidazole moiety have been synthesized in moderate yield by the condensation of 1,10-phenanthroline-5,6-dione with substituted aromatic aldehydes and 4-methoxyaniline in the presence of ammonium acetate in ethanol medium. The photophysical properties of these imidazole derivatives were studied in several solvents. These derivatives were evaluated concerning their solvatochromic properties and molecular optical nonlinearities. Their electric dipole moment (μ) and hyperpolarizability (β) have been calculated theoretically and the results indicate that the extension of the π-framework of the ligands has an effect on the NLO properties of these imidazole derivatives. The non-zero tensor components of these imidazole derivatives reveal that they possess potent non-linear optical (NLO) behavior. The energies of the HOMO and LUMO levels and the molecular electrostatic potential (MEP) energy surface studies have exploited the existence of intramolecular charge transfer (ICT) within the molecule.

Torsion of space-time in f (R) gravity

In this paper, we first review some aspects of the f (R) gravity, and then the concept of the torsion of space-time due to metric-affine formalism in f (R) gravity is studied. Within this formalism, in which the matter action is supposed to be dependent on the connection, we achieve interesting cases including nonzero torsion tensor. Then with the physical interpretation of the torsion of space-time in high energy limit, the modified expression of Mach’s principle in a very strong gravitational region is obtained.

Three classes of Weitzenböck manifolds

A Weitzenbock manifold is a triplet defined by a differentiable manifold with a metric g of certain signature and a linear connection with zero curvature tensor and nonzero torsion tensor which is a metric connection with respect to g. The theory of such manifolds is called the “new theory of gravity”. We study properties of three classes of Weitzenbock manifolds and prove some vanishing thorems.

Photophysical studies of some heterocyclic chromophores as potential NLO materials

Some new heterocyclic chromophores have been synthesized by greenway method. These chromophores have been evaluated by analysing their solvatochromic properties and molecular optical nonlinearities. Their hyperpolarizability (β) has been calculated theoretically. The non-zero tensor components of the imidazole derivatives reveal that they possess potent non-linear optical (NLO) behaviour. Measurements of absorption solvatochromism have been interpreted with Marcus and Reichardt–Dimroth solvent functions to estimate the transition dipoles. Good correlation exists between absorption as well as fluorescence wavenumbers obtained by the multi-component linear regression employing the Taft and Catalan solvent parameters with the experimental values.

Investigation of all Ricci semi-symmetric and all conformally semi-symmetric spacetimes

We find all Ricci semi-symmetric as well as all conformally semi-symmetric spacetimes. Neither of these properties implies the other. However, we find that for spacetimes (3+1 dim) with nonzero Weyl tensor and nonzero tracefree part of the Ricci tensor conformal semi-symmetry and Ricci semi-symmetry is equivalent.

Physicochemical studies of bioactive heterocycles of some novel imidazole derivatives as sensitive NLO materials

Some novel imidazole derivatives were developed as highly sensitive chemisensors for transition metal ions. A prominent fluorescence enhancement was found in the presence of transition metal ions such as Hg 2+, Pb 2+, Cu 2+, Zn 2+, Co 2+ and Fe 2+ and this was suggested to result from the suppression of radiationless transitions from the n–π* state in the chemisensors. By DFT calculation HOMO–LUMO energies were calculated, the electric dipole moment ( μ) and the hyperpolarizability ( β) of the investigated molecules have been studied experimentally and also theoretically. These synthesized molecules were found to have microscopic non-linear optical (NLO) behaviour with non-zero tensor components.

Empirical study of nonlinearity tensor dominating THz generation in barium borate crystal through optical rectification

The optical rectification is an important optical method to generate the THz wave. However, there is a lack of knowledge about the properties of the nonlinearity tensor which governs the optical rectification process. In this work, we demonstrate that some key information of the nonlinearity tensor of barium borate (BBO) crystal could be revealed by 2-dimensional time-domain spectroscopic measurements. The experimental results indicate that d 22 of the nonlinearity tensor coefficients of BBO crystal plays negligible role during the THz generation by optical rectification. At the same time, a proportional relationship among three other nonzero nonlinearity tensor coefficients, i.e., d 33, d 31, and d 15, could be obtained empirically. It is worth noting that our method is also applicable to similar nonlinearity study in THz region of other types of crystals.

Phenomenological coefficients in the equations of thermodynamics of irreversible processes for anisotropic media

The phenomenological coefficients of the phenomenological equations (laws) obtained for anisotropic media, in particular, interphase separation regions, were studied. Generally, these coefficients are tensors of rank from 0 to 4. An attempt was made to find a general procedure for the determination of nonzero tensor components when cross phenomenological coefficient are present in phenomenological equations including generalized thermodynamic forces with various tensor ranks.

Barbero-Immirzi parameter as a scalar field:K-inflation from loop quantum gravity?

We consider a loop-quantum gravity inspired modification of general relativity, where the Holst action is generalized by making the Barbero-Immirzi (BI) parameter a scalar field, whose value could be dynamically determined. The modified theory leads to a nonzero torsion tensor that corrects the field equations through quadratic first derivatives of the BI field. Such a correction is equivalent to general relativity in the presence of a scalar field with nontrivial kinetic energy. This stress energy of this field is automatically covariantly conserved by its own dynamical equations of motion, thus satisfying the strong equivalence principle. Every general relativistic solution remains a solution to the modified theory for any constant value of the BI field. For arbitrary time-varying BI fields, a study of cosmological solutions reduces the scalar-field stress energy to that of a pressureless perfect fluid in a comoving reference frame, forcing the scale-factor dynamics to be equivalent to those of a stiff equation of state. Upon ultraviolet completion, this model could provide a natural mechanism for k inflation, where the role of the inflaton is played by the BI field and inflation is driven by its nontrivial kinetic energy instead of a potential.

Impact of prior assumptions on Bayesian estimates of inflation parameters and the expected gravitational waves signal from inflation

There has been much recent discussion, and some confusion, regarding the use of existing observational data to estimate the likelihood that next-generation cosmic microwave background (CMB) polarization experiments might detect a nonzero tensor signal, possibly associated with inflation. We examine this issue in detail here in two different ways: (1) first we explore the effect of choice of different parameter priors on the estimation of the tensor-to-scalar ratio r and other parameters describing inflation, and (2) we examine the Bayesian complexity in order to determine how effectively existing data can constrain inflationary parameters. We demonstrate that existing data are not strong enough to render full inflationary parameter estimates in a parametrization- and prior-independent way and that the predicted tensor signal is particularly sensitive to different priors. For parametrizations where the Bayesian complexity is comparable to the number of free parameters we find that a flat prior on the scale of inflation (which is to be distinguished from a flat prior on the tensor-to-scalar ratio) leads us to infer a larger, and in fact slightly nonzero tensor contribution at 68% confidence level. However, no detection is claimed. Our results demonstrate that all that is statistically relevant at the current time ismore » the (slightly enhanced) upper bound on r, and we stress that the data remain consistent with r=0.« less

Toward the AdS/CFT gravity dual for high energy collisions. II. The stress tensor on the boundary

In this second paper of the series, we calculate the stress tensor of excited matter, created by debris of high energy collisions at the boundary. The falling open strings, connected to receding charges, produce a nonzero stress tensor which we found analytically from time-dependent linearized Einstein equations in the bulk. It corresponds to exploding nonequilibrium matter: we discuss its behavior in some detail, including its internal energy density in a comoving frame and the 'freeze-out surfaces'. We then discuss what happens for the ensemble of strings.

Lift of noninvariant solutions of heavenly equations from three to four dimensions and new ultra-hyperbolic metrics

We demonstrate that partner symmetries provide a lift of noninvariant solutions of the three-dimensional Boyer–Finley equation to noninvariant solutions of the four-dimensional hyperbolic complex Monge–Ampère equation. The lift is applied to noninvariant solutions of the Boyer–Finley equation, obtained earlier by the method of group foliation, to yield noninvariant solutions of the hyperbolic complex Monge–Ampère equation. Using these solutions we construct new Ricci-flat ultra-hyperbolic metrics with non-zero curvature tensor that have no Killing vectors.

Interaction of a One-Dimensional Continuum with an Inertial Object Moving over the Continuum

Free transverse oscillations in a system consisting of an infinite moment continuum, such as the Euler-Bernoulli beam lying on the Winkler foundation, and a rigid body moving along the beam with a constant velocity and having a point contact with the guide are studied. The range of the considered velocities of the concentrated inertial object along the continuum is limited by the requirement of a finite energy of elastic deformation of the infinite continuum, corresponding to cojoint free osillations of an unbounded system. An analytical solution of the corresponding spectral problem in a system with a mixed spectrum is constructed. Limiting situations are analyzed, where the inertial rigid object moving along the beam is devoid of one “oscillatory” degree of freedom for some reasons. In particular, an inertial object devoid of mass but having a nonzero tensor of inertia is considered. Dependences of all characteristics of the discrete spectrum of oscillations and their shapes on the magnitude of object velocity along the moment elastoinertial guide are given.

Relativistic field theories in a magnetic background as noncommutative field theories

We study the connection of the dynamics in relativistic field theories in a strong magnetic field with the dynamics of noncommutative field theories (NCFT). As an example, the Nambu-Jona-Lasinio models in spatial dimensions $d \geq 2$ are considered. We show that this connection is rather sophisticated. In fact, the corresponding NCFT are different from the conventional ones considered in the literature. In particular, the UV/IR mixing is absent in these theories. The reason of that is an inner structure (i.e., dynamical form-factors) of neutral composites which plays an important role in providing consistency of the NCFT. An especially interesting case is that for a magnetic field configuration with the maximal number of independent nonzero tensor components. In that case, we show that the NCFT are finite for even $d$ and their dynamics is quasi-(1+1)-dimensional for odd $d$. For even $d$, the NCFT describe a confinement dynamics of charged particles. The difference between the dynamics in strong magnetic backgrounds in field theories and that in string theories is briefly discussed.

Phenomenology of magnetic second harmonic generation from low symmetry surfaces and interfaces

Low dimensional magnetic structures show interesting and novel phenomena such as oscillatory magnetic coupling and giant magnetoresistance. Magnetic second harmonic generation (MSHG) can provide unique information on magnetic surfaces and interfaces because, within the dipole approximation, broken space-inversion symmetry at the surface or interface of centrosymmetric media, and broken time-reversal symmetry arising from the magnetization, are both required in order to observe a magnetic-field-dependent second harmonic response. However, the additional reduction in symmetry arising from the magetization produces many non-zero susceptibility tensor components, particularly in the case of vicinal, stepped surfaces of 1m symmetry, and care is needed in designing experiments that will produce readily interpretable results. Phenomenological expressions for the MSHG response from systems of 1m symmetry are presented, where combinations of input and output polarizations and magnetic field orientations allow the essential physics of these systems to be explored, particularly in relation to distinguishing terrace and step contributions to the magnetization from vicinal surfaces and interfaces. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Cosmological constant and gravitational theory on a D-brane

In a toy model we derive the gravitational equation on a self-gravitating curved D-brane. The effective theory on the brane is drastically changed from the ordinal Einstein equation. The net cosmological constant on the brane depends on a tuning between the brane tension and the brane charges. Moreover, the nonzero matter stress tensor exists if the net cosmological constant is not zero. This fact indicates a direct connection between matter on the brane and dark energy.

Ab initioembedded cluster study of optical second-harmonic generation below the gap of a NiO(001) surface

An embedded cluster approach was applied to study the electronic excitations on the NiO(001) surface. Using a quantum chemical calculation, a small $({\mathrm{NiO}}_{5}{)}^{8\ensuremath{-}}$ cluster was embedded in a set of point charges to model the NiO(001) surface. Starting from the unrestricted Hartree-Fock level of theory, we calculate the ground-state properties to provide some insight into electronic structure and excitation. We estimate the excitation energies and oscillator strengths using the single excitation configuration-interaction (CIS) technique. Our results show that the CIS method is reasonably accurate for estimating the low-lying $d\ensuremath{-}d$ excitations below the gap. We then demonstrate the electron correlation effects on the $d\ensuremath{-}d$ transitions at several levels of ab initio correlated theory [CID (with all double substitutions), CISD (with all single and double substitutions), (quadratic) QCISD, and (with all single, double, and triple substitutions) QCISD $(T)].$ The electron correlation tends to decrease the magnitude of d-electron excitation energies. Using the many-body wave functions and energies resulting from CID and $\mathrm{QCISD}(T)$ calculations, we compute the second harmonic generation (SHG) tensor for the NiO(001) surface. In contrast to bulk NiO, where the SHG response is forbidden within the electric-dipole approximation because of the inversion symmetry, the ${C}_{4v}$ symmetry of the surface leads to five nonzero tensor elements. From that, the intensity of the nonlinear optical response as a function of photon energy at different polarizations of the incident and outgoing photons is obtained. This quantity can be directly measured in experiment, and we suggest possible conditions in order to detect it.