Linear Tensor Research Articles

Negative energy and stability in scalar-tensor gravity

Linearized gravitational waves in Brans-Dicke and scalar-tensor theories carry negative energy. A gauge-invariant analysis shows that the background Minkowski space is stable at the classical level with respect to linear scalar and tensor inhomogeneous perturbations.

Fast and compact smoothing on large multidimensional grids

A framework of penalized generalized linear models and tensor products of B-splines with roughness penalties allows effective smoothing of data in multidimensional arrays. A straightforward application of the penalized Fisher scoring algorithm quickly runs into storage and computational difficulties. A novel algorithm takes advantage of the special structure of both the data as an array and the model matrix as a tensor product; the algorithm is fast, uses only a moderate amount of memory and works for any number of dimensions. Examples are given of how the method is used to smooth life tables and image data.

Spin Hall and spin-diagonal conductivity in the presence of Rashba and Dresselhaus spin-orbit coupling

We investigate the spin-current linear response conductivity tensor to an electric field in a paramagnetic two-dimensional electron gas with both Rashba and Dresselhaus spin-orbit coupling in the weak scattering regime within the Born approximation. In the usual sample parameters, and for cross-sectional size smaller than the spin-coherence length, the spin-Hall conductivity depends only on the sign of the difference in magnitude of the Rashba and Dresselhaus coupling except within a narrow window where both coupling strengths are equal. We also find that a spin current is generated in the direction of the driving field for a non-zero Dresselhaus term. Possible experimental setups for its detection, taking into account the finite mobility and typical parameters of current samples, are discussed.

Quasi-Analytical Calculation of Thermal Magnetization Fluctuation Noise in Giant Magnetoresistive Sensors

Noise caused by thermal magnetization fluctuations in giant magnetoresistive sensors, mainly in the free layer, limits the achievable signal-to-noise ratio and thus the density of magnetic recording systems. Here, we describe a quasi-analytical method to study this noise. First, by discretizing the free layer into sufficiently small rectangular cells, an equilibrium state of the free layer is obtained using a quasi-static energy minimization technique. A linear tensor relation between the magnetization spectra and the thermal fluctuations is found for the two approaches: 1)Landau-Lifshitz-Gilbert-Brown and 2) collective spin wave excitation. In the former, damping and thermal fields are added to each cell and then a Fourier transform is taken to obtain the spectra. For the eigenmode approach, the lossless dynamic equations are diagonalized, yielding the system's intrinsic eigenmodes. Then damping and thermal fluctuations are added to each eigenmode, independently. The sensor playback noise power spectrum density, a measurable quantity, is calculated by summing up the contributions from each eigenmode or cell magnetization. This computationally light treatment yields a clear physical picture of the phenomenon, relating damping, thermal fluctuation, and noise. We describe each step of the calculation procedure in detail and give examples.

From subfactors to categories and topology II: The quantum double of tensor categories and subfactors

For every tensor category C there is a braided tensor category Z( C) , the ‘center’ of C . It is well known to be related to Drinfel'd's notion of the quantum double of a finite dimensional Hopf algebra H by an equivalence Z(H -mod) ≃ ⊗ br D(H) -mod of braided tensor categories. In the Hopf algebra situation, whenever D( H)-mod is semisimple (which is the case iff D( H) is semisimple iff H is semisimple and cosemisimple iff S 2=id and char F∤ dim H ) it is modular in the sense of Turaev, i.e. its S-matrix is invertible. (This was proven by Etingof and Gelaki in characteristic zero. We give a fairly general proof in the appendix.) The present paper is concerned with a generalization of this and other results to the quantum double (center) of more general tensor categories. We consider F -linear tensor categories C with simple unit and finitely many isomorphism classes of simple objects. We assume that C is either a ∗-category (i.e. F= C and there is a positive ∗-operation on the morphisms) or semisimple and spherical over an algebraically closed field F . In the latter case we assume dim C≡∑ id(X i) 2≠0 , where the summation runs over the isomorphism classes of simple objects. We prove that Z( C) (i) is a semisimple spherical (or ∗-) category and (ii) is weakly monoidally Morita equivalent (in the sense of Müger (J. Pure Appl. Algebrea 180 (2003) 81–157)) to C⊗ F C op . This implies dim Z( C)=( dim C) 2 . (iii) We analyze the simple objects of Z( C) in terms of certain finite dimensional algebras, of which Ocneanu's tube algebra is the smallest. We prove the conjecture of Gelfand and Kazhdan according to which the number of simple objects of Z( C) coincides with the dimension of the state space H S 1×S 1 of the torus in the triangulation TQFT built from C . (iv) We prove that Z( C) is modular and we compute Δ ±( Z( C))≡∑ iθ(X i) ±1d(X i) 2= dim C . (v) Finally, if C is already modular then Z( C) ≃ ⊗ br C⊗ F C ̃ ≃ ⊗ C⊗ F C op , where C ̃ is the tensor category C with the braiding c ̃ X,Y=c Y,X −1 .

Magnetization-induced second-harmonic generation in electrochemically synthesized magnetic films of ternary metal Prussian blue analogs

We observed magnetic field effects on transmitted second-harmonic generation (SHG) in electrochemically synthesized (FexIICr1−xII)1.5[CrIII(CN)6]⋅7.5H2O magnetic films. These films showed a variety of temperature dependences for SH intensities below magnetic phase transition temperatures (TC). The SH intensity for x=0.25 increased monotonically with decreasing temperature and that for x=0.13 exhibited a minimum value around the magnetic compensation temperature under a zero magnetic field. These temperature dependences resembled those of the absolute value of magnetization, indicating that the magnetic strain of the films is responsible for the increase in SH below TC. In addition, the polarization of SH light was rotated by an applied external magnetic field. The observed SH rotation angle of 1.3° was much larger than the Faraday rotation angle of 0.079° at 388 nm. This SH rotation can be understood by the mechanism of magnetization-induced SHG caused by interaction between the electric polarization along the out-of-plane of film and spontaneous magnetization. The magnetic linear term [χijkLmagn(1)] contributed particularly to the SH rotation. The value of the magnetic linear tensor component relative to the crystallographic tensor component [|χyyyXmagn(1)|/|χzyycr], which induced the SH rotation, was 0.023 at 50 K under 10 kOe.

Linear pre-metric electrodynamics and deduction of the light cone

We formulate a general framework for describing the electromagnetic properties of spacetime. These properties are encoded in the ‘constitutive tensor of the vacuum’, a quantity analogous to that used in the description of material media. We give a generally covariant derivation of the Fresnel equation describing the local properties of the propagation of electromagnetic waves for the case of the most general possible linear constitutive tensor. We also study the particular case in which a light cone structure is induced and the circumstances under which such a structure emerges. In particular, we will study the relationship between the dual operators defined by the constitutive tensor under certain conditions and the existence of a conformal metric. Closure and symmetry of the constitutive tensor will be found as conditions which ensure the existence of a conformal metric. We will also see how the metric components can be explicitly deduced from the constitutive tensor if these two conditions are met. Finally, we will apply the same method to explore the consequences of relaxing the condition of symmetry and how this affects the emergence of the light cone.

Linear pre‐metric electrodynamics and deduction of the light cone

AbstractWe formulate a general framework for describing the electromagnetic properties of spacetime. These properties are encoded in the ‘constitutive tensor of the vacuum’, a quantity analogous to that used in the description of material media. We give a generally covariant derivation of the Fresnel equation describing the local properties of the propagation of electromagnetic waves for the case of the most general possible linear constitutive tensor. We also study the particular case in which a light cone structure is induced and the circumstances under which such a structure emerges. In particular, we will study the relationship between the dual operators defined by the constitutive tensor under certain conditions and the existence of a conformal metric. Closure and symmetry of the constitutive tensor will be found as conditions which ensure the existence of a conformal metric. We will also see how the metric components can be explicitly deduced from the constitutive tensor if these two conditions are met. Finally, we will apply the same method to explore the consequences of relaxing the condition of symmetry and how this affects the emergence of the light cone.

Linear electro-optical properties of tetragonal BaTiO3

Linear optical susceptibility and clamped linear electro-optical tensor coefficients of tetragonal BaTiO3 are calculated using a formalism based on bond charge theory. Calculated values are in close agreement with experimental data. The covalent Ti-O bonds constituting distorted TiO6 octahedral groups are found to be major contributors to the electro-optic coefficients making them more sensitive than the BaO12 groups for these properties. Orientations of chemical bonds play an important role in determining these properties.

Circular dichroism spectra of DNA quadruplexes [d(G(5)T(5))](4) as formed with G(4) and T(4) tetrads and [d(G(5)T(5)). d(A(5)C(5))]2 as formed with Watson-Crick-like (G-C)(2) and (T-A)(2) tetrads.

We utilize electrophoresis and find that a thermally treated equimolar mixture of the oligonucleotide d(G(5)T(5)) and its complementary oligonucleotide d(A(5)C(5)) exhibits either two bands or a single band in one lane, depending on the conditions of the incubation solutions. The thermally treated d(G(5)T(5)) solution loaded in a different lane exhibits a single band of the parallel quadruplex [d(G(5)T(5))](4), which is composed of homocyclic hydrogen-bonded G(4) and T(4) tetrads previously proposed. For the thermally treated equimolar mixture of d(G(5)T(5)) and d(A(5)C(5)), the fast band is assigned to a Watson-Crick d(G(5)T(5)). d(A(5)C(5)) duplex, so that the slow band with the same low mobility as that of [d(G(5)T(5))](4) may be assigned to either [d(G(5)T(5))](4) itself or a [d(G(5)T(5)). d(A(5)C(5))](2) quadruplex. If the latter compound is true, this may be the antiparallel quadruplex composed of the heterocyclic hydrogen-bonded G-C-G-C and T-A-T-A tetrads proposed previously. After removing these three bands for the duplex and two kinds of hypothetical quadruplexes, we electrophoretically elute the corresponding compounds in the same electrophoresis buffer using an electroeluter. The eluted compounds are ascertained to be stable by electrophoresis. The circular dichroism (CD) and UV absorption spectra measured for the three isolated compounds are found to be clearly different. For the electrophoretic elution of the hypothetical [d(G(5)T(5))](4) quadruplex, the result of the molecularity of n = 4 obtained from the CD melting curve analysis provides further support for the formation of the parallel [d(G(5)T(5))](4) quadruplex already proposed. For the thermally treated equimolar mixture of d(G(5)T(5)) and d(C(5)A(5)), the fast band with a molecularity of n = 2 corresponds to the Watson-Crick duplex, d(G(5)T(5)). d(A(5)C(5)). The slow band with a molecularity of n = 4 indicates the antiparallel quadruplex [d(G(5)T(5)). d(A(5)C(5))](2), whose observed CD and UV spectra are different from those of [d(G(5)T(5))](4). By electrophoresis, after reannealing the eluted compound [d(G(5)T(5)). d(A(5)C(5))](2), a distinct photograph showing the band splitting of this quadruplex band into the lower duplex and upper quadruplex bands is not possible; but by a transilluminator, we occasionally observe this band splitting with the naked eye. The linear response polarizability tensor calculations for the thus determined structures of the [d(G(5)T(5))](4) quadruplex, the McGavin-like [d(G(5)T(5)). d(A(5)C(5))](2) quadruplex, and the Watson-Crick d(G(5)T(5)). d(A(5)C(5)) duplex are found to qualitatively predict the observed CD and UV spectra.

Curvature-induced polarization in carbon nanoshells

We investigate the normal polarization induced by bending of graphite shells, which microscopically occurs because of a shift in sp 2 hybridization at each atomic site. Based on a rehybridization model we analytically estimate the dependence on curvature of electronic charge spill into convex region. We further performed DFT calculations and extract the radial atomic dipole by direct electronic charge density integration. A continuum analysis assigns a linear susceptibility tensor to the curvature-induced polarization and shows that this tensor is isotropic for hexagonal lattice, in agreement with microscopic model and computations. The intrinsic polarization effect can be important for nanoscale electronics.

Effects of negative-energy components in two-body deuteron photodisintegration

Several observables in two-body deuteron photodisintegration are investigated in the framework of the Bethe-Salpeter formalism. Apart from keeping the Lorentz covariance throughout, special attention is paid to inclusion of both the positive-energy and negative-energy partial-wave components of the deuteron state. Using the Bethe-Salpeter equation for the deuteron in the ladder approximation with one-boson exchanges as a driving term, the contribution of the negative-energy states is studied for the unpolarized differential cross section as well as for linear photon and tensor target asymmetries. These states are found to have an impact on the observables and, thus, should be taken into account in a complete theoretical treatment of the reaction in the intermediate energy regime.

Formal elasticity offour carbon allotropes: I. The inner elastic constants, internalstrain tensors, and zone-centre optic mode frequencies and theirpressure dependences

The symmetry structure of the six families of inner elasticconstants (derivatives of the free energy with respect to one,two, or three components of the relative sublattice displacement)that enter the elasticity, through the third order, of the cubic andhexagonal diamond allotropes and of the hexagonal andrhombohedral graphite allotropes is analysed in detail. This isfollowed by derivations (i) of the forms of the linear andquadratic internal strain tensors, (ii) of the expressions forthe zone-centre optic mode frequencies and eigenvectors, and(iii) of the effective inner elastic constants that determinethese frequencies in arbitrarily strained crystals together with(iv) the derived pressure dependences of those frequencies.

Linear electro-optical properties of orthorhombic KNbO 3

Linear optical susceptibility and clamped linear electro-optical tensor coefficients of orthorhombic KNbO 3 are calculated using a formalism based on bond charge theory. Calculated values are in close agreement with experimental data. The covalent Nb–O bonds constituting distorted NbO 6 octahedral groups are found to be the major contributors making these groups more sensitive than KO 12 groups to electro-optic coefficients.

Structure, crystal growth and physical anisotropy of KYb(WO4)2, a new laser matrix

The crystal structure of monoclinic KYb(WO4)2(KYbW) crystals has been refined (in space groupC2/c) at room temperature by using single-crystal X-ray diffraction data. KYbW undoped crystals were grown by the TSSG (top-seeded-solution growth) slow-cooling method. The crystals show {110}, {\bar{1}11}, {010} and {310} faces, which basically define their habit. The linear thermal expansion tensor has been determined and the principal axis with maximum thermal expansion (\alpha ^{\,\prime}_{33} = 16.68 × 10−6 K−1), {\bf X}^{\,\prime}_{3}, was located 12° from thecaxis. Its principal {\bf X}^{\,\prime}_{1}, {\bf X}^{\,\prime}_{2} and {\bf X}^{\,\prime}_{3} axes are [302], [010] and [106] directions, respectively, in the crystallographic system. The optical tensor has been studied at λ = 632.8 nm at room temperature; two principal axes,NgandNm, are located in theacplane, while the other,Np, is parallel to [010]. The principal axis with maximum refractive index (ng= 2.45),Ng, was located 19° from thecaxis.

Mindlin's problem for an anisotropic piezoelectric half–space with general boundary conditions

This paper considers Mindlin's problem in an anisotropic and piezoelectric halfspace with general boundary conditions, including 16 different sets of surface conditions. The Green's function due to...

Photorefractive properties of bifunctional N-arylated carbazole derivatives in a carbazole polymer host matrix

We report on the synthesis and the molecular properties of new N-arylated carbazole derivatives that are used as bifunctional chromophores in photorefractive (PR) polymer composites. The C–N bond of the N-aryl carbazole chromophore was formed directly by a nucleophilic aromatic substitution and Ullmann type coupling of carbazole with aryl halides. We performed calculations on the molecular conformation, the magnitude of the dipole moment and the linear polarizability tensor and their relative orientation. The PR performance of the chromophores, doped in an inert polymer host matrix and in a carbazole matrix, with C 60 as sensitizer, was evaluated using four-wave mixing experiments and photoconductivity measurements at 680 nm. The impact of the relative orientation of dipole moment and polarizability tensor on the Figure-Of-Merit (FOM) of photorefractive experiments was clearly demonstrated.

NONCOMMUTATIVITY IN LINEAR DILATON BACKGROUND

We consider quantization of open string theories in linear dilaton and constant antisymmetric tensor backgrounds and discuss the noncommutativity of space–time coordinates arising in such theories, including their relationship with light-like noncommutativity as well as backgrounds with null isometries. It is argued that the results can also be understood using space–time equations of motion of the string modes. We then present N = 2 supersymmetric generalization of these theories and the associated noncommutative structure.

Self-consistent Numerical Simulation of Isotope Separation by Selective Ion Cyclotron Resonance Heating in a Magnetically Confined Plasma

A self-consistent nonlinear model of an isotope separation process based on selective ion cyclotron resonance heating in a magnetized plasma is presented, and its numerical resolution is described. The response of the electrons to the electromagnetic field is modeled by a cold and linear conductivity tensor, while a particle method is used to solve nonlinear Vlasov equations for the ions. The resolution of the time-harmonic Maxwell equations is achieved by a finite-element method. Both steps are coupled by an iterative procedure, which shows fast convergence. Results are presented for the case of a solenoidal launching antenna.

Features of the magnetoelectric properties of BiFeO3 in high magnetic fields

It is shown that the destruction of the cycloidal structure of the magnetic ferroelectric BiFeO3 by a high magnetic field (Hn≈200 kOe) leads to the onset of a linear magnetoelectric effect and the appearance of a toroidal moment. The proof of the existence of a toroidal moment T in a high magnetic field (H>Hn) is based on the experimental observation that the off-diagonal components of the linear ME effect tensor are asymmetric (α12=−α21 for L‖c, where L is the antiferromagnetic vector), inasmuch as Tz∼α12−α21.