Transverse Vector Research Articles

Interaction of electrons with polaritons

The electromagnetic (EM) waves associated with the polariton modes of bulk dielectrics are quantized using a procedure that accounts for both the EM and matter fields. The interaction of electrons with these polariton fields is described using the minimal coupling (e/m*)A.p interaction Hamiltonian where A is the transverse vector potential operator of the polariton field, p the electronic momentum and m* its effective mass. The electron-polariton interaction in the bulk is demonstrated to be closely linked to the behaviour of the polariton group and phase velocities. The same quantization procedure is then employed to describe the EM fields associated with the interface polaritons of a GaAs/AlAs quantum well system. The coupling leads to a dependence of the scattering rate on the group and phase velocities of the surface modes, just as it does for the bulk excitations. In contrast to the case in the bulk, it is shown that these modes are important for relaxing the electron energy in narrow wells.

Aperp

The interface optical-phonon modes and their interaction with electrons in layered semiconductor structures are considered. In a canonical theory where retardation effects are retained from the outset, the theory leads naturally to the quantization of the free interface oscillations in the radiation gauge for which the scalar potential is zero and the vector potential is transverse (O=0, ⊇.A=0). The description is thus entirely in terms of a Transverse vector potential A ⊥ which satisfies ⊇.A ⊥=0 everywhere, except at the interfaces where, as usual, only boundary conditions apply. The interaction between the two subsystems (electrons and interface modes) is the well-known minimal-coupling Hamiltonian which is in the form eA ⊥.p/m *

Polarization properties of the freely propagating electromagnetic field of arbitrary spatial and temporal form

The angular spectrum of plane waves representation of the freely propagating electromagnetic field in the half-space z ≥ z0 of a homogeneous, isotropic, locally linear, temporally dispersive medium is employed to describe the polarization properties of the field throughout the half-space z > z0 in terms of the polarization behavior of either field vector on the plane at z = z0. Both the spatial and the temporal dependence of the initial field vectors on this plane are assumed to be known but are otherwise arbitrary functions of the transverse position vector rT and time t on that plane. The general relationship between the electric and the magnetic polarization ellipses is obtained, along with the general orthogonality relations between the field vectors. Finally, the conditions under which either or both field vectors may be uniformly polarized are described.

Vector polarization at high momentum transfers in QCD.

We show in the context of perturbative QCD that all single transverse vector polarizations or analyzing powers are zero in the high-momentum-transfer limit. The proof depends on hadron helicity conservation, which applies to exclusive processes that are dominated by a short-distance reaction mechanism. Some comments are made about the available data.

3-dimensional affine hypersurfaces in ℝ4 with parallel cubic form

In this paper, we study 3-dimensional locally strongly convex affine hypersurfaces in ℝ4. Since the publication of Blaschke’s book [B] in the early twenties, it is well-known that on a nondegenerate affine hyper-surface M there exists a canonical transversal vector field called the affine normal. The second fundamental form associated to the affine normal is called the affine metric. In the special case that M is locally strongly convex, this affine metric is a Riemannian metric. Also, using the affine normal, by the Gauss formula one can introduce an affine connection on M, called the induced connection ∇. So on M, we can consider two connections, namely the induced affine connection ∇ and the Levi Civita connection of the affine metric h.

Magnetic field rotation of a strong resonance radiation polarization plane in the media with Doppler-broadened transitions of 01 and 10 types

For atomic media with resonant Doppler-broadened transitions of J=0 to J'=1 or J=1 to J'=0 type and taking into account the relaxation due to depolarizing collisions a theory of nonlinear magneto-optic polarization phenomena is developed. The theory is valid in the case of both arbitrary resonance linearly-polarized radiation intensity and arbitrary external magnetic field spatial orientation. The Faraday and Voigt geometries are analysed in detail, and in the case of the Faraday geometry the effect is considered of a noncompensated magnetic field transverse component on the shape of a dependence relating the radiation polarization plane rotation angle to a magnetic field longitudinal component. In the case of the Voigt geometry an essential effect is found of the angle between the radiation initial polarization and transverse magnetic field vectors on the character of the dependence relating the radiation polarization plane rotation angle to the transverse magnetic field magnitude.

Transversal Dirac families in Riemannian foliations

We describe a family of differential operators parametrized by the transversal vector potentials of a Riemannian foliation relative to the Clifford algebra of the foliation. This family is non-elliptic but in certain ways behaves like a standard Dirac family in the absolute case as a result of its elliptic-like regularity properties. The analytic and topological indices of this family are defined as elements of K-theory in the parameter space. We indicate how the cohomology of the parameter space is described via suitable maps to Fredholm operators. We outline the proof of a theorem of Vafa-Witten type on uniform bounds for the eigenvalues of this family using a spectral flow argument. A determinant operator is also defined with the appropriate zeta function regularization dependent on the codimension of the foliation. With respect to a generalized coupled Dirac-Yang-Mills system, we indicate how chiral anomalies are located relative to the foliation.

On the Cartan-Norden theorem for affine Kähler immersions

In [N-Pi-Po] the notion of affine Kähler immersion for complex manifolds has been introduced: if Mn is an n-dimensional complex manifold and f: Mn -→ Cn+1 is a holomorphic immersion together with an anti-holomorphic transversal vector field ζ, we can induce a connection ▽ on Mn which is Kähler-like, that is, its curvature tensor R satisfies R(Z, W) = 0 as long as Z, W are (1, 0) complex vector fields on M.

High-energy scatterings of many electroweak gauge bosons

We present an application of the equivalence theorem and the multispinor representation of gauge fields to the standard model of electroweak interactions at very high energies. The equivalence theorem allows us to efficiently treat the longitudinal vector bosons while the multispinor formalism makes the transverse vector bosons easy to handle. We generalize the work of Berends and Giele to derive a recursion relation for a current consisting of a pair of longitudinal vector bosons plus any number of transverse vector bosons. It is shown that for certain helicity configurations this current is related to a corresponding current involving only transverse vector bosons. Consideration of a U( N), rather than an SU( N), gauge theory enables us to incorporate the mixing in the SU(2) × U(1) electroweak theory and to derive certain sum rules for the currents for transverse gauge bosons. We also give explicit expressions for four-particle and five-particle scattering amplitudes involving a pair of longitudinal vector bosons.

T-Jperp model and a possible pairing mechanism in the oxide superconductors.

We introduce the ``t-${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$'' model as the presence of holes in a two-dimensional XY spin-1/2 antiferromagnet, which gives rise to charged particles that carry flux. We find that the problem can be mapped into electrodynamics with constraints, leading to scalar and transversal vector potentials generated by the vorticity charges Q(x)=m(x)+(1/2\ensuremath{\pi}\ensuremath{\theta})\ensuremath{\rho}(x) and their currents. Here m(x)=0,\ifmmode\pm\else\textpm\fi{}1 are chargeless vortices, and \ensuremath{\rho}(x) is the density of the electric charges. The scalar potential between the electric charges \ensuremath{\rho}(x) is generated by the neutral vortices m(x). The direct repulsive interaction between the electric charges is screened out by the neutral vortex excitations giving rise to attraction at large distance. The currents produced by the vortices give rise to gauge fields that also include a Chern-Simons term. The gauge fields represent the transversal part of electrodynamics in 2+1 dimensions and might be responsible for normal-state properties such as linear resistivity.

Linearized lattice QED

We present a linearized formulation of lattice QED. The cutoff theory is locally gauge invariant and satisfies the associated Ward identities exactly, even though the physical transverse vector potential enters the action only linearly. The quenched version of the model is simulated and a continuous chiral symmetry breaking transition is found at strong coupling. Lattice monopoles are found to be unimportant near the transition, which supports the picture that chiral symmetry breaking is due solely to strong vector forces. The critical region of the model is very narrow and estimates of critical indices are very sensitive to which value of the critical coupling is taken. The critical index δ is 2.5(1), distinct from mean field theory.

Polar region Birkeland current, convection, and aurora for northward interplanetary magnetic field

Viking magnetic field, electric field, and image data have been used to assess polar region phenomena for steady state northward interplanetary magnetic field (IMF) conditions. Regions of polar Birkeland current (NBZ currents) and convection and their extent from the vicinity of the magnetic pole are determined. Also discussed are mechanisms that could produce polar aurora in general; two suggestions are (1) converging electric fields from convection patterns alone and (2) the bifurcation of the magnetotail with its associated plasma transport and convection patterns. Macroscopic (> 1° latitude) systems of Birkeland currents and convection in the polar regions have been established for a case on April 9,1986, from Viking spacecraft data. The current systems were confined to the highest latitudes of the polar regions and occurred during strongly northward IMF with a significantly negative Bx. An arc extends across the polar region within the dawn cell of Birkeland current. The arc is located at a sunward to antisunward convection reversal that corresponds to a converging electric field. A converging electric field (▽ · E < 0) alone is suggested as the cause of this polar arc. The signature of both transverse disturbance vectors indicates that the polar region dawn NBZ Birkeland current does not connect to the dayside auroral region. It is inferred that the dawn polar region convection cell associated with this Birkeland current is also limited in the sunward direction and does not connect to the dayside auroral region convection.

Computation of Flow around Spheroid at Small Incidence and Study on Vorticity Field

In the present study, Navier-Stokes equation is numerically solved by use of a finite difference method to obtain the 3-dimensional flow field around a prolate spheroid at small incidence. The computed flow field shows the same characteristics to that of the observation by a flow visualization technique which was reported in the author's previous report. The existence of a bubble-type separation at the rear end and the nodal point in the surface shear-stress pattern are recognised in the computed results.The 3-dimensional vorticity field is derived from the result of the computation. The vorticity structure is analysed by dissolving the vorticity vector into two components, i. e. the one is the component along the flow direction (locally streamwise vorticity) and the other component is in the locally transverse plane. The two components of the vorticity show different characteristics, i. e. the locally transverse vorticity vector shows a maximum value near the fore end and decreases in the downstream as the boundary layer grows. On the other hand, the streamwise vorticity grows in the after region and keeps its value in the wake region, although the magnitude of the streamwise vorticity is quite small compare to that of the transverse vorticity.

The role of F-actin in determining the division plane of carrot suspension cells. Drug studies

Abstract Following the report that a network of F-actin is associated with the nucleus throughout the division cycle, we have examined the involvement of F-actin in determining the division plane of carrot suspension cells. This was achieved by treating cells with drugs and then staining the unfixed cells with rhodaminyl lysine phallotoxin in detergent extraction buffer. In interphase, actin cables radiate from the nucleus but at the cortex become more or less transversely arranged in the pattern already known for cortical microtubules. Concentration of the cortical F-actin into a band at preprophase draws most of the nucleus-associated actin into a transvacuolar disc, thereby forming the phragmosome within which mitosis and cytokinesis occur. In addition to this transversely aligned structure, F-actin is also associated with the spindle poles during mitosis but these filaments tend to align at right angles to the phragmosomal actin. F-actin therefore defines transverse and longitudinal vectors as division approaches. Depolymerization of F-actin with cyto-chalasin D can cause the spindle axis to reorientate such that the pole-pole axis comes to lie, abnormally, parallel with the phragmosome. The cytokinetic apparatus (the phragmoplast) develops centrifugally within the phragmosome. There has been considerable speculation on the nature of the elements that guide the phragmoplast to the cortical site previously occupied by the preprophase band of microtubules. This study demonstrates that F-actin bridges the leading margin of the outgrowing phragmoplast to the opposing cortex. Radial actin strands therefore provide a ‘memory’ of the predetermined division plane whose perimeter had been marked at preprophase by a band composed of microtubules and F-actin. This relationship was perturbed with the herbicide, chloroisopropylphenyl carbamate. Preprophase bands of actin appear to form normally in herbicidetreated cells. However, cytokinesis does not occur within this predicted plane since the drug perturbs the mitotic spindle, forming three nuclei which become separated by Y-shaped, actin-containing phragmoplasts. Cytoplasmic actin strands connect the edges of the phragmoplast to the cortex. It is suggested that the irregular distribution of F-actin, which radiates from the herbicide-altered mitotic apparatus, provides alternative paths for outgrowth of the abnormal phragmoplasts. Caffeine is known to cause failure of cell plate formation. But apart from inducing cytoplasmic ‘starbursts’ of F-actin in interphase cells it does not appear to have any effect on F-actin-containing division structures. It is concluded that the formation of a transvacuolar phragmosome, spindle alignment and the ‘correct’ outgrowth of a planar cytokinetic apparatus to the predetermined boundary of the division site all involve F-actin.

Singularities in the transverse fields of electromagnetic waves. I. Theory

Electromagnetic waves generally contain three kinds of singularities called C lines, S surfaces and disclinations. These singularities are features of the transverse electric and transverse magnetic fields of the waves and all three kinds usually occur in any given wavefield. We show that in the case of nominally uniformly polarized waves, the simple line zeros predicted for interference fringes by scalar wave theory in fact have an underlying polarization structure consisting of two C lines and an S surface. In consequence, virtually all monochromatic electromagnetic waves contain polarization states ranging from right-hand circular, through linear to left-hand circular polarization. Singularities of the electric and magnetic fields are not generally coincident in space; in fact they can be separated by arbitrarily large distances. The separation of the electric and magnetic S surfaces means that there are regions where the transverse electric and transverse magnetic vectors counterrotate. C lines are probably the most significant of the singularities, since they are not only structural features of polarization, but also organize the time structure of electromagnetic waves. They play a crucial role in determining the topology of disclinations in paraxial wavefields. In pulsed electromagnetic waves all three singularities move through space. Their behaviour, including interactions between pairs of C lines, S surfaces or disclinations, which are likely to be frequent events in pulsed waves, is discussed.

Observations of transverse energy for P waves recorded on a deep-ocean borehole seismometer located in the northwest Pacific

In the classical radially stratified earth, P waves are confined to the sagittal plane, implying that there should be no energy observed in the transverse direction. However, a transverse fraction of the energy is observed in the initial part of the P -wave train and can be measured by separating the P -wave energy into its radial (lying in the sagittal plane) and transverse vectors. We refer to this fraction as the T/R energy ratio. The data consist of P -wave signals recorded on a borehole seismometer and explosion-source data recorded on the North American continent. The borehole instrument is the Hawaii Institute of Geophysics' three-component Ocean Sub-bottom Seismometer (OSS IV) located in the northwest Pacific in DSDP Hole 581C. We compare transverse energy observations of initial P waves from regional earthquakes and teleseismic events recorded in the deep ocean with continental records at similar distances. Envelope maxima and integrated energy on three components of motion, as well as T/R energy ratios, were measured for a range of frequency bands: 1 to 12 Hz for regional events and 1 to 3 Hz for teleseismic event. The T/R energy ratios obtained from envelope maxima for earthquakes recorded in the northwest Pacific are comparable to the ratios observed at Long-Range Seismic Monitoring stations on the North American continent: approximately 0.1 for events at teleseismic distances and 0.2 for regional events. We speculate that the two important constituents to the T/R energy ratios observed are near-source and near-receiver scattering.

Plasmon Spectra in Metallic Superlattices††Project supported by the Science Fund of the Chinese Academy of Sciences.

We present results of a hydrodynamic study of the plasmon spectra in metallic superlattices by treating the different layers as jelliums. Interesting changes in the plasmon dispersions and relative growth and decline of the bulk and interface modes with modulation wavelength and transversal wave vector are noted. A variation of the electronic effective mass with the modulation wavelength has also been found.

Assessment of left ventricular hypertrophy by ECG and VCG in patients with inferior and posterior myocardial infarction. A comparison with echocardiographic data

Electrocardiographic (ECG) and vectorcardiographic (VCG) QRS voltage criteria have been analyzed in 26 patients with inferior and 17 with posterior myocardial infarction (MI) in comparison with left ventricular (LV) mass and global and regional wall motion as assessed by M-mode and two-dimensional (2D) echocardiography. Transverse plane QRS maximal vector correlated significantly with LV mass in patients with both inferior and posterior MI (r = 0.65 and 0.87, respectively, p less than 0.01). A transverse plane QRS maximal vector greater than 1.5 mV correctly recognized 12 of 15 (80%) and 9 of 12 (75%) patients with respectively inferior and posterior MI and LV mass greater than 221 gm. Of the ECG measurements, S V1-2 + R V5-6 correlated moderately with LV mass in patients with inferior MI (r = 0.47), and R V1-2 + R V5-6 correlated moderately with LV mass in those with posterior MI (r = 0.67). ECG and VCG QRS voltage data did not correlate with global and regional LV function as assessed by M-mode and 2D echocardiography. We conclude that: ECG and VCG QRS voltage parameters can be utilized for assessing non-invasively LV enlargement in patients with postero-inferior MI; ECG and VCG QRS voltage parameters should be utilized with caution for analyzing LV function or MI size in postero-inferior MI.

Propagation of transverse electromagnetic waves with gravitational perturbations in an isotropic universe

The combined behavior of gravitational and electromagnetic perturbations in the radiation-dominated plasma of an isotropic universe is considered. It is shown that transverse electromagnetic waves and vector and tensor gravitational perturbations are independent of one another. The propagation of transverse electromagnetic waves during the lepton and radiation-dominated phases is determined. It is shown that the gravitational perturbations help to excite longitudinal electromagnetic fields in the radiation-dominated plasma.

Dynamic conductivity of a two-dimensional Josephson junction array

The author calculates the response of an N*N Josephson junction array to an oscillatory transverse vector potential. Duality transformations, and a dynamic version of Kosterlitz real space scaling, are used with the resistivity shunted junction model as a starting point. The long-wavelength low-frequency conductivity sigma (q to 0, omega , T) identical to sigma 1+i sigma 2 is calculated, for T near TKT, the Kosterlitz-Thouless transition temperature. For fixed frequency, sigma 1( omega ,T) peaks at, and sigma 2( omega ,T) falls off at, a frequency-dependent T=Tw>TKT. In the limit of mod T-TKT mod /TKT<<1,(1n( Gamma 0/ omega ))-1<<1, dispersion relations and a sum rule are approximately satisfied. The sigma 1,2( omega ,T) behaviour is similar to the (phenomenological) response function of helium films to an oscillating substrate, with the difference that the quantum phase relaxation rate Gamma 0 is not a fitted parameter, but is related to the isolated-junction resistance.