Quadrupole Contributions Research Articles

Monopole and quadrupole contributions to the angular momentum density

The energy-momentum tensor form factors contain a wealth of information about the nucleon. It is insightful to visualize this information in terms of 3D or 2D densities related by Fourier transformations to the form factors. The densities associated with the angular momentum distribution were recently shown to receive monopole and quadrupole contributions. We show that these two contributions are uniquely related to each other. The quadrupole contribution can be viewed as induced by the monopole contribution, and contains no independent information. Both contributions however play important roles for the visualization of the angular momentum density.

Constraining alternative polarization states of gravitational waves from individual black hole binaries using pulsar timing arrays

Pulsar timing arrays are sensitive to gravitational wave perturbations produced by individual supermassive black hole binaries during their early inspiral phase. Modified gravity theories allow for the emission of gravitational dipole radiation, which is enhanced relative to the quadrupole contribution for low orbital velocities, making the early inspiral an ideal regime to test for the presence of modified gravity effects. Using a theory-agnostic description of modified gravity theories based on the parametrized post-Einsteinian framework, we explore the possibility of detecting deviations from General Relativity using simulated pulsar timing array data, and provide forecasts for the constraints that can be achieved. We generalize the {\tt enterprise} pulsar timing software to account for possible additional polarization states and modifications to the phase evolution, and study how accurately the parameters of simulated signals can be recovered. We find that while a pure dipole model can partially recover a pure quadrupole signal, there is little possibility for confusion when the full model with all polarization states is used. With no signal present, and using noise levels comparable to those seen in contemporary arrays, we produce forecasts for the upper limits that can be placed on the amplitudes of alternative polarization modes as a function of the sky location of the source.

Magnetic mirror metasurface based on the in-phase excitation of magnetic dipole and electric quadrupole resonances

We consider the design of magnetic mirrors that consist of a layer of two-dimensional high-refractive-index dielectric particles. The central idea is to search for conditions for which the electric field of the light backscattered by a single particle has a zero phase difference with respect to the incident field. Employing physical arguments, we conclude that this can occur when the electric dipolar contribution vanishes. Optimizing the form of the cross section, we find a situation in which the vanishing of the dipolar contribution coincides with an in-phase condition for the magnetic dipole and the electric quadrupole contributions. The resulting scattering pattern of the particle resembles that of an electric dipole, with the difference that the forward and backscattered electric fields have opposite signs. Based on these results, we design a metasurface reflector that behaves as a magnetic mirror at a specific wavelength within a wideband spectral response. Subsequently, we extend the results to the design of supported structures where a magnetic mirror condition at a single wavelength is similarly found.

Ideal magnetic dipole resonances with metal-dielectric-metal hybridized nanodisks.

Magnetic resonances generated with nonmagnetic nanostructures have been widely used to design various functional nanophotonic devices, and it is important to realize pure magnetic dipole scattering for the unambiguous study of magnetic light-matter interactions. However, the magnetic responses often spectrally overlapping with other multipoles, which is the main obstacle to achieve ideal magnetic dipole resonances. This study proposes and theoretically demonstrates that an ideal magnetic dipole resonance can be excited with metal-dielectric-metal hybridized nanodisks. It is shown that although the generated magnetic dipole scattering around the bonding resonance of the hybridized nanodisk is spectrally overlapping with strong electric dipole and electric quadrupole contributions, an almost perfect current loop can be generated by adjusting the geometry parameters and the refractive index of the dielectric layer, thereby leading to the suppressing of the overlapping multipoles and the formation of an ideal magnetic dipole scattering. What's more important is that both electric and magnetic near-fields are enhanced simultaneously with the increasing of the refractive index of the dielectric layer, which makes the hybridized nanodisk a promising platform for enhanced magnetic light-matter interactions.

Dynamical enhancement of nonparaxial effects in the electromagnetic field of a vortex electron

A quantum state of an electron influences its electromagnetic field. If a spatial profile of the electron wave packet is not Gaussian, the particle may acquire additional intrinsic multipole moments, which alter its field, especially at small distances. Here the fields of a vortex electron with orbital angular momentum $\ell$ are obtained in a form of a multipole expansion with an electric quadrupole term kept by using the generalized (non-paraxial) Laguerre-Gaussian beams. The quadrupole contribution arises beyond a paraxial approximation, is linearly enhanced for highly twisted packets with $|\ell| \gg 1$, and can be important for the interactions of twisted beams with bulk matter and artificial structures. Moreover, this term results in an azimuthal asymmetry of the magnetic field in a rest frame of the electron, which appears thanks to the spreading of the packet with time. Thus, somewhat contrary to physical intuition, the spreading may enhance non-paraxial phenomena. For the available electron beams, this asymmetry can in principle be reliably detected, which would be experimental evidence of a non-paraxial effect with the vortex electrons.

Electric dipole and quadrupole contributions to valence electron binding in a charge-screening environment

We make a multipole expansion of the atomic/molecular electrostatic charge distribution as seen by the valence electron up to the quadrupole term. The Tridiagonal Representation Approach (TRA) is used to obtain an exact bound state solution associated with an effective quadrupole moment and assuming that the electron-molecule interaction is screened by suborbital electrons. We show that the number of states available for binding the electron is finite forcing an energy jump in its transition to the continuum that could be detected experimentally in some favorable settings. We expect that our solution gives an alternative, viable and simple description of the binding of valence electron(s) in atoms/molecules with electric dipole and quadrupole moments. We also ascertain that our model implies that a pure quadrupole-bound anion cannot exist in such a charge-screening environment.

Analysis of the hypothesis of a giant gaussian process as a means for describing secular variations of the geomagnetic field vector

The consistency of the empirical data on paleointensity and paleoinclinations contained in the BOROKPINT paleointensity world database with the Geocentric Axial Dipole (GAD) hypothesis and Giant Gaussian Process (GGP) model describing the geomagnetic field variations in the Brunhes epoch is tested. The calculations are based on the geomagnetic field potential representation by the sum of spherical functions of spatial coordinates with random coefficients, enabling computer simulation of the data with the given statistical characteristics of the coefficients. The estimates show that the Kolmogorov–Smirnov and Anderson–Darling tests reject the GAD hypothesis in its canonical form. The extension of GAD to GGD with nonzero time-average quadrupole and octupole terms makes the paleointensity and paleoinclination data to comply with GGP model realizations; however, these models are mutually exclusive because of mutual inconsistency of their parameters. Testing the paleoinclination data against GDP model shows that a small correction to the purely dipole component of the geomagnetic field should be introduced. At the same time, the paleointensity data analysis suggests that these data highly probably agree with GGP models with a high quadrupole contribution making up 1/3 of the dipole coefficient, which is strongly at odds with the parameters of the model corresponding to paleoinclination data. This inconsistency is most likely to be due to the artifacts associated with incorrect paleointensity determinations; however, this interpretation does not explain the causes of the strong latitudinal dependence of the intensity of the Virtual Axial Dipole Moment (VADM) which follows from the empirical data.

Beyond the Rosenfeld Equation: Computation of Vibrational Circular Dichroism Spectra for Anisotropic Solutions.

The difference in absorption of left and right circularly polarized light by chiral molecules can be described by the Rosenfeld equation for isotropic samples. It allows the assignment of the absolute stereochemistry by comparing experimental and computationally derived spectra. Despite the simple form of the Rosenfeld equation, its evaluation in the infrared regime remained challenging, as the contribution from the magnetic dipole operator is zero within the Born-Oppenheimer (BO) approximation. In order to resolve this issue, "beyond BO" theories had to be developed, among which Stephen's magnetic field perturbation (MFP) approach offers a computationally easily accessible form. In this work, optical activity is discussed for cylindrically symmetric solutions, which cannot be described anymore by Rosenfeld's equation due to broken spherical symmetry. Mathematical properties of natural and electric-field induced anisotropies are discussed on the basis of the gauge-independent theoretical framework of Buckingham and Dunn. The issue of achiral noise arising from external field perturbations is considered, and potential remedies are introduced. Natural anisotropic vibrational circular dichroism (VCD) equations are solved numerically by applying the MFP approach within the Hartree-Fock (HF) formalism. Properties of anisotropic VCD spectra are discussed for R-(+)-methyloxirane and (1 S,2 S)-cyclopropane-1,2-dicarbonitrile. In particular, by using a group theoretical argument, a gauge-independent lower bound for the quadrupole contribution of C2-symmetric molecules can be identified, which allows the importance of additional quadrupole terms in anisotropic VCD spectra calculation to be assessed.

Magnetic characterization and variability study of the magnetic SPB staroLupi

Thanks to large dedicated surveys, large-scale magnetic fields have been detected for about 10% of early-type stars. We aim to precisely characterize the large-scale magnetic field of the magnetic component of the wide binaryoLupi, by using high-resolution ESPaDOnS and HARPSpol spectropolarimetry to analyze the variability of the measured longitudinal magnetic field. In addition, we have investigated the periodic variability using space-based photometry collected with the BRITE-Constellation by means of iterative prewhitening. The rotational variability of the longitudinal magnetic field indicates a rotation periodProt = 2.95333(2) d and that the large-scale magnetic field is dipolar, but with a significant quadrupolar contribution. Strong differences in the strength of the measured magnetic field occur for various chemical elements as well as rotational modulation for Fe and Si absorption lines, suggesting a inhomogeneous surface distribution of chemical elements. Estimates of the geometry of the large-scale magnetic field indicatei = 27 ± 10°,β= 74−9+7°, and a polar field strength of at least 5.25 kG. The BRITE photometry reveals the rotation frequency and several of its harmonics, as well as two gravity mode pulsation frequencies. The high-amplitudeg-mode pulsation atf = 1.1057 d−1dominates the line-profile variability of the majority of the spectroscopic absorption lines. We do not find direct observational evidence of the secondary in the spectroscopy. Therefore, we attribute the pulsations and the large-scale magnetic field to the B5IV primary of theoLupi system, but we discuss the implications should the secondary contribute to or cause the observed variability.

Mechanisms of spontaneous chain formation and subsequent microstructural evolution in shear-driven strongly confined drop monolayers.

It was experimentally demonstrated by Migler and his collaborators [Phys. Rev. Lett., 2001, 86, 1023; Langmuir, 2003, 19, 8667] that a strongly confined drop monolayer sheared between two parallel plates can spontaneously develop a flow-oriented drop-chain morphology. Here we show that the formation of the chain-like microstructure is driven by far-field Hele-Shaw quadrupolar interactions between drops, and that drop spacing within chains is controlled by the effective drop repulsion associated with the existence of confinement-induced reversing streamlines, i.e., the swapping trajectory effect. Using direct numerical simulations and an accurate quasi-2D model that incorporates quadrupolar and swapping-trajectory contributions, we analyze microstructural evolution in a monodisperse drop monolayer. Consistent with experimental observations, we find that drop spacing within individual chains is usually uniform. Further analysis shows that at low area fractions all chains have the same spacing, but at higher area fractions there is a large spacing variation from chain to chain. These findings are explained in terms of uncompressed and compressed chains. At low area fractions most chains are uncompressed (spacing equals lst, which is the stable separation of an isolated pair). At higher area fractions compressed chains (with tighter spacing) are formed in a process of chain zipping along y-shaped structural defects. We also discuss the relevance of our findings to other shear-driven systems, such as suspensions of spheres in non-Newtonian fluids.

Analysis of the Hypothesis of a Giant Gaussian Process as a Means for Describing Secular Variations of the Geomagnetic Field Vector

The consistency of the empirical data on the paleointensity and paleoinclinations contained in the BOROKPINT paleointensity world database with the Geocentric Axial Dipole (GAD) hypothesis and the Giant Gaussian Process (GGP) model describing the geomagnetic field variations in the Brunhes epoch is tested. The calculation procedure is based on the representation of the geomagnetic field potential by the sum of the spherical functions of a spatial coordinate with random coefficients, which enables the computer simulation of the data that correspond to the given statistical characteristics of the coefficients. The estimation shows that according to the Kolmogorov–Smirnov and Anderson–Darling tests, the GAD hypothesis in its canonical form should be rejected. The extension of GAD to GGD with nonzero time-average quadrupole and octupole terms brings the paleointensity and paleoinclination data into agreement with the GGP model realizations; however, these models turn out to be mutually exclusive because their parameters are inconsistent with each other. Testing the paleoinclination data against GDP model demonstrates the necessity of introducing a small correction to the purely dipole component of the geomagnetic field. At the same time, the analysis of the paleointensity data shows that these data with a very high probability agree with the GGP models with a high quadrupole contribution making up 1/3 of the dipole coefficient, which is strongly at odds with the parameters of the model corresponding to the paleoinclination data. This inconsistency is most probably caused by the artifacts due to the incorrect determinations of paleointensity; however, this interpretation leaves unsolved the question about the causes of such a strong latitudinal dependence of the intensity of the Virtual Axial Dipole Moment (VADM) what follows from the empirical data.

Effects of nanodots shape and lattice constants on the spin wave dynamics of patterned permalloy dots

Micromagnetic simulations studies on Permalloy (Ni80Fe20) nanodots with different shapes and edge-to-edge separations (s) down to 25nm arranged in square lattice are reported. We observe the significant variation of spin-wave (SW) dynamics of nanodots of different shapes (triangular, diamond and hexagon) and of fixed dot diameter 100nm with varying s. Modes for single dot are transformed in an array into multiple quantized, edge and centre modes for different shapes and edge-to-edge separations, with different spin wave frequencies and peak intensities. Specifically, in the triangular dot sample, a broad range of mode frequencies is observed with highest SW frequency 14.7 GHz. For separation less than 100nm, the SW frequencies undergoes significant modification due to the varying nature of the magnetostatic and dipolar interaction in the array while for separations above 100nm, the SW frequency mostly remain constant. The power profiles confirm the nature of the observed modes. The spatial profiles of magnetostatic field are determined by a combination of internal magnetic-field profiles within the nanodots and the magnetostatic fields within the lattice. The inter-dots interaction of magnetostatic field shows dipolar and quadrupole contributions for all the shapes. Interestingly, vortex states with shifted core and polarity are observed in the array for all the shapes at Hbias = 0. Our results provide important understanding about the tunability of SW spectra in the array of triangular, diamond and hexagon shaped nanoelements.

Separating Dipole and Quadrupole Contributions to Single-Photon Double Ionization.

We report on a kinematically complete measurement of double ionization of helium by a single 1100eV circularly polarized photon. By exploiting dipole selection rules in the two-electron continuum state, we observed the angular emission pattern of electrons originating from a pure quadrupole transition. Our fully differential experimental data and companion abinitio nonperturbative theory show the separation of dipole and quadrupole contributions to photo-double-ionization and provide new insight into the nature of the quasifree mechanism.

Giant Optical Activity in an All-Dielectric Spiral Nanoflower.

Optical activity is an effect of prominent importance in stereochemistry, analytical chemistry, metamaterials, spin photonics, and astrobiology, but is naturally minuscule. Metallic nanostructures are commonly exploited as basic elements for artificially producing large optical activity by virtue of surface plasmon resonance (SPR) on the nanostructures. However, their intrinsic high ohmic loss amplified by the SPR results in low energy efficiency and large photothermal heat generation, severely limiting their performance and practical utility. Giant optical activity by inducing magnetic resonance in an all-dielectric spiral nanoflower (spiral-flower-shaped nanostructure) is demonstrated here. Specifically, a large circular-intensity difference of ≈35% is theoretically predicted and experimentally demonstrated by optimizing the magnetic quadrupole contribution of the nanoflower to scattered light. The nanoflower overcomes the bottleneck of the traditional metallic platforms and enables the development of diverse chiroptical devices and applications.

Path integral approach for Stark broadening of Lyman lines in hydrogen plasma

New results for Lyman lines from hydrogen plasmas are presented using the path integral approach. The influence of plasma components (electrons and ions) on the radiator is analysed separately. The ionic contribution is treated within the path integral approach, while the electronic contribution is estimated by the standard collision operator. The Stark effect, including the ion quadrupole contribution, is considered. The time‐dependent ionic microfield is treated within the path integral approximation using the model microfield method (MMM). The comparison with the quantum statistical approach is performed using a wide range of temperatures (T = 104–107 K) and electron densities (Ne = 1023–1026 m−3). Good agreement is mainly obtained for low density and high temperature.

Structure of the charge density wave in cuprate superconductors: Lessons from NMR

Using a mix of numerical and analytic methods, we show that recent NMR $^{17}$O measurements provide detailed information about the structure of the charge-density wave (CDW) phase in underdoped YBa$_2$Cu$_3$O$_{6+x}$. We perform Bogoliubov-de Gennes (BdG) calculations of both the local density of states and the orbitally resolved charge density, which are closely related to the magnetic and electric quadrupole contributions to the NMR spectrum, using a microscopic model that was shown previously to agree closely with x-ray experiments. The BdG results reproduce qualitative features of the experimental spectrum extremely well. These results are interpreted in terms of a generic "hotspot" model that allows one to trace the origins of the NMR lineshapes. We find that four quantities---the orbital character of the Fermi surface at the hotspots, the Fermi surface curvature at the hotspots, the CDW correlation length, and the magnitude of the subdominant CDW component---are key in determining the lineshapes.

Bond Model of Second‐ and Third‐Harmonic Generation in Body‐ and Face‐Centered Crystal Structures

In this work, we describe the third‐ and fourth‐rank tensors of body‐ and face‐centered cubic systems and derive the s‐ and p‐polarized SHG far field using the simplified bond‐hyperpolarizability model. We also briefly discuss bulk nonlinear sources in such structures: quadrupole contribution, spatial dispersion, electric‐field second‐harmonic generation, and third‐harmonic generation, deriving the corresponding fourth rank tensor. We show that all the third‐ and fourth‐rank tensorial elements require only one independent fitting parameter.

On the isotropy of induced multipole moments in heavy ion complexes.

Polarization effects have been proven to play an important role in the theoretical description of chemical processes. With this respect, we report ab initio calculations describing multiconfigurational and relativistic effects as well as electron correlation to determine dipole- and quadrupole polarizabilities for all trivalent actinide and lanthanide ions. The results are used in an iterative point-multipole model to compute polarization interaction for different metal compounds. Significant differences between the usage of isotropic polarizabilities for the coordinating ligands compared to the full tensor representation is found. Quadrupole contributions are found to be negligible for symmetric geometries but can contribute up to 30 kJ/mol to the polarization energy in specific cases. The employed method allows a parameter free study of multipole interactions for a wide variety of systems. © 2017 Wiley Periodicals, Inc.

Unraveling 5f-6d hybridization in uranium compounds via spin-resolved L-edge spectroscopy

The multifaceted character of 5f electrons in actinide materials, from localized to itinerant and in between, together with their complex interactions with 6d and other conduction electron states, has thwarted efforts for fully understanding this class of compounds. While theoretical efforts abound, direct experimental probes of relevant electronic states and their hybridization are limited. Here we exploit the presence of sizable quadrupolar and dipolar contributions in the uranium L3-edge X-ray absorption cross section to provide unique information on the extent of spin-polarized hybridization between 5f and 6d electronic states by means of X-ray magnetic circular dichroism. As a result, we show how this 5f-6d hybridization regulates the magnetism of each sublattice in UCu2Si2 and UMn2Si2 compounds, demonstrating the potentiality of this methodology to investigate a plethora of magnetic actinide compounds.

Bulk quadrupole contribution to second harmonic generation from classical oscillator model in silicon.

We predict the frequency-dependent bulk quadrupole contribution to second harmonic generation in silicon quantitatively from the linear susceptibility by means of a generalized classical anharmonic oscillator model and the simplified bond hyperpolarizability model. We show that in single-beam setups the main contribution is found for the silicon (111) surface, and only a minor contribution for the (001) and (011) facets. The dipole contribution obtained from our model is compared to literature values for SiC, AlAs and GaAs to demonstrate the viability of the method.