Monopole Contributions Research Articles

Anomalous Hall effect sensitive to magnetic monopoles and skyrmion helicity in spin–orbit coupled systems

Magnetic textures, such as skyrmions and domain walls, engender rich transport phenomena, including anomalous Hall effect and nonlinear response. In this work, we discuss an anomalous Hall effect proportional to the net magnetic monopole charge and dependent on the skyrmion helicity that occurs by a skew scattering in a noncentrosymmetric two-dimensional magnet. This mechanism, which arises from the spin–orbit interaction (SOI), gives rise to a finite anomalous Hall effect in a ferromagnetic domain wall whose spins rotate in the xy plane despite no out-of-plane magnetic moment. We show that the presence and absence of the monopole contribution is related to crystal symmetry, which gives a guideline for finding candidate materials beyond the Rashba model. The results demonstrate the rich features arising from the interplay of SOI and magnetic textures, and their potential for detecting various magnetic textures in micrometer devices.

Mechanical structure of a spin-1 particle

We investigate the mechanical structure of a spin-1 particle. Introducing three different frameworks, i.e., the three-dimensional (3D) Breit frame, the two-dimensional (2D) Breit frame, and the 2D infinite momentum frame (equivalently the two-dimensional Drell-Yan frame), we scrutinize the 2D and 3D energy-momentum tensor (EMT) distributions in these frames. We first derive the EMT distributions in the 2D Breit frame by performing the Abel transformation. The mass distribution in the 2D Breit frame contains an additional monopole contribution induced geometrically. The pressure distribution in the 2D Breit frame also gets an induced monopole structure. When the Lorentz boost is carried out, the mass distribution in the 2D infinite-momentum frame acquires the induced dipole term. Similarly, we also have the induced dipole contributions to the pressure and shear-force densities. We visualize the 2D mass distributions when the spin-1 particle is polarized along the $x$- and $z$-axes. We observe that the 2D mass distribution in the infinite momentum frame exhibit clearly the induced dipole structure when the spin-1 particle is polarized along the $x$-axis. We also discuss the strong force fields inside a polarized spin-1 particle.

Asymptotic symmetries and soft charges of fractons

The asymptotic structure of gauge theories describing fracton interactions is analyzed. Two sets of asymptotic conditions are proposed. Both encompass all known solutions, lead to finite charges and resolve the problem of the divergent energy coming from the monopole contribution. While the first set leads to the expected fracton symmetry algebra, including a dipole charge, the second set provides a soft infinite-dimensional extension of it. These soft charges provide evidence of a rich infrared structure for fractonlike theories and provide one corner of a possible fracton infrared triangle.

Vacuum polarization of Dirac fermions in the cosmological de Sitter global monopole spacetime

We study the vacuum polarization effects of the Dirac fermionic field induced by a pointlike global monopole located in the cosmological de Sitter spacetime. First we derive the four orthonormal Dirac modes in this background in a closed form. Quantizing the field using these modes, we then compute the fermionic condensate, $⟨0|\overline{\mathrm{\ensuremath{\Psi}}}\mathrm{\ensuremath{\Psi}}|0⟩$, as well as the vacuum expectation value of the energy-momentum tensor for a massive Dirac field, regularized in a particular way. We have used the Abel-Plana summation formula in order to extract the global monopole contribution to these quantities and have investigated their variations numerically with respect to relevant parameters.

Power spectrum multipole expansion for H i intensity mapping experiments: unbiased parameter estimation

ABSTRACT We assess the performance of the multipole expansion formalism in the case of single-dish H i intensity mapping, including instrumental and foreground removal effects. This formalism is used to provide Markov chain Monte Carlo forecasts for a range of H i and cosmological parameters, including redshift space distortions and the Alcock–Paczynski effect. We first determine the range of validity of our power spectrum modelling by fitting to simulation data, concentrating on the monopole, quadrupole, and hexadecapole contributions. We then show that foreground subtraction effects can lead to severe biases in the determination of cosmological parameters, in particular the parameters relating to the transverse Baryon Acoustic Oscillations (BAO) rescaling, the growth rate, and the H i bias (α⊥, $\overline{T}_\rm{H{\small I}}f\sigma _8$, and $\overline{T}_{\mathrm {H}\,{\small I}}b_{\mathrm {H}\,{\small I}}\sigma _8$, respectively). We attempt to account for these biases by constructing a two-parameter foreground modelling prescription, and find that our prescription leads to unbiased parameter estimation at the expense of increasing the estimated uncertainties on cosmological parameters. In addition, we confirm that instrumental and foreground removal effects significantly impact the theoretical covariance matrix, and cause the covariance between different multipoles to become non-negligible. Finally, we show the effect of including higher order multipoles in our analysis, and how these can be used to investigate the presence of instrumental and systematic effects in H i intensity mapping data.

Monopole contributions to refined Vafa–Witten invariants

We study the monopole contribution to the refined Vafa-Witten invariant, recently defined by Maulik and Thomas [13]. We apply results of Gholampour and Thomas [7] to prove a universality result for the generating series of contributions of Higgs pairs with 1-dimensional weight spaces. For prime rank, these account for the entire monopole contribution, by a theorem of Thomas. We use toric computations to determine part of the generating series, and find agreement with the conjectures of G\"ottsche and Kool [10] for rank 2 and 3.

New Abelian-like monopoles and the dual Meissner effect

Violation of non-Abelian Bianchi identity can be regarded as $N^2-1$ Abelian-like monopole currents in the continuum SU(N) QCD. Three Abelian-like monopoles, when defined in SU(2) gluodynamics on the lattice \`{a} la DeGrand-Toussaint, are shown to have the continuum limit with respect to the color-invariant monopole density and the effective monopole action. Since each Abelian-like monopole is not gauge invariant, we have introduced various partial gauge fixing for the purpose of reducing lattice artifact monopoles in the thermalized vacuum. Here we investigate Abelian and monopole dominances and the Abelian dual Meissner effects adopting the same gauges like the maximal center gauge (MCG) in comparison with the maximal Abelian gauge (MAG). Abelian and monopole contributions to the string tension in these gauges are observed to be a little smaller than the non-Abelian string tension. However, we find that the monopole dominance is improved well when use is made of the block-spin transformations with respect to Abelian-like monopoles. We find each electric field is squeezed by the corresponding colored Abelian-like monopole in such gauges and the Abelian dual Meissner effect is observed independently for each color. Moreover, we confirm the dual Amp\`{e}re's law in these new gauges as well as in MAG. The SU(2) vacuum is shown to be near the border between the type 1 and type 2 dual superconductors. The penetration length is almost equal for the four gauge fixings and the vacuum type in MCG is almost the same value as the previous results. These results are consistent with the previous results suggesting the continuum limit and the gauge-independence of Abelian monopoles.

Monopole Contribution to the Stark Width of Hydrogenlike Spectral Lines in Plasmas: Analytical Results

One of the most reliable and frequently used methods for diagnosing various laboratory and astrophysical plasmas is based on the Stark broadening of spectral lines. It allows for determining from the experimental line profiles important parameters, such as the electron density and temperature, the ion density, the magnetic field, and the field strength of various types of the electrostatic plasma turbulence. Since, in this method, radiating atoms or ions are used as the sensitive probes of the above parameters, these probes have to be properly calibrated. In other words, an accurate theory of the Stark broadening of spectral lines in plasmas is required. In the present paper, we study, analytically, the monopole contribution to the Stark width of hydrogen-like spectral lines in plasmas. For this purpose, we use the formalism from paper by Mejri, Nguyen, and Ben Lakhdar. We show that the monopole contribution to the width has a non-monotonic dependence on the velocity of perturbing electrons. Namely, at relatively small electron velocities, the width decreases as the velocity increases. Then it reaches a minimum and (at relatively large electron velocities), as the velocity further increases, the width increases. The non-monotonic dependence of the monopole contribution to the width on the electron velocity is a counter-intuitive result. The outcome that at relatively large electron velocities, the monopole contribution to the width increases with the increase in the electron velocity is in a striking distinction to the dipole contribution to the width, which decreases as the electron velocity increases. We show that, in the situation encountered in various areas of plasma research (such as in magnetically-controlled fusion), where there is a relativistic electron beam (REB) in a plasma, the monopole contribution to the width due to the REB exceeds the corresponding dipole contribution by four orders of magnitude and practically determines the entire Stark width of hydrogenic spectral lines due to the REB.

Equivariant K-Theory and Refined Vafa\u2013Witten Invariants

In Maulik and Thomas (in preparation) the Vafa–Witten theory of complex projective surfaces is lifted to oriented {mathbb {C}}^*-equivariant cohomology theories. Here we study the K-theoretic refinement. It gives rational functions in t^{1/2} invariant under t^{1/2}leftrightarrow t^{-1/2} which specialise to numerical Vafa–Witten invariants at t=1. On the “instanton branch” the invariants give the virtual chi ^{}_{-t}-genus refinement of Göttsche–Kool, extended to allow for strictly semistable sheaves. Applying modularity to their calculations gives predictions for the contribution of the “monopole branch”. We calculate some cases and find perfect agreement. We also do calculations on K3 surfaces, finding Jacobi forms refining the usual modular forms, proving a conjecture of Göttsche–Kool. We determine the K-theoretic virtual classes of degeneracy loci using Eagon–Northcott complexes, and show they calculate refined Vafa–Witten invariants. Using this Laarakker (Monopole contributions to refined Vafa–Witten invariants. arXiv:1810.00385) proves universality results for the invariants.

Energy momentum tensor and the D term in the bag model

The energy-momentum tensor (EMT) form factors pave new ways for exploring hadron structure. Especially the D-term related to the EMT form factor D(t) has received a lot of attention due to its attractive physical interpretation in terms of mechanical properties. We study the nucleon EMT form factors and the associated densities in the bag model which we formulate for an arbitrary number of colors Nc and show that the EMT form factors are consistently described in this model in the large-Nc limit. The simplicity of the model allows us to test in a lucid way many theoretical concepts related to EMT form factors and densities including recently introduced concepts like normal and tangential forces, or monopole and quadrupole contributions to the angular momentum distribution. We also study the D-terms of rho-meson, Roper resonance, other N* states and Delta-resonances. Among the most interesting outcomes is the lucid demonstration of the deeper connection of EMT conservation, stability, the virial theorem and the negative sign of the D-term.

Electric Hyperfine Interactions of 57Fe Impurity Atoms in ACrO3 Perovskite-Type Chromites (A = Sc, In, Tl, Bi)

Perovskite-type chromites ACr0.9557Fe0.05O3 (A = Sc, In, Tl, Bi) have been studied by probe Mossbauer spectroscopy on 57Fe nuclei. The spectra of the ACr0.9557Fe0.05O3 samples (A = Sc, In, Bi) measured above the Neel temperature TN indicate the presence of several nonequivalent positions occupied by impurity iron atoms in all chromites. To explain significant differences in quadrupole splittings, semi-empirical calculations of the electric field gradient have been performed for all studied compounds within the ionic model taking into account monopole and dipole contributions. The performed calculations are in satisfactory agreement with experimental data.

\u2019t Hooft defects and wall crossing in SQM

In this paper we study the contribution of monopole bubbling to the expectation value of supersymmetric ’t Hooft defects in Lagrangian theories of class S on ℝ3× S1. This can be understood as the Witten index of an SQM living on the world volume of the ’t Hooft defect that couples to the bulk 4D theory. The computation of this Witten index has many subtleties originating from a continuous spectrum of scattering states along the non-compact vacuum branches. We find that even after properly dealing with the spectral asymmetry, the standard localization result for the ’t Hooft defect does not agree with the result obtained from the AGT correspondence. In this paper we will explicitly show that one must correct the localization result by adding an extra term to the standard Jeffrey-Kirwan residue formula. This extra term accounts for the contribution of ground states localized along the non-compact branches. This extra term restores both the ex- pected symmetry properties of the line defect expectation value and reproduces the results derived using the AGT correspondence.

Background photon temperature T¯ : A new cosmological Parameter?

The background photon temperature $\bar T$ is one of the fundamental cosmological parameters. Despite its significance, $\bar T$ has never been allowed to vary in the data analysis, owing to the precise measurement of the comic microwave background (CMB) temperature by COBE FIRAS. However, even in future CMB experiments, $\bar T$ will remain unknown due to the unknown monopole contribution $\Theta_0$ at our position to the observed (angle-averaged) temperature $\langle T\rangle^{\rm obs}$. By fixing $\bar T\equiv\langle T\rangle^{\rm obs}$, the standard analysis underestimates the error bars on cosmological parameters, and the best-fit parameters obtained in the analysis are biased in proportion to the unknown amplitude of $\Theta_0$. Using the Fisher formalism, we find that these systematic errors are smaller than the error bars from the $Planck$ satellite. However, with $\bar T\equiv\langle T\rangle^{\rm obs}$, these systematic errors will always be present and irreducible, and future cosmological surveys might misinterpret the measurements.

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.

The contribution of magnetic monopoles to the ponderomotive force

When magnetic monopoles are assumed to exist in plasma dynamics, the propagation of electromagnetic waves is modified as Maxwell equations acquire a symmetrical structure due to the existence of electric and magnetic charge and current densities. This work presents a theoretical exploration on how far we can push the limits of a plasma theory under the presence of magnetic monopoles. In particular, we study the modification of ponderomotive forces in a plasma composed by electric and magnetic charges. We show that the general ponderomotive force on this plasma depends non-trivially on the magnetic monopoles, through the slow temporal and spatial variations of the electromagnetic field amplitudes. The magnetic charges introduce corrections even if the plasma is unmagnetized. Also, it is shown that the magnetic monopoles also experience a ponderomotive force due to the electrons. This force is in the direction of propagation of the electromagnetic waves.

Non-perturbative probability distribution function for cosmological counts in cells

We present a non-perturbative calculation of the 1-point probability distribution function (PDF) for the spherically-averaged matter density field. The PDF is represented as a path integral and is evaluated using the saddle-point method. It factorizes into an exponent given by a spherically symmetric saddle-point solution and a prefactor produced by fluctuations. The exponent encodes the leading sensitivity of the PDF to the dynamics of gravitational clustering and statistics of the initial conditions. In contrast, the prefactor has only a weak dependence on cosmology. It splits into a monopole contribution which is evaluated exactly, and a factor corresponding to aspherical fluctuations. The latter is crucial for the consistency of the calculation: neglecting it would make the PDF incompatible with translational invariance. We compute the aspherical prefactor using a combination of analytic and numerical techniques. We demonstrate the factorization of spurious enhanced contributions of large bulk flows and their cancellation due to the equivalence principle. We also identify the sensitivity to the short-scale physics and argue that it must be properly renormalized. The uncertainty associated with the renormalization procedure gives an estimate of the theoretical error. For zero redshift, the precision varies from sub percent for moderate density contrasts to tens of percent at the tails of the distribution. It improves at higher redshifts. We compare our results with N-body simulation data and find an excellent agreement.

Born approximation of acoustic radiation force and torque on soft objects of arbitrary shape

When the density and compressibility of an object are similar to the corresponding properties of the surrounding fluid, and the dominant contribution to the acoustic radiation force depends on gradients of the energy densities as occurs in plane standing waves, the Born approximation may be used to calculate both the radiation force and torque. The approximation consists of integrating the monopole and dipole contributions to the force throughout the volume of the object, and thus it is applicable to objects with arbitrary shapes and material property distributions. Here, an axisymmetric object in a plane standing wave is considered, resulting in one-dimensional integral expressions for the radiation force and torque. The integrals are evaluated analytically for homogeneous spheres and cylinders. The accuracy of the approximation is assessed via comparison with full solutions for spheres and prolate spheroids based on eigenfunction expansions for the corresponding scattering problem. Different densities and compressibilities of the object and the surrounding medium, as well as different sizes, shapes, and orientations of the object relative to the standing wave field, are considered. Limitations of the approximation and potential extensions to more complex wave fields are discussed. [T.S.J. supported by the ARL:UT McKinney Fellowship in Acoustics.]

Born approximation of acoustic radiation force and torque on soft objects of arbitrary shape

When the density and compressibility of an object are similar to the corresponding properties of the surrounding fluid and the incident sound field is a standing wave, the Born approximation may be used to calculate the acoustic radiation force and torque on an object of arbitrary shape. The approximation consists of integration over the monopole and dipole contributions to the force acting at each point within the region occupied by the object. The method is applied to axisymmetric objects, for which the force and torque may be expressed as a single integral along the axis of symmetry. The integral is evaluated analytically for spheres and cylinders. The accuracy of the Born approximation is assessed by comparison with complete solutions for compressible spheres and prolate spheroids that are based on expansions of the incident, scattered, and transmitted fields in terms of eigenfunctions of the corresponding separable coordinate system. Results are presented for objects with various densities and compressibilities relative to the surrounding fluid, as well as different shapes, sizes, and orientations of the object with respect to the standing wave field. The method also accommodates spatial variations of the density and compressibility within the object.

Probe Mössbauer Spectroscopy of BiNi0.9657Fe0.04O3

This paper presents results of a 57Fe probe Mossbauer spectroscopy study of the BiNi0.9657Fe0.04O3 nickelate. The spectra measured above its TN demonstrate that Fe3+ cations heterovalently substitute for Ni2+ nickel (←Fe3+), being stabilized on four sites of the nickel sublattice in the structure of BiNiO3. Calculations in an ionic model with allowance for monopole and dipole contributions to the electric field gradient indicate that the parameters of electric hyperfine interactions between 57Fe probe atom nuclei reflect the specifics of the local environment of the nickel in the structure of the unsubstituted BiNiO3 nickelate. Below TN, Mossbauer spectra transform into a complex Zeeman structure, which is analyzed in terms of first-order perturbation theory with allowance for electric quadrupole interactions as a small perturbation of the Zeeman levels of the 57Fe hyperfine structure, as well as for specific features of the magnetic ordering of the Ni2+ cations in the nickelate studied.

Scalar radiation from a radially infalling source into a Schwarzschild black hole in the framework of quantum field theory

We investigate the radiation to infinity of a massless scalar field from a source falling radially towards a Schwarzschild black hole using the framework of the quantum field theory at tree level. When the source falls from infinity, the monopole radiation is dominant for low initial velocities. Higher multipoles become dominant at high initial velocities. It is found that, as in the electromagnetic and gravitational cases, at high initial velocities the energy spectrum for each multipole with l ge 1 approximately is constant up to the fundamental quasinormal frequency and then drops to zero. We also investigate the case where the source falls from rest at a finite distance from the black hole. It is found that the monopole and dipole contributions in this case are dominant. This case needs to be carefully distinguished from the unphysical process where the source abruptly appears at rest and starts falling, which would result in radiation of an infinite amount of energy. We also investigate the radiation of a massless scalar field to the horizon of the black hole, finding some features similar to the gravitational case.