Showing papers on "Scalar potential published in 2022"

Relativistic motions of spin-zero quantum oscillator field in a global monopole space-time with external potential and AB-effect

Abstract: In this paper, we analyze a spin-zero relativistic quantum oscillator in the presence of the Aharonov-Bohm magnetic flux in a space-time background produced by a point-like global monopole (PGM). Afterwards, we introduce a static Coulomb-type scalar potential and subsequently with the same type of vector potential in the quantum system. We solve the generalized Klein-Gordon oscillator analytically for different functions (e.g. Coulomb- and Cornell-type functions) and obtain the bound-states solutions in each case. We discuss the effects of topological defects associated with the scalar curvature of the space-time and the Coulomb-type external potentials on the energy profiles and the wave function of these oscillator fields. Furthermore, we show that the obtained energy eigenvalues depend on the magnetic quantum flux which gives rise to the gravitational analogue of the Aharonov-Bohm (AB) effect.

Systematics of type IIB moduli stabilisation with odd axions

Abstract: Moduli stabilisation in superstring compactifications on Calabi-Yau orientifolds remains a key challenge in the search for realistic string vacua. In particular, odd moduli arising from the reduction of 2-forms $(B_2,C_2)$ in type IIB are largely unexplored despite their relevance for inflationary model building. This article provides novel insights into the general structure of 4D $\mathcal{N}=1$ $F$-term scalar potentials at higher orders in the $\alpha^{\prime}$ and $g_{s}$ expansion for arbitrary Hodge numbers. We systematically examine superpotential contributions with distinct moduli dependences which are induced by fluxes or non-perturbative effects. Initially, we prove the existence of a no-scale structure for odd moduli in the presence of $(\alpha^\prime)^{3}$ corrections to the K\"ahler potential. By studying a partially $\mathrm{SL}(2,\mathbb{Z})$-completed form of the K\"ahler potential, we derive the exact no-scale breaking effects at the closed string $1$-loop and non-perturbative D-instanton level. These observations allow us to present rigorous expressions for the $F$-term scalar potential applicable to arbitrary numbers of moduli in type IIB Calabi-Yau orientifold compactifications. Finally, we compute the Hessian for odd moduli and discuss potential phenomenological implications.

Cornell potential in generalized Soft Wall holographic model

Abstract: We derive and analyze the confinement potential of the Cornell type within the framework of the generalized Soft Wall holographic model that includes a parameter controlling the intercept of the linear Regge spectrum. In the phenomenology of Regge trajectories, this parameter is very important for the quantitative description of experimental data. Our analysis shows that the "linear plus Coulomb'' confinement potential obtained in the scalar channel is quantitatively consistent with the phenomenology and lattice simulations while the agreement in the vector channel is qualitative only. This result indicates the key role of the vacuum scalar sector in the formation of the confinement potential. As a by-product the overall consistency of our holographic description of confinement potential seems to confirm the glueball nature of the scalar meson f0(1500).

The robustness of slow contraction and the shape of the scalar field potential

Abstract: We use numerical relativity simulations to explore the conditions for a canonical scalar field ϕ minimally coupled to Einstein gravity to generate an extended phase of slow contraction that robustly smooths the universe for a wide range of initial conditions and then sets the conditions for a graceful exit stage. We show that to achieve robustness it suffices that the potential V(ϕ) is negative and M Pl|V, ϕ /V|≳5 during the smoothing phase. We also show that, to exit slow contraction, the potential must have a minimum. Beyond the minimum, we find no constraint on the uphill slope including the possibility of ending on a positive potential plateau or a local minimum with V min > 0. Our study establishes ultralocality, i.e., all spatial gradients quickly becoming negligible, for a wide range of potentials as a key both to robust smoothing and to graceful exit.

A Quasi-Mixed-Potential Layered Medium Green’s Function for Non-Galerkin Surface Integral Equation Formulations

Abstract: A quasi-mixed-potential layered medium Green’s function (QMP-LMGF) is proposed for non-Galerkin surface integral equation (SIE) formulations in the modeling of homogeneous dielectric objects in layered medium. The formulation is derived based on the pilot vector potential approach. In this method, the field-type LMGF in the $L$ -operator is decomposed into two parts, a “vector potential” term in a dyadic form, and a “scalar potential” term in a vector form, to represent the field components from current and charge sources, respectively. Since the proposed two potential terms (vector potential and scalar potential) do not satisfy the Lorenz gauge, we term them as quasi-mixed-potentials. The property of the two potentials is investigated to reveal that the proposed QMP-LMGF is compatible with the vector and scalar potentials in free space. Moreover, due to the continuity of the integration kernels across the interfaces, undesired line integrals are absent in the proposed QMP-LMGF when the objects are straddling different layers. Three popular non-Galerkin SIEs for dielectric objects in layered medium are studied, and the corresponding numerical results are demonstrated to validate the proposed method.

Active Electric Dipole Energy Sources: Transduction via Electric Scalar and Vector Potentials

Abstract: An active electrical network contains a voltage or current source that creates electromagnetic energy through a method of transduction that enables the separation of opposite polarity charges from an external source. The end result is the creation of an active dipole with a permanent polarisation and a non-zero electric vector curl. The external energy input impresses a force per unit charge within the voltage source, to form an active physical dipole in the static case, or an active Hertzian dipole in the time dependent case. This system is the dual of an electromagnet or permanent magnet excited by a circulating electrical current or fictitious bound current respectively, which supplies a magnetomotive force described by a magnetic vector potential with a magnetic geometric phase proportional to the enclosed magnetic flux. In contrast, the active electric dipole may be described macroscopically by a circulating fictitious magnetic current boundary source described by an electric vector potential with an electric geometric phase proportional to the enclosed electric flux density. This macroscopic description of an active dipole is an average description of some underlying microscopic description exhibiting emergent nonconservative behaviour not found in classical conservative laws of electrodynamics. We show that the electromotive force produced by an active dipole must have both electric scalar and vector potential components to account for the magnitude of the voltage it produces. Following this we analyse an active cylindrical dipole in terms of scalar and vector potential and confirm that the electromotive force produced, and hence potential difference across the terminals is a combination of vector and scalar potential difference depending on aspect ratio of the dipole.

A comparison of φ formulae for three-dimensional geo-electromagnetic induction problems

Abstract: Geo-electromagnetic forward modeling problems are ill-posed due to the low signal frequencies being used and electrically insulating air space. To overcome this numerical issue, the $A - \phi $ formula using the magnetic vector potentials ($\bf A$) and electric scalar potentials ($\phi $) was developed. At present, there are two sets of $A - \phi $ formulae being used: one has a curl–curl ($ abla \times abla $) structure and another one has a Laplace (${ abla ^2}$) structure where the Coulomb gauge is enforced. The question as to which of the two approaches have superior performance for 3D geo-electromagnetic induction problems still remains open. In this study, we systemically compared the performances of these two $A - \phi $ systems in terms of both numerical accuracy and convergence rate. Numerical experiments suggest that for both magnetotelluric and controlled-source electromagnetic problems, the $A - \phi $ system with Laplace structure has better performance than the variant with curl–curl structure in terms of convergence rates.

Comparison of nodal and edge basis functions for the forward modelling of three‐dimensional frequency‐domain wire source electromagnetic data using a potentials formulation

Abstract: An investigation of forward modelling 3‐D wire source electromagnetic data in the frequency domain using nodal and edge finite‐element basis functions is presented. The equations solved are those for the coupled secondary vector–scalar potentials (i.e. magnetic vector potential A and electric scalar potential φ), which give rise to a less ill‐conditioned system of equations to be solved. The effectiveness of these two methods is validated with two 3‐D examples, i.e. multi‐blocks models and topography models, which considered the computation of the A–φ potentials and the electromagnetic fields due to a grounded electric line source by inter‐comparing the numerical solutions computed from each method and by comparing them against the equivalent solutions for the same model computed using other methods. Based on the multiple‐blocks models, we compare the relative contributions of the inductive and galvanic parts to the E‐field for different frequencies. Results show that for the type of source considered in this paper, the galvanic parts dominate for a relatively low frequency (10 Hz), but that for a relatively high frequency (10 kHz), the inductive parts also contribute. The extent to which the Coulomb gauge condition is satisfied when using nodal basis functions for A is also investigated, with results showing that the divergence of the numerically calculated A is almost zero as desired. Based on the topography models, we analyse the electromagnetic response characteristics at different survey planes, with results of this investigation indicating that the electromagnetic responses measured over a plane close to the target will carry more accurate geometry information (such as position, shape and size) of the target, which is expected, and less distortion due to topography compared to those measured at the earth's surface. This suggests that when conducting electromagnetic prospecting in an area with complex topography, it is possible to obtain better anomaly detection affected less by topography if the electromagnetic measurement is carried out underground (such as in a borehole).

Lower Tensor to Scalar Ratio in a SUGRA Motivated Inflationary Potential

Abstract: A scalar potential obtained from the $D$-term in the Supergravity models, which dominates over $F$ term and is mainly responsible for the inflationary phase in the early universe, is studied. The potential with canonical kinetic terms for scalar fields in the Lagrangian, has a very slow roll feature in comparison to various other plateau type inflationary potentials. In this case, a much lower tensor-to-scalar ratio ($r$) of $\mathcal{O}(10^{-3})$ is achievable. The requirement of slow roll condition for the inflation potential implies that the up type neutral scalar and the down type neutral scalar in Supergravity models are with equal field strength at the time of inflation. If this relationship holds down to the electroweak scale for the corresponding $vev$ values of these fields, then it will indicate a higher SUSY breaking scale around 100 TeV. The predicted values of the inflationary observables are well within the 1-$\sigma$ bounds of the recent constraints from {\it Planck'18} observations. The era of reheating after the inflationary phase, is also studied and the bounds on the reheating temperature ($T_{re}$) is calculated for a different equation of states during reheating ($w_{re}$) for the {\it Planck'18} allowed values of the scalar spectral index ($n_s$). For our model with $w_{re}=2/3$ and $w_{re}=1$, after satisfying all the bounds due to gravitino overproduction, we can have big parameter space for $T_{re}$ which is well inside {\it Planck'18} 1-$\sigma$ bound on $n_s$.

A 3D Phase Space Analysis of Scalar Field Potentials

Abstract: In this study, we present the phase-space analysis of Quintessence models specified by the choice of two potentials, namely the Recliner potential and what we call the broken exponential-law potential, which is a new proposal. Using a dynamical system analysis we provide a systematic study of the cosmological evolution of the two models and their properties. We find new scaling solutions characterised by a constant ratio between the energy density of the scalar field and that of the matter component. These solutions are of high interest in light of the possibility to alleviate the coincidence problem. Additionally, the models also show attractor solutions. We finally construct concrete models built using a double potential according to which one potential realises the early-time scaling regime and the second one allows to exit this regime and to enter in the epoch of cosmic acceleration driven by a scalar-field dominated attractor point.

Regular Electric Field in Electromagnetic Coupled to a Scalar Field

Abstract: In the framework of an electromagnetic field coupled nonminimally with a scalar field in flat spacetime, the existence of a non‐singular electric field is proved for a point electric charge or electric monopole. In analogy with the Maxwell‐dilaton system introduced by Gibbons and Wells, first, a Maxwell‐anti‐dilaton system is constructed where the radial electric field of a static electric monopole is coupled to an anti‐dilaton. The field equations are solved analytically for the electric and dilaton fields and observe the nonsingular electric field. Also, the self‐energy of the electric monopole is found to be finite. Furthermore, the formalism to a Maxwell‐scalar field is generalized where a mechanism is introduced upon which the coupled regular‐electric field and scalar field is obtained. The formalism shows that for a given regular electric field there are two supersymmetric coupling functions corresponding to a scalar and a phantom field.

Generating a Cauer Ladder Network Representation of Eddy Current Fields Using Scalar Potentials

Abstract: Formulations in terms of scalar potentials are proposed to solve the static field problems occurring when computing the parameters of a Cauer ladder network representation of two-pole devices involving eddy-current effects. The curl equations are satisfied by efficiently generating vector potentials describing the known flux density and current density and introducing unknown scalar potentials to represent the electric and magnetic field intensities. The scalar potentials are approximated using nodal basis functions in the finite-element realization, thus leading to Poisson equations to be easily solved. A simple numerical example illustrates the method.

Finite-element modelling of magnetic fields for superconducting magnets with magnetic vector and total scalar potentials using COMSOL Multiphysics®

Abstract: The finite-element modelling of superconducting magnets is a resource-hungry and challenging work. For these devices, the high-quality requirements for focusing fields are usually superimposed by complexity of the model geometries and nonlinearity of the magnetic materials. The precise field simulations could result therefore in substantial number of the degrees of freedom and, as a consequence, in significant usage of the computational resources. To achieve the acceptable accuracy with lower number of finite elements, the magnetic field distributions are calculated in terms of the magnetic vector potential (A-formulation) as well as the total scalar potential (V-formulation) with COMSOL Multiphysics® and is compared. For these calculations, we utilise the model of a superconducting dipole magnet recently designed for operation of the compact isochronous cyclotron SC200. The performance of both methods is analysed in terms of accuracy and quality of the obtained fields as well as in terms of the computational cost.

The iBEM for potential problems

Abstract: Following the application of iBEM for elastic analysis, this chapter introduces the iBEM application and implementation for the scalar potential problems, which is applicable to linear flows such as heat, electric, magnetic, or ground water flows. Using heat conduction as an example, we extend similar development process for elastic problems with displacement potentials to a scalar potential such as temperature. We introduce an eigentemperature gradient to simulate the mismatch of thermal conductivities of inhomogeneities. A case study shows the application of iBEM toward virtual experiments.

FiPo FDTD: Computational Electrodynamics Technique Producing Both Fields and Potentials

Abstract: We present the field-potential finite-difference time-domain (FiPo FDTD) algorithm, which solves a set of first-order equations for the electric and magnetic fields (E and H), as well as the magnetic vector potential A and the scalar electric potential $\phi$ in the Lorenz gauge. We also present the derivation and implementation of a convolutional perfectly matched layer absorbing boundary condition for this new set of equations. Potentials A and $\phi$ can be used as input for the single-particle electron Hamiltonian in quantum transport solvers.

Mathematical apparatus for modeling of the propagation the magnetic field electric machines with a given accuracy

Abstract: . The problem of modeling the propagation local magnetic fields and spatially dispersed sources is large errors compared to field measurements. An important aspect of adequate modeling is the use of the correct mathematical apparatus. It is shown that in order to obtain reliable models of the propagation magnetic fields around electrical machines (generators, electric motors of different power, geometric dimensions and poles), it is advisable to apply the Gauss equation for a scalar potential. The solution of the equation in polar coordinates makes it possible to take into account not only the fundamental, but also other harmonics of the magnetic field (dipole, quadrupole, octupole). This allows, depending on the number of spatial harmonics taken into account, to obtain a model with the required accuracy (error) for predicting the magnetic field strength at any point around the machine. It is considered in the paper that an electronic machine is an object of base radius R0. The presented approach makes it possible to unambiguously determine the location of zero field points at a distance from the source (for a quadrupole source and zero field lines, for an octupole source). The results of modeling and their verification by full-scale measurements for the most common four-pole machines (quadrupole source) are presented. The main task of modeling the propagation the magnetic field of such sources is to ensure the required accuracy based on the goals of modeling. It is shown that the modeling accuracy and the presence of zero field points are due to different field levels near the electrical machine housing for different harmonics. The dipole harmonic at the cabinet is 20% of its own harmonic. But it falls more slowly with distance. This necessitates taking into account a different number of harmonics depending on the value of the ratio R0/R, R is the distance to the point of determining the field strength from the source. Therefore, with the ratio R0/R=2/3, the eighth harmonic is essential. At R0/R=1/5, already the fourth spatial harmonic can be neglected. Such data allow you to choose a rational number of harmonics. This reduces the amount of calculations and simplifies the process of modeling the propagation of the magnetic field around the source.

Klein-Gordon Oscillator with Scalar and Vector Potentials in Topologically Charged Ellis-Bronnikov type Wormhole

Abstract: In this work, we study the Klein-Gordon oscillator with equal scalar and vector potentials in a topologically charged Ellis-Bronnikov wormhole space-time background. The behaviour of a relativistic oscillator field is studied with a position-dependent mass via transformation $M^{2}\rightarrow (M+S(x))^{2}$ and vector potential through a minimal substitution in the wave equation. Simplifying the Klein-Gordon oscillator equation for three different types of potential, such as linear confining, Coulomb-type, and Cornell-type potential and we arrive at a second-order differential equation known as the biconfluent Heun (BCH) equation and the corresponding confluent Heun function. Finally, we solve the wave equation by the Frobenius method as a power series expansion around the origin and obtain the energy levels and the wave function.

Vacuum decay in quadratic gravity

Abstract: Metastable states decay at zero temperature through quantum tunneling at an exponentially small rate, which depends on the Coleman-de Luccia instanton, also known as bounce. In some theories, the bounce may not exist or its on-shell action may be ill-defined or infinite, thus hindering the vacuum decay process. In this paper, we test this possibility in modified theories of gravity interacting with a real scalar field. We consider an Einstein-Hilbert term with a non-minimally coupled scalar field and a quadratic Ricci scalar contribution. To tackle the problem we use a new analytic method, with which we prove that the scalar field on the bounce has a universal behaviour at large Euclidean radii, almost independently of the potential. Our main result is that the quadratic Ricci scalar prevents the decay, regardless of the other terms in the action.

Analytical Approach to Calculate Idealized Surface Current for a Shielded Magnetic Field Coil in a Separable Coordinate System

Abstract: <p>A theoretical method is described to analytically calculate a pair of surface current densities which produce a desired static magnetic field in one region of the space, and zero magnetic field in another. The analysis is based on the known relationship between a surface current density and a stream function, the equivalence of stream functions and surface magnetic dipole density, and the scalar potential representation of the associated magnetic field in free space. From these relations, we formulate the magnetostatics problem, which is often treated as a vector field problem, as a scalar field problem in which a two-dimensional scalar field (stream function) is related to a three-dimensional one (magnetic scalar potential) via the differentiation of the electrostatic Green’s function 1/|r-r_s|. It is shown that, in a coordinate system in which a separated form of the Green’s function exists (separable coordinate system), there exists a simple relationship between a harmonic component of a stream function and a harmonic component of the magnetic scalar potential. The method is applied to calculate idealized surface current patterns for actively shielded, magnetic resonance imaging (MRI) gradient coils in the Cartesian, cylindrical, and spherical coordinates.</p>

Generalized Hertz vector in the dissipative electrodynamics

Abstract: In the electromagnetic theory, the Hertz vector reduces the number of potentials in the free fields. The further advantage of this potential is that it is much easier to solve some radiation processes. It indicates that the related method is sometimes more effective than the scalar and vector potential-based relations. Finally, the measurable field variables, the electric and magnetic fields, can be deduced by direct calculation from the Hertz vector. However, right now, the introduction of the Hertz vector operates if the conductive currents j = {\sigma}E are neglected. We suggest a generalization for the case of conductive currents, i.e., for such cases when the electromagnetic field dissipates irreversibly into Joule heat. The presented procedure enables us to introduce also the Lagrangian formulation of the discussed dissipated electromagnetic waves. It opens a new way for future studies.

Dirac-harmonic maps with potential

Abstract: We study the influence of an additional scalar potential on various geometric and analytic properties of Dirac-harmonic maps. We will create a mathematical wish list of the possible benefits from inducing the potential term and point out that the latter cannot be achieved in general. Finally, we focus on several potentials that are motivated from supersymmetric quantum field theory.

Effect of magnetic field on fermions in graphene through time-oscillating potential

Abstract: We study the effect of a magnetic field on Dirac fermions in graphene subject to a scalar potential oscillating in time. Using the Floquet theory and resonance approximation, we show that the energy spectrum exhibits extra subbands resulted from the oscillating potential in addition to quantized Landau levels. It is found that a current density can be generated in $ x $ and $ y $-directions that is strongly dependent on the magnetic field and potential. Our numerical analysis show that the energy spectrum possesses a symmetry and the current density oscillates with different amplitudes under various conditions.

A Generalized Scalar Potential Integral Equation Formulation for the DC Analysis of Conductors

Abstract: The electrostatic modeling of conductors is a fundamental challenge in various applications, including the prediction of parasitic effects in electrical interconnects, the design of biasing networks, and the modeling of biological, microelectromechanical, and sensing systems. The boundary element method (BEM) can be an effective simulation tool for these problems because it allows modeling three-dimensional objects with only a surface mesh. However, existing BEM formulations can be restrictive because they make assumptions specific to particular applications. For example, capacitance extraction formulations usually assume a constant electric scalar potential on the surface of each conductor and cannot be used to model a flowing current, nor to extract the resistance. When modeling steady currents, many existing techniques do not address mathematical challenges such as the null space associated with the operators representing the internal region of a conductor. We propose a more general BEM framework based on the electric scalar potential for modeling conductive objects in various scenarios in a unified manner. Restrictive application-specific assumptions are not made, and the aforementioned operator null space is handled in an intuitive and rigorous manner. Numerical examples drawn from diverse applications confirm the accuracy and generality of the proposed method.

Modeling and Simulation of Magnetic Balance Current Sensor Based on Magnetic Scalar Potential Volume Integral

Abstract: In this paper, a field–circuit combined simulation method, based on the magnetic scalar potential volume integral equation (MSP-VIE) and its fast algorithms, are proposed for the transient simulation and nonlinear distortion analysis of the magnetic balance current sensor. The magnetic part of the sensor is modeled and simulated by MSP-VIE with the field matrices extracted by the method of moments. By directly implementing the magnetic field equation in the circuit, these field matrices can be regarded as equivalent circuit parameters of the magnetic part, to construct the corresponding SPICE model. Finally, the field–circuit combined model of the entire sensor is unified in a circuit, so with the SPICE solver, the transient simulation is accomplished in the time domain. Moreover, aiming at the time-consuming problem, this paper presents a corresponding fast method to accelerate the simulation. The comparison of measurement and simulation demonstrates that the proposed method not only realizes the transient simulation of the whole sensor, but also simulates some hidden performance details; thus, it can be applied to practical engineering, to guide and test the early design of the product.

Stress Function Formulation

Abstract: AbstractNewton’s law of gravitation states that two heavy bodies attract each other with a force proportional to the inverse square of their distance — thus it is essentially a vector theory, being concerned with forces. However, the idea of a scalar gravitational potential can be introduced by defining the work done in moving a unit mass from infinity to a given point in the field. The principle of conservation of energy requires that this be a unique function of position and it is easy to show that the gravitational force at any point is then proportional to the gradient of this scalar potential. Thus, the original vector problem is reduced to a problem about a scalar potential and its derivatives.

Co-positivity of tensors and Stability conditions of CP conserving two-Higgs-doublet potential

Abstract: We give how to calculate the vacuum stability conditions of scalar potential for two Higgs doublet model with explicit CP conservation. Moreover, the analytical sufficient and necessary conditions are obtained. The argument methods are first used to study the tensor with two parameters.