Static Electromagnetic Fields Research Articles

On Lorentz Invariant Complex Scalar Fields

We obtain a Lorentz covariant wave equation whose complex wave function transforms under a Lorentz boost according to the following rule, Ψ x ⟶ e i / ℏ f x Ψ x . We show that the spacetime-dependent phase f x is the most natural relativistic extension of the phase associated with the transformation rule for the nonrelativistic Schrödinger wave function when it is subjected to a Galilean transformation. We then generalize the previous analysis by postulating that Ψ x transforms according to the above rule under proper Lorentz transformations (boosts or spatial rotations). This is the most general transformation rule compatible with a Lorentz invariant physical theory whose observables are bilinear functions of the field Ψ x . We use the previous wave equations to describe several physical systems. In particular, we solve the bound state and scattering problems of two particles which interact both electromagnetically and gravitationally (static electromagnetic and gravitational fields). The former interaction is modeled via the minimal coupling prescription while the latter enters via an external potential. We also formulate logically consistent classical and quantum field theories associated with these Lorentz covariant wave equations. We show that it is possible to make those theories equivalent to the Klein-Gordon theory whenever we have self-interacting terms that do not break their Lorentz invariance or if we introduce electromagnetic interactions via the minimal coupling prescription. For interactions that break Lorentz invariance, we show that the present theories imply that particles and antiparticles behave differently at decaying processes, with the latter being more unstable. This suggests a possible connection between Lorentz invariance-breaking interactions and the matter-antimatter asymmetry problem.

Nonlinear electromagnetic fields in strictly stationary spacetimes

We prove two theorems which imply that any stationary nonlinear electromagnetic field obeying a dominant energy condition in a strictly stationary, everywhere regular, asymptotically flat spacetime must be either trivial or a stealth field. The first theorem holds in static spacetimes and is independent of the gravitational part of the action, as long as the coupling of the electromagnetic field to the gravitational field is minimal. The second theorem assumes Einstein--Hilbert gravitational action and relies on the positive energy theorem, but does not assume that the spacetime metric is static. In addition, we discuss possible generalizations of these results, to theories with charged matter, as well as higher-dimensional nonlinear electromagnetic fields.

Single Charged Particle Motion in a Flat Surface with Static Electromagnetic Field and Quantum Hall Effect

Taking into account the non separable solution for the quantum problem of the motion of a charged particle in a flat surface of lengths Lx and Ly with transversal static magnetic field B and longitudinal static electric field E, the quantum current, the transverse (Hall) and longitudinal resistivities are calculated for the state n = 0 and j = 0. We found that the transverse resistivity is proportional to an integer number, due to the quantization of the magnetic flux, and longitudinal resistivity can be zero for times t >> LxB/cE. In addition, using a modified periodicity of the solution, a modified quantization of the magnetic flux is found which allows to have IQHE and FQHE of any filling factor of the form v = k/l, with k, l ∈ Z.

Riemannian geometry of resonant optical responses

The geometry of quantum states is well-established as a basis for understanding the response of electronic systems to static electromagnetic fields, as exemplified by the theory of the quantum and anomalous Hall effects. However, it has been challenging to relate quantum geometry to resonant optical responses. The main obstacle is that optical transitions involve a pair of states, while existing geometrical properties are defined for a single state. As a result, a concrete geometric understanding of optical responses has so far been limited to two-level systems, where the Hilbert space is completely determined by a single state and its orthogonal complement. Here, we construct a general theory of Riemannian geometry for resonant optical processes by identifying transition dipole moment matrix elements as tangent vectors. This theory applies to arbitrarily high-order responses, suggesting that optical responses can generally be thought of as manifestations of the Riemannian geometry of quantum states. We use our theory to show that third-order photovoltaic Hall effects are related to the Riemann curvature tensor and demonstrate an experimentally accessible regime where they dominate the response.

Design and electromagnetic analysis of switched reluctance linear generator in electric vehicle

The structural characteristics and basic design requirements of design of switched reluctance linear generator are introduced. According to the general principles and design experience of electromechanical design, the dimension of design of switched reluctance linear generator is determined, and the two-dimensional and three-dimensional static finite element models of design of switched reluctance linear generator are established in Flux 2D and Flux 3D respectively. By comparing the simulation results of the two-dimensional model and the three-dimensional model, it is found that the difference between the real simulation results of the 2D model and the 3D model is small, and the calculation time cost of the 2D finite element simulation is much lower than that of the 3D model. Therefore, the subsequent work of this paper adopts the 2D finite element model. Finally, the static electromagnetic field and electromagnetic characteristics of the design of switched reluctance linear generator are analyzed by finite element analysis.

Two-point polarization correlations of random paraxial and nonparaxial electromagnetic fields

We investigate the two-point polarization correlation properties of random, statistically stationary, two-dimensional (2D) and three-dimensional (3D) electromagnetic fields. To this end two specific mutual polarization correlation functions are introduced, one based on a geometric approach using the Poincar\'e vectors and the other on the energy distribution employing the Jones vectors. Both approaches provide equivalent information about the space-time polarization correlations and enable one to associate with the field a polarization length over which the equal-time polarization states remain essentially unchanged. For fields obeying Gaussian statistics, the polarization correlation functions take on simple forms in terms of measurable quantities representing electromagnetic coherence. The formalism is demonstrated with two examples: blackbody radiation inside a cavity and in the far zone of a cavity wall aperture.

Dynamics of dipole in a stationary non-homogeneous electromagnetic field

The non-relativistic equations of motion for a dipole in a stationary non-homogeneous electromagnetic field are derived and analysed. It is shown that they are Hamiltonian with respect to a certain degenerated Poisson structure. Described by them dynamics is complex because the motion of the centre of mass of the dipole is coupled with its rotational motion. The problem of the existence of linear in momenta first integrals which can be useful for the separation of rotational motion is discussed. The presence of such first integral appears to be related with a linear symmetry of electric and magnetic fields. Also results of search of quadratic in momenta first integrals for uniform and stationary electromagnetic fields are reported. Deriving equations of motion of a dipole in arbitrary stationary electromagnetic fields and analysis of described by them dynamics is important for the construction of electromagnetic traps for polar particles.

Effect of non-ionizing radiation on the health of medical staff of magnetic resonance imaging rooms

Summary: The working conditions of medical staff in the offices of magnetic resonance imaging (MRI) are associated with high levels of stationary magnetic fields (SMF) and electromagnetic fields (EMF) of various frequencies and increased work intensity. It can affect cognitive, psychological and hemodynamic changes of the body with health disorders. It requires not only high professional training, but also compliance with safety measures, as well as monitoring of working conditions, health status and carrying out of medical and preventive measures.

Electric-field-promoted photo-electrochemical production of hydrogen from water splitting

Given that conversion efficiencies of incident solar radiation to liquid fuels, e.g., H2, are of the order of a few percent or less, as quantified by ‘solar to hydrogen’ (STH), economically inexpensive and operationally straightforward ways to boost photo-electrochemcial (PEC) H2 production from solar-driven water splitting are important. In this work, externally-applied static electric fields have led to enhanced H2 production in an energy-efficient manner, with up to ~30–40% increase in H2 (bearing in mind field-input energy) in a prototype, open-type solar cell featuring rutile/titania and hematite/iron-oxide (Fe2O3), respectively, in contact with an alkaline aqueous medium (corresponding to respective relative increases of STH by ~12 and 16%). We have also performed non-equilibrium ab-initio molecular dynamics in both static electric and electromagnetic (e/m) fields, for water in contact with a hematite/iron-oxide (001) surface, observing enhanced break-up of water molecules, by up to ~70% in the linear-response régime. We discuss the microscopic origin of such enhanced water-splitting, based on experimental and simulation-based insights. In particular, we external-field direction at the hematite surfaces, and scrutinise properties of the adsorbed water molecules and OH– and H3O+ species, e.g., hydrogen bonds between water-protons and the hematite surfaces’ bridging oxygen atoms, as well as interactions between oxygen atoms in adsorbed water molecules and underlying iron atoms.

Coupling the Cell Method with the Boundary Element Method in Static and Quasi–Static Electromagnetic Problems

A unified discretization framework, based on the concept of augmented dual grids, is proposed for devising hybrid formulations which combine the Cell Method and the Boundary Element Method for static and quasi-static electromagnetic field problems. It is shown that hybrid approaches, already proposed in literature, can be rigorously formulated within this framework. As a main outcome, a novel direct hybrid approach amenable to iterative solution is derived. Both direct and indirect hybrid approaches, applied to an axisymmetric model, are compared with a reference third-order 2D FEM solution. The effectiveness of the indirect approach, equivalent to the direct approach, is finally tested on a fully 3D benchmark with more complex topology.

Betaboltz: A Monte-Carlo simulation tool for gas scattering processes

We present an open-source code for the simulation of electron and ion transport for user-defined gas mixtures with static uniform electric and magnetic fields. The program provides microscopic interaction simulation and is interfaced with cross-section tables published by LXCat[1]. The framework was validated against drift velocity tables available in literature obtaining an acceptable match for atomic and non-polar molecular gases with spherical symmetry. The code is written in C++17 and is available as a shared library for easy integration into other simulation applications. Program summaryProgram Title: BetaboltzCPC Library link to program files:https://doi.org/10.17632/hjhx8bj45c.1Licensing provisions: LGPL v3Programming language: C++17Nature of problem: Simulations of electron and ion transport in arbitrary gas mixture under static uniform electric and magnetic fields.Solution method: Particle motion using classical and relativistic equation via interaction sampling using Monte-Carlo techniques.Additional comments including restrictions and unusual features: At the time of writing only static uniform electromagnetic fields are supported. However, the implementation of arbitrary fields can be added given an analytical solution is available. A custom XML format for cross-section was developed, because full compatibility with LXCat [1] XML format was not possible. Cross-section databases in the new format are available in the download section of the LXCat site [2].

Quantum gravity modifications of magnetized ideal gas thermodynamics

In this article, we study minimal length effects on the statistical thermodynamic properties of a magnetized ideal gas. We reformulate the Lagrangian density of the 3-D spatial dimensional static electromagnetic field by employing Kempf Algebra to get the modified magnetostatic potential energy. We derive the modified thermodynamic properties of a magnetized ideal gas such as the mean energy, Helmholtz free energy and entropy. Also, we derive the magnetization, susceptibility, and permeability in the presence of a minimal length. It is found that quantum gravity affects all thermodynamic properties. In addition, we derive the respective upper bounds on the deformation parameter and minimal length.

Electromagnetic resonance of nonlinear vacuum in one-dimensional cavity

Nonlinear corrections on electromagnetic fields in vacuum have been expected. In this study, we have theoretically considered nonlinear Maxwell’s equations in a one-dimensional cavity for a classical light and external static electromagnetic fields. A general solution for the electromagnetic corrective components including that of a longitudinal standing wave was derived after a linearization. The main purpose is to give a detailed feature of the previously reported resonant behavior [Shibata, Euro. Phys. J. D 74:215 (2020)], such as the effect of external static fields and the polarization fluctuation. These results favor the development of new and effective method for experiment.Graphic abstract

Electromagnetic Hanbury Brown and Twiss Effect in Atmospheric Turbulence

The evolution of the 4 × 4 matrix with elements being the scintillation indices of the single-point Stokes parameters of a stationary electromagnetic beam-like optical field in classic, weak atmospheric turbulence is revealed. It is shown that depending on the choice of the source parameters, the source-induced changes in the matrix elements of the propagating beam and those produced by turbulence can be either range-separated or conjoined. For theoretical analysis, the unified theory of coherence and polarization is used together with the extended Huygens-Fresnel integral approach. The results can be of interest for building robust communication and sensing systems operating in the presence of atmospheric fluctuations.

Modeling a Stationary Electromagnetic Field Based on the Maxwell Equations

Modeling a Stationary Electromagnetic Field Based on the Maxwell Equations

Dynamics of massive point vortices in a binary mixture of Bose-Einstein condensates

We study the massive point-vortex model introduced in Ref. [Phys. Rev. A 101, 013630 (2020)], which describes two-dimensional point vortices of one species that have small cores of a different species. We derive the relevant Lagrangian itself, based on the time-dependent variational method with a two-component Gross-Pitaevskii (GP) trial function. The resulting Lagrangian resembles that of charged particles in a static electromagnetic field, where the canonical momentum includes an electromagnetic term. The simplest example is a single vortex with a rigid circular boundary, where a massless vortex can only precess uniformly. In contrast, the presence of a sufficiently large filled vortex core renders such precession unstable. A small core mass can also lead to small radial oscillations, which are, in turn, clear evidence of the associated inertial effect. Detailed numerical analysis of coupled two-component GP equations with a single vortex and small second-component core confirms the presence of such radial oscillations, implying that this more realistic GP vortex also acts as if it has a small massive core.

Frequency-induced negative magnetic susceptibility in epoxy/magnetite nanocomposites

The epoxy/magnetite nanocomposites express superparamagnetism under a static or low-frequency electromagnetic field. At the microwave frequency, said the X-band, the nanocomposites reveal an unexpected diamagnetism. To explain the intriguing phenomenon, we revisit the Debye relaxation law with the memory effect. The magnetization vector of the magnetite is unable to synchronize with the rapidly changing magnetic field, and it contributes to diamagnetism, a negative magnetic susceptibility for nanoparticles. The model just developed and the fitting result can not only be used to explain the experimental data in the X-band but also can be used to estimate the transition frequency between paramagnetism and diamagnetism.

Quantum Charged Particle in a Flat Box under Static Electromagnetic Field with Landau’s Gauge and Special Case with Symmetric Gauge

We summarize our results about the quantization of a charged particle motion without spin inside a flat box under a static electromagnetic field with Landau’s gauge for the magnetic field, where Fourier’s transformation was used to analyze the problem, to point out that there exists a wave function which is different to that one given by Landau with the same Landau’s levels. The quantization of the magnetic flux is deduced differently to previous one, and a new solution is presented for the case of symmetric gauge of the magnetic field, and having the same Landau’s levels.

Second-order charge currents and stress tensor in a chiral system

We study Wigner equations for massless spin-$1/2$ charged fermions at global equilibrium in static and uniform vorticity and electromagnetic fields. The Wigner functions can be solved order by order from Wigner equations through the power expansion of the vorticity and electromagnetic fields. The nondissipative charge currents and the stress tensor up to the second order can be obtained from Wigner functions. The charge and energy densities and the pressure have contributions from vorticity and electromagnetic fields at the second order. The vector and axial Hall currents can be induced along the direction orthogonal to vorticity and electromagnetic fields at the second order. We also find that the trace anomaly emerges naturally in renormalization of the stress tensor by including quantum corrections from electromagnetic fields.

Relativistic Rotating Electromagnetic Fields

In this work, we consider axially symmetric stationary electromagnetic fields in the framework of special relativity. These fields have an angular momentum density in the reference frame at rest with respect to the axis of symmetry; their Poynting vector form closed integral lines around the symmetry axis. In order to describe the state of motion of the electromagnetic field, two sets of observers are introduced: the inertial set, whose members are at rest with the symmetry axis; and the noninertial set, whose members are rotating around the symmetry axis. The rotating observers measure no Poynting vector, and they are considered as comoving with the electromagnetic field. Using explicit calculations in the covariant 3 + 1 splitting formalism, the velocity field of the rotating observers is determined and interpreted as that of the electromagnetic field. The considerations of the rotating observers split in two cases, for pure fields and impure fields, respectively. Moreover, in each case, each family of rotating observers splits in two subcases, due to regions where the electromagnetic field rotates with the speed of light. These regions are generalizations of the light cylinders found around magnetized neutron stars. In both cases, we give the explicit expressions for the corresponding velocity fields. Several examples of relevance in astrophysics and cosmology are presented, such as the rotating point magnetic dipoles and a superposition of a Coulomb electric field with the field of a point magnetic dipole.