Electromagnetic Tensor Research Articles

Resummation of QED radiative corrections in a strong constant crossed field

By considering radiative corrections of up to 3rd-loop order, Ritus and Narozhny conjectured that the proper expansion parameter for QED in a strong constant crossed field is $g=\alpha\chi^{2/3}$, where the dynamical quantum parameter $\chi=e\sqrt{-(Fp)^2}/m^3$ combines the particle momentum $p$ with the external field strength tensor $F$. Here we present and discuss the first non-perturbative result in this context, the resummed bubble-type polarization corrections to the electron self-energy in a constant crossed field. Our analysis confirms the relevance of the scaling parameter $g$ to the enhancement of bubble-type radiative corrections. This parameter actually represents the characteristic value of the ratio of the 1-loop polarization bubble to the photon virtuality. After an all-order resummation we identify and discuss two contributions to the self-energy with different formation regions and asymptotic behavior for $g\gg1$. Whereas the breakdown of perturbation theory occurs already for $g\gtrsim1$, the leading-order result remains dominant until the asymptotic regime $g\gg 1$ is reached. However, the latter is specific to processes like elastic scattering or photon emission and does not have to remain true for general higher-order QED processes.

Optimal Control of SiC Crystal Growth in the RF-TSSG System Using Reinforcement Learning

We have developed a reinforcement learning (RL) model to control the melt flow in the radio frequency (RF) top-seeded solution growth (TSSG) process for growing more uniform SiC crystals with a higher growth rate. In the study, the electromagnetic field (EM) strength is controlled by the RL model to weaken the influence of Marangoni convection. The RL model is trained through a two-dimensional (2D) numerical simulation of the TSSG process. As a result, the growth rate under the control of the RL model is improved significantly. The optimized RF-coil parameters based on the control strategy for the 2D melt flow are used in a three-dimensional (3D) numerical simulation for model validation, which predicts a higher and more uniform growth rate. It is shown that the present RL model can significantly reduce the development cost and offers a useful means of finding the optimal RF-coil parameters.

Spin 1 Spinor Construction with Clifford Algera and Dirac Spin 1/2 Spinors

A compatible spin 1 spinor representation with Clifford algebra (1,3) (or 1,3 Cl ) is derived for both (1 / 2,1 / 2) and (1, 0) (0,1)  Lorentz group representations with spin 1/2 particles Dirac spinors in 1,3 Cl . The relation between the two different representations of spin 1 spinors is analogous to the relation between the electromagnetic vector potential field A and the electromagnetic field strength tensor F  . From this relationship, the two representations are combined by the formula u( p, )  ( p, )  p / m. We also note that the Grassmann basis provides more convenient basis for spin 1 spinors especially in chiral representations of (1, 0) (0,1)  , even though the Clifford basis is more fitting for spin 1/2 and (1/ 2,1/ 2) spinor representations for both helicity and handedness.

Minkowski tensor in electrodynamics of moving media and three rules for construction of the physical tensors in Einstein's special relativity

Minkowski applied Einstein's principle of relativity to moving media and developed electrodynamics of moving media, with Minkowski tensor as the stress-energy-momentum tensor. Recently, Partanen and Tulkki criticize that Minkowski tensor contradicts special relativity, and proposed a mass-polariton stress-energy-momentum (MP SEM) tensor to replace Minkowski tensor. In this paper, I reasonably argue: (i) all the physical results obtained from Minkowski tensor are already embodied in two EM field-strength tensors; (ii) all physical tensors in Einstein's special relativity must satisfy three rules, with Minkowski tensor following all the rules while both Abraham tensor and the MP SEM tensor not. Thus the two arguments provide a strong theoretical basis to solve the problem of the momentum of light in a medium. Finally, by enumerating a specific example I show that the Lorentz covariance of a tensor provides no guarantee of the consistency of the tensor with the principle of relativity.

The Gravitomagnetic Effects in Rapidly Rotating Neutron Stars: A Theoretical Study

Electromagnetic measurements of a general relativistic gravitomagnetic effect can be done within the conductor embedded in a rotating gravitational object’s spacetime. Neutron stars are rotating gravitational object that have strong magnetic field. The gravitomagnetic effect in a neutron star can be determined from the distribution density in the conductor. Neutron star is assumed as a conductor and it rotates rapidly. The distribution density inside the conductor is obtained from the electromagnetic contravariant tensor and the relativistic rotational speed of the conductor. It has obtained the distribution density inside the conductor for the rapidly rotating neutron star. The results are compared to the slowly rotating neutron star which depends on the angular veolocity and the gravitational field.

Electromagnetic Analysis of Vertical Resistive Memory with a Sub-nm Thick Electrode.

Resistive random access memories (RRAMs) are a type of resistive memory with two metal electrodes and a semi-insulating switching material in-between. As the persistent technology node downscaling continues in transistor technologies, RRAM designers also face similar device scaling challenges in simple cross-point arrays. For this reason, a cost-effective 3D vertical RRAM (VRRAM) structure which requires a single pivotal lithography step is attracting significant attention from both the scientific community and the industry. Integrating an extremely thin plane electrode to such a structure is a difficult but necessary step to enable high memory density. In addition, experimentally verifying and modeling such devices is an important step to designing RRAM arrays with a high noise margin, low resistive-capacitive (RC) delays, and stable switching characteristics. In this work, we conducted an electromagnetic analysis on a 3D vertical RRAM with atomically thin graphene electrodes and compared it with the conventional metal electrode. Based on the experimental device measurement results, we derived a theoretical basis and models for each VRRAM design that can be further utilized in the estimation of graphene-based 3D memory at the circuit and architecture levels. We concluded that a 71% increase in electromagnetic field strength was observed in a 0.3 nm thick graphene electrode when compared to a 5 nm thick metal electrode. Such an increase in the field led to much lower energy consumption and fluctuation range during RRAM switching. Due to unique graphene properties resulting in improved programming behavior, the graphene-based VRRAM can be a strong candidate for stacked storage devices in new memory computing platforms.

Four-dimensional gravity on a covariant noncommutative space

We formulate a model of noncommutative four-dimensional gravity on a covariant fuzzy space based on SO(1, 4), that is the fuzzy version of the dS4. The latter requires the employment of a wider symmetry group, the SO(1, 5), for reasons of covariance. Addressing along the lines of formulating four-dimensional gravity as a gauge theory of the Poincaré group, spontaneously broken to the Lorentz, we attempt to construct a four-dimensional gravitational model on the fuzzy de Sitter spacetime. In turn, first we consider the SO(1, 4) subgroup of the SO(1, 5) algebra, in which we were led to, as we want to gauge the isometry part of the full symmetry. Then, the construction of a gauge theory on such a noncommutative space directs us to use an extension of the gauge group, the SO(1, 5)×U(1), and fix its representation. Moreover, a 2-form dynamic gauge field is included in the theory for reasons of covariance of the transformation of the field strength tensor. Finally, the gauge theory is considered to be spontaneously broken to the Lorentz group with an extension of a U(1), i.e. SO(1, 3)×U(1). The latter defines the four-dimensional noncommutative gravity action which can lead to equations of motion, whereas the breaking induces the imposition of constraints that will lead to expressions relating the gauge fields. It should be noted that we use the Euclidean signature for the formulation of the above programme.

A relativistic particle pusher for ultra-strong electromagnetic fields

Kinetic plasma simulations are nowadays commonly used to study a wealth of nonlinear behaviours and properties in laboratory and space plasmas. In particular, in high-energy physics and astrophysics, the plasma usually evolves in ultra-strong electromagnetic fields produced by intense laser beams for the former or by rotating compact objects such as neutron stars and black holes for the latter. In these ultra-strong electromagnetic fields, the gyro-period is several orders of magnitude smaller than the time scale on which we desire to investigate the plasma evolution. Some approximations are required such as, for instance, artificially decreasing the electromagnetic field strength, which is certainly not satisfactory. The main flaw of this downscaling is that it cannot reproduce particle acceleration to ultra-relativistic speeds with a Lorentz factor above$\gamma \approx 10^3$–$10^4$. In this paper, we design a new algorithm able to catch particle motion and acceleration to a Lorentz factor of up to$10^{15}$or even higher by using Lorentz boosts to special frames where the electric and magnetic field are parallel. Assuming that these fields are locally uniform in space and constant in time, we solve analytically the equation of motion in a tiny region smaller than the length scale of the spatial and temporal gradient of the field. This analytical integration of the orbit severely reduces the constraint on the time step, allowing us to use large time steps, avoiding resolving the ultra-high gyro-frequency. We performed simulations in ultra-strong spatially and time-dependent electromagnetic fields, showing that our particle pusher is able to follow accurately the exact analytical solution for very long times. This property is crucial to properly capture for instance lepton electrodynamics in electromagnetic waves produced by fast rotating neutron stars. We conclude with a simple implementation of our new pusher into a one-dimensional relativistic electromagnetic particle-in-cell code, testing it against plasma oscillations, two-stream instabilities and strongly magnetized relativistic shocks.

The Linear Stability of Reissner–Nordström Spacetime for Small Charge

In this paper, we prove the linear stability to gravitational and electromagnetic perturbations of the Reissner-Nordstr\"om family of charged black holes with small charge. Solutions to the linearized Einstein-Maxwell equations around a Reissner-Nordstr\"om solution arising from regular initial data remain globally bounded on the black hole exterior and in fact decay to a linearized Kerr-Newman metric. We express the perturbations in geodesic outgoing null foliations, also known as Bondi gauge. To obtain decay of the solution, one must add a residual pure gauge solution which is proved to be itself controlled from initial data. Our results rely on decay statements for the Teukolsky system of spin $\pm2$ and spin $\pm1$ satisfied by gauge-invariant null-decomposed curvature components, obtained in earlier works. These decays are then exploited to obtain polynomial decay for all the remaining components of curvature, electromagnetic tensor and Ricci coefficients. In particular, the obtained decay is optimal in the sense that it is the one which is expected to hold in the non-linear stability problem.

Second Gradient Electromagnetostatics: Electric Point Charge, Electrostatic and Magnetostatic Dipoles

In this paper, we study the theory of second gradient electromagnetostatics as the static version of second gradient electrodynamics. The theory of second gradient electrodynamics is a linear generalization of higher order of classical Maxwell electrodynamics whose Lagrangian is both Lorentz and U ( 1 ) -gauge invariant. Second gradient electromagnetostatics is a gradient field theory with up to second-order derivatives of the electromagnetic field strengths in the Lagrangian. Moreover, it possesses a weak nonlocality in space and gives a regularization based on higher-order partial differential equations. From the group theoretical point of view, in second gradient electromagnetostatics the (isotropic) constitutive relations involve an invariant scalar differential operator of fourth order in addition to scalar constitutive parameters. We investigate the classical static problems of an electric point charge, and electric and magnetic dipoles in the framework of second gradient electromagnetostatics, and we show that all the electromagnetic fields (potential, field strength, interaction energy, interaction force) are singularity-free, unlike the corresponding solutions in the classical Maxwell electromagnetism and in the Bopp–Podolsky theory. The theory of second gradient electromagnetostatics delivers a singularity-free electromagnetic field theory with weak spatial nonlocality.

Geometric phase of a two-level atom near a dissipative and dispersive dielectric slab

In this paper, we study the geometric phase of a two-level atom near a dielectric slab. For this purpose, by applying the Von-Neumann equation, we obtain eigenvalues and eigenvectors of the reduced density operator of the atomic system. Then, we obtain the Lamb shift and transition rates of the atomic system in term of the electromagnetic Green tensor. Finally, by calculating the electromagnetic Green tensor of the system and making use of the kinematic approach, we study the geometric phase of the atomic system near the dielectric slab. We show that the geometric phase can be used as a sensitive probe to the surface-phonon polariton waves.

Stability of magnetic black holes in general nonlinear electrodynamics

We study the perturbative stability of magnetic black holes in a general class of nonlinear electrodynamics, where the Lagrangian is given by a general function of the field strength of electromagnetic field $F_{\mu\nu}$ and its Hodge dual $\widetilde{F}_{\mu\nu}$. We derive sufficient conditions for the stability of the black holes. We apply the stability conditions to Bardeen's regular black holes, black holes in Euler-Heisenberg theory, and black holes in Born-Infeld theory. As a result, we obtain a sufficient condition for the stability of Bardeen's black holes, which restricts $F_{\mu\nu}\widetilde{F}^{\mu\nu}$ dependence of the Lagrangian. We also show that black holes in Euler-Heisenberg theory are stable for a sufficiently small magnetic charge. Moreover, we prove the stability of black holes in the Born-Infeld electrodynamics even when including $F_{\mu\nu}\widetilde{F}^{\mu\nu}$ dependence.

Remarks on Plücker embedding and totally antisymmetric gauge fields

We make a number of comments about the way the Plücker embedding, which can be derived via the Grassmann-Plücker relations, can be associated to totally antisymmetric gauge fields. As a first step we discuss the case of the electromagnetic field strength, showing that the Plücker map implies both the true degrees of freedom of the electromagnetic field and the 1-brane (string) structure. The procedure is generalized in order to prove that the true degrees of freedom of a totally antisymmetric field and the p-brane structure are, in part, consequence of the Plücker coordinates.

The confining color field in SU(3) gauge theory

We extend a previous numerical study of SU(3) Yang–Mills theory in which we measured the spatial distribution of all components of the color fields surrounding a static quark–antiquark pair and provided evidence that the simulated gauge invariant chromoelectric field can be separated into a Coulomb-like ‘perturbative’ field and a ‘non-perturbative’ confining field. In this paper we hypothesize that the fluctuating color fields not measured in our simulations do not contribute to the string tension. Under this assumption the string tension is determined by the color fields we measure, which form a field strength tensor pointing in a single direction in color space. We call this the ‘Maxwell picture of confinement’. We provide an additional procedure to isolate the confining field. We then extract the string tension from a stress energy-momentum tensor having the Maxwell form, constructed from the simulated non-perturbative part of the field strength tensor. To test our hypothesis we calculate the string tension for values of the quark–antiquark separation ranging from 0.37 fm to 1.2 fm. We also calculate the spatial distributions of the energy-momentum tensor surrounding static quarks for this range of separations, and we compare with the distributions obtained from direct simulations of the energy-momentum tensor.

Field-induced shaping of sessile paramagnetic drops

We use the electromagnetic stress tensor to describe the elongation of paramagnetic drops in uniform magnetic fields. This approach implies a linear relationship between the shape of the drops and the square of the applied field, which we confirm experimentally. We show that this effect scales with the volume and susceptibility of the drops. By using this unified electromagnetic approach, we highlight the potential applications of combining electric and magnetic techniques for controlled shaping of drops in liquid displays, liquid lenses, and chemical mixing of drops in microfluidics.

Implications of axionic hair on the shadow of M87*

Detection of axion field can unfold intriguing facets of our universe in several astrophysical and cosmological scenarios. In four dimensions, such a field owes its origin to the completely anti-symmetric Kalb-Ramond field strength tensor. Its invisibility in the solar system based tests compels one to look for its signatures in the strong field regime. The recent observation of the shadow of the supermassive black hole in the galaxy M87 ushers in a new opportunity to test for the footprints of axion in the near horizon region of black holes, where the gravity is expected to be strong. In this paper, we explore the impact of axion on the black hole shadow and compare the result with the available image of M87*. Our analysis indicates that axion which violates the energy condition seems to be favored by observations. The implications are discussed.

Spontaneous emission of a quantum emitter near a Chern insulator: Interplay of time-reversal symmetry breaking and Van Hove singularity

We consider the generic problem of a two-level quantum emitter near a two-dimensional Chern insulator in the dipole approximation, and study how the frequency-dependent response and electronic density of states of the insulator modifies the transition rate of the emitter between the ground and excited levels. To this end, we obtain the full real-frequency behavior of the conductivity tensor by performing a tight-binding calculation based on the Qi-Wu-Zhang model and using a Kubo formula, and derive the full electromagnetic Green tensor of the system, which breaks Onsager reciprocity. This enables us to find that for frequencies smaller than the maximum band gap, the system is sensitive to time reversal symmetry-breaking, whereas for much larger frequencies the system becomes insensitive, with implications for the discrimination of the state of a circularly polarised dipole emitter. We also study the impact of a van Hove singularity on the surface-induced correction to the transition rate, finding that it can enhance its amplitude by a few orders of magnitude compared to the case where the conductivity is set to its static value. By considering configurations in which the dipole is circularly polarised or parallel with the surface of the Chern insulator, we find that the surface correction to the transition rate can exhibit a novel decay with sine integral-like oscillations.

Spinorial structure of O(3) and application to dark matter

An O(3) spinor, Φ, as a doublet denoted by 2D consists of an SO(3) spinor, ϕ, and its complex conjugate, ϕ⁎, which form Φ=(ϕ,ϕ⁎)T to be identified with a Majorana-type spinor of O(4). The four gamma matrices Γμ (μ=1∼4) are given by Γi=diag.(τi,τi⁎) (i=1,2,3) and Γ4=−τ2⊗τ2, where τi denote the Pauli matrices. The rotations and axis-reflections of O(3) are, respectively, generated by Σij and Σi4, where Σμν=[Γμ,Γν]/2i. While Φ is regarded as a scalar, a fermionic O(3) spinor is constructed out of an SO(3) doublet Dirac spinor and its charge conjugate. These O(3) spinors are restricted to be neutral and cannot carry the standard model quantum numbers because they contain particles and antiparticles. Our O(3) spinors serve as candidates of dark matter. The O(3) symmetry in particle physics is visible when the invariance of interactions is considered by explicitly including their complex conjugates. It is possible to introduce a dark gauge symmetry based on SO(3)×Z2 equivalent to O(3), where the Z2 parity is described by a U(1) charge giving 1 for a particle and −1 for an antiparticle. The SO(3) and U(1) gauge bosons turn out to transform as the axial vector of O(3) and the pseudoscalar of O(3), respectively. This property is related to the consistent definition of the nonabelian field strength tensor of O(3) or of the U(1) charge of the O(3)-transformed spinor. To see the feasibility of our dark matter models, we discuss scalar dark matter phenomenology based on the dark U(1) gauge model.

On metric transformations with a U(1) gauge field

We study metric transformations including not just the field strength tensor of a $U(1)$ gauge field, but also its dual tensor. We first consider an arbitrary symmetric matrix built up with these two tensors in the metric transformation. It turns out the form of transformation reduces to a quite simple form on imposing the parity evenness of the transformed metric and by utilising the Cayley-Hamilton theorem as well as other useful identities. Interestingly, the same form for the transformation was recently argued in the process of seeking for a generic metric transformation but without the inclusion of the dual tensor.

An Accelerated Total-Variation Compressive Sensing Approach to Field Strength Reconstruction

An innovative and computationally efficient compressive sensing (CS) inversion scheme is proposed for the prediction of the 2-D distribution of the electromagnetic (EM) field strength (FS) in a region of interest (RoI) starting from a limited set of FS measurements, but without any information on the EM radiating source. Toward this end, the inverse problem at hand is recast to the minimization of the augmented Lagrangian function, and then it is efficiently solved by means of a novel accelerated total-variation CS (ATV-CS) approach. The ATV-CS, which is based on a smart implementation of the involved matrix–vector multiplications, is exploited to remarkably reduce the computational cost of the standard total variation (TV)-CS so that a reliable and efficient prediction of the FS is enabled in realistic applications concerned with wide areas, as well. A set of representative test cases, from a wide numerical assessment concerned with different sources and propagation scenarios, is reported to assess both the reliability/effectiveness and the computational efficiency of the proposed approach in comparison with competitive state-of-the-art sparseness-promoting techniques, as well.