Classical Electromagnetic Field Research Articles

Electromagnetism as Quantum Physics

One can interpret the Dirac equation either as giving the dynamics for a classical field or a quantum wave function. Here I examine whether Maxwell's equations, which are standardly interpreted as giving the dynamics for the classical electromagnetic field, can alternatively be interpreted as giving the dynamics for the photon's quantum wave function. I explain why this quantum interpretation would only be viable if the electromagnetic field were sufficiently weak, then motivate a particular approach to introducing a wave function for the photon (following Good, 1957). This wave function ultimately turns out to be unsatisfactory because the probabilities derived from it do not always transform properly under Lorentz transformations. The fact that such a quantum interpretation of Maxwell's equations is unsatisfactory suggests that the electromagnetic field is more fundamental than the photon.

Tunable single-photon quantum router

We propose an efficient single-photon router comprising two resonator waveguide channels coupled by several sequential cavities with embedded three-level atoms. We show that the system can operate as a perfect four-way single-photon switch. We also demonstrate that an incident single photon propagating in one of the waveguides can be routed into one or the other output channels; such routing can be controlled by the external classical electromagnetic field driving the atoms. We argue that, under appropriate conditions, the efficiency of such routing can be close to 100% within a broad operational bandwidth, suggesting various applications in photonics.

Axion-electrodynamics: a quantum field calculation

An axion background field induces tiny oscillating electric and magnetic fields in an external static magnetic field. This signature is used to search for axion dark matter. We use standard quantum field theory techniques to obtain an expression for a transition amplitude, from which we identify the classical electromagnetic fields induced by the background axion field. We confirm previous results, that if the spatial size R of the applied static magnetic field is small compared to the axion Compton wavelength λ, the induced electric and magnetic fields are parametrically suppressed by the small numbers (R/λ)2 and R/λ, respectively, relative to the case when R is larger than λ. Our approach allows an intuitive interpretation in terms of 4-momentum conservation and momentum exchange via the photon propagator.

Balancing Multi-Manned Assembly Lines With Walking Workers: Problem Definition, Mathematical Formulation, and an Electromagnetic Field Optimisation Algorithm

Assembly lines are widely used in industrial environments that produce standardised products in high volumes. Multi-manned assembly line is a special version of them that allows simultaneous operation of more than one worker at the same workstation. These lines are widely used in large-sized product manufacturing since they have many advantages over the simple one. This article has dealt with multi-manned assembly line balancing problem with walking workers for minimising the number of workers and workstations as the first and second objectives, respectively. A linear mixed-integer programming formulation of the problem has been firstly addressed after the problem definition is given. Besides that, a metaheuristic based on electromagnetic field optimisation algorithm has been improved. In addition to the classical electromagnetic field optimisation algorithm, a regeneration strategy has been applied to enhance diversification. A particle swarm optimisation algorithm from assembly line balancing literature has been modified to compare with the proposed algorithm. A group of test instances from many precedence diagrams were generated for evaluating the performances of all solution methods. Deviations from lower bound values of the number of workers/workstations and the number of optimal solutions obtained by these methods are concerned as performance criteria. The results obtained by the proposed programming formulations have been also compared with the solutions obtained by the traditional mathematical model of the multi-manned assembly line. Through the experimental results, the performance of the metaheuristic has been found very satisfactory according to the number of obtained optimal solutions and deviations from lower bound values.

Effects of pulsed electromagnetic field therapy on pain, stiffness and physical function in patients with knee osteoarthritis: A systematic review and meta-analysis of randomized controlled trials.

To evaluate the efficacy of classical pulsed electromagnetic field therapy on patients with knee osteoarthritis. The databases PubMed, EMBASE, Web of Science and Cochrane Library were searched for relevant studies. Randomized controlled trials comparing classical pulsed electromagnetic field with placebo for patients with knee osteoarthritis were included. Data for primary outcomes, including pain, stiffness and physical function, were extracted. Data from 8 randomized controlled trials involving 421 patients were pooled. Pulsed electromagnetic field therapy had an effect on improving physical function (weighted mean difference; WMD = -5.28, 95% confidence interval; 95% CI -9.45 to -1.11, p = 0.01), but showed no advantage in the reduction of Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) total score (WMD = -7.80, 95% CI -16.08 to 0.47, p = 0.06), WOMAC pain score (WMD = -1.06, 95% CI -2.30 to 0.17, p = 0.09), visual analogue scale pain score (WMD=-0.88, 95% CI -2.06 to 0.31, p = 0.15) or WOMAC stiffness score (WMD = -0.50, 95% CI -1.09 to 0.09, p = 0.1). Pulsed electromagnetic field therapy is beneficial for improving physical function despite having no advantage in treating pain and stiffness. Further randomized controlled trials are needed to confirm these findings and determine the optimal parameters and treatment regimen for pulsed electromagnetic field therapy.

Dynamical Casimir effect meets material science

The aim of this study is to analyze attempts to observe the so called Dynamical Casimir effect in cavities, changing their optical lengths by means of fast time variations of material properties (dielectric permeability or conductivity) of thin slabs attached to the cavity walls. The emphasis is made on the case of semiconductor slabs excited by short laser pulses. Considering the evolution of the classical electromagnetic field in this case, an approximate analytical solution for an infinite set of coupled ordinary differential equations for the mode amplitudes is derived under certain simplifying assumptions. According to this solution, an amplification of the initial field can be made, provided the induced dielectric permeability can become negative with a large absolute value. Evaluations of the feasibility of such a scenario are given.

Perturbation Theory in the Analysis of Quantum Vortices Formed by Impact of Ultrashort Electromagnetic Pulse on Atom

Nonstationary perturbation theory is used to study generation of quantum vortices resulting from ionization of hydrogen-like atom by an ultrashort pulse of classical electromagnetic field. It is shown that the vortices are determined by quantum interference effects.

A new development in quantum field equations of dyons

In this study, we describe a novel approach to quantum phenomena of the generalized electromagnetic fields of dyons with quaternionic analysis. Starting with quaternionic quantum wave equations, we have established a quantized condition for time coordinate that transforms microscopic to macroscopic fields. In view of the classical electromagnetic field equations, we propose a new set of quantized Proca–Maxwell’s equations for dyons. Furthermore, a quantized form of four-current densities and the quantized Lorentz gauge conditions for electric and magnetic potentials, respectively, of dyons are obtained. We have established the new quantized continuity equations for electric and magnetic densities of dyons, which are associated with a torque density result from the two spin states. The quantized Klein–Gordon-like field equations and the unified quaternionic electromagnetic potential wave equations for massive dyons are demonstrated. Moreover, we investigate the quaternionic quantized relativistic Dirac field equations for massive dyons, which indicate that the antiparticle of dyons will exist, called antidyons.

Optical bistability in a low-photon-density regime

We give a microscopic description of the optical bistability, where the transmission coefficient has two different values as a function of input light intensity, and the system exhibits a discontinuous jump with a hysteresis loop. We developed an efficient numerical algorithm to treat the quantum master equation for hybridized systems of many photons and a large number of two-level atoms. By using this method, we characterize the bistability from the viewpoint of eigenmodes and eigenvalues of the time evolution operator of the quantum master equation. We investigate the optical bistability within the low photon-density regime, where the hybridization of photon and atom degrees of freedom occurs and the resonance spectrum has a double peak structure. We compared it with the standard optical bistability between the low photon-density regime and the high photon-density regime, where the photons can be treated as a classical electromagnetic field and the resonance spectrum has a single peak structure. We discuss the steady-state properties of the optical bistability: dependencies of the photon number density on the intensity and the double peak structure of the photon number distribution inside the bistable region. As for the dynamical properties, we find that the relaxation timescale shows an exponential growth with the system size, and reveal how the hysteresis loop of the optical bistability depends on the size of the system and the sweeping rate of the driving amplitude. Finally, by investigating the effects of detuning frequency of the input field, we clarify the characteristic properties of the present optical bistability within the low photon-density regime, which are qualitatively different from the standard optical bistable phenomena.

The Property of Phase Velocity in the Cloak Shell

According to classical EM field theory, the dispersion relation for anisotropic media in the 2-D cylinder cloak have been calculated in the KDB system(consisting of k vector and the DB plane ). Due to the special and variable Electromagnetic (EM) parameters, theoretical results indicate that the phase velocities of EM waves are non-uniform in the cloak shell. The numerical simulations show that the phase velocity is reduced, and less than that of light in vacuum in the front and rear of cloak shell. While in the upper and lower region of cloak shell, the phase velocities are larger than that of other regions, and exceed that of light in vacuum.

On the Number of Photons in a Classical Electromagnetic Field

Relations determining the number of photons in an electromagnetic field are considered from the point of view of a classical electromagnetic field. A relativistically invariant expression is obtained for the number of emitted photons in terms of charges and currents producing the electromagnetic field. Examples are considered for calculating the numbers of photons in the electromagnetic field for the case of the electric dipole radiation field, as well as the field of a finite and spatially restricted electromagnetic pulse.

The Transition from Quantum Field Theory to One-Particle Quantum Mechanics and a Proposed Interpretation of Aharonov–Bohm Effect

In this article we demonstrate a sense in which the one-particle quantum mechanics (OPQM) and the classical electromagnetic four-potential arise from quantum field theory (QFT). In addition, the classical Maxwell equations are derived from a QFT scattering process, while both classical electromagnetic fields and potentials serve as mathematical tools to approximate the interactions among elementary particles described by QFT physics. Furthermore, a plausible interpretation of the Aharonov-Bohm (AB) effect is raised within the QFT framework. We provide a quantum treatment of the source of electromagnetic potentials and argue that the underlying mechanism in the AB effect can be understood via interactions among electrons described by QFT where the interactions are mediated by virtual photons.

A New Class of Retrocausal Models.

Globally-constrained classical fields provide a unexplored framework for modeling quantum phenomena, including apparent particle-like behavior. By allowing controllable constraints on unknown past fields, these models are retrocausal but not retro-signaling, respecting the conventional block universe viewpoint of classical spacetime. Several example models are developed that resolve the most essential problems with using classical electromagnetic fields to explain single-photon phenomena. These models share some similarities with Stochastic Electrodynamics, but without the infinite background energy problem, and with a clear path to explaining entanglement phenomena. Intriguingly, the average intermediate field intensities share a surprising connection with quantum “weak values”, even in the single-photon limit. This new class of models is hoped to guide further research into spacetime-based accounts of weak values, entanglement, and other quantum phenomena.

Entangled Photonic-Nuclear Molecular Dynamics of LiF in Quantum Optical Cavities.

The quantum photodynamics of a simple diatomic molecule with a permanent dipole immersed within an optical cavity containing a quantized radiation field is studied in detail. The chosen molecule under study, lithium fluoride (LiF), is characterized by the presence of an avoided crossing between the two lowest 1Σ potential energy curves (covalent-ionic diabatic crossing). Without field, after prompt excitation from the ground state 1 1Σ, the excited nuclear wave packet moves back and forth in the upper 2 1Σ state, but in the proximity of the avoided crossing, the nonadiabatic coupling transfers part of the nuclear wave packet to the lower 1 1Σ state, which eventually leads to dissociation. The quantized field of a cavity also induces an additional light crossing in the modified dressed potential energy curves with similar transfer properties. To understand the entangled photonic-nuclear dynamics, we solve the time-dependent Schrödinger equation by using the multiconfigurational time-dependent Hartree method (MCTDH). The single mode quantized field of the cavity is represented in the coordinate space instead of in the Fock space, which allows us to deal with the field as an additional vibrational mode within the MCTDH procedure on equal footing. We prepare the cavity with different quantum states of light, namely, Fock states, coherent states, and squeezed coherent states. Our results reveal pure quantum light effects on the molecular photodynamics and the dissociation yields of LiF, which are quite different from the light-undressed case and which cannot be described in general by a semiclassical approach using classical electromagnetic fields.

Quasi-superradiant soliton state of matter in quantum metamaterials

Strong interaction of a system of quantum emitters (e.g., two-level atoms) with electromagnetic field induces specific correlations in the system accompanied by a drastic increase of emitted radiation (superradiation or superfluorescence). Despite the fact that since its prediction this phenomenon was subject to a vigorous experimental and theoretical research, there remain open question, in particular, concerning the possibility of a first order phase transition to the superradiant state from the vacuum state. In systems of natural and charge-based artificial atom this transition is prohibited by “no-go” theorems. Here we demonstrate numerically and confirm analytically a similar transition in a one-dimensional quantum metamaterial – a chain of artificial atoms (qubits) strongly interacting with classical electromagnetic fields in a transmission line. The system switches from vacuum state to the quasi-superradiant (QS) phase with one or several magnetic solitons and finite average occupation of qubit excited states along the transmission line. A quantum metamaterial in the QS phase circumvents the “no-go” restrictions by considerably decreasing its total energy relative to the vacuum state by exciting nonlinear electromagnetic solitons.

The Concept of the Photon—Revisited

concept is one of the most debated issues in the history of physical science. Some thirty years ago, we published an article in Physics Today entitled The Concept of the Photon, 1 in which we described the photon as a classical electromagnetic field plus the fluctuations associated with the vacuum. However, subsequent developments required us to envision the as an intrinsically quantum mechanical entity, whose basic physics is much deeper than can be explained by the simple 'classical wave plus vacuum fluctuations' picture. These ideas and the extensions of our conceptual understanding are discussed in detail in our recent quantum optics book. 2 In this article we revisit the concept based on examples from these sources and more.

QUANTUM MODEL OF A CHARGED BLACK HOLE

A canonical approach for constructing of the classical and quantum description spherically-symmetric con guration gravitational and electromagnetic fields is considered. According to the sign of the square of the Kodama vector, space-time is divided into R-and T-regions. By virtue of the generalized Birkho theorem, one can choose coordinate systems such that the desired metric functions in the T-region depend on the time, and in the R-domain on the space coordinate. Then, the initial action for the configuration breaks up into terms describing the elds in the T- and R-regions with the time and space evolutionary variable, respectively. For these regions, Lagrangians of the configuration are constructed, which contain dynamic and non-dynamic degrees of freedom, leading to constrains. We concentrate our attention on dynamic T-regions. There are two additional conserved physical quantities: the charge and the total mass of the system. The Poisson bracket of the total mass with the Hamiltonian function vanishes in the weak sense. A classical solution of the eld equations in the con guration space (minisuperspace) is constructed without xing non-dynamic variable. In the framework of the canonical approach to the quantum mechanics of the system under consideration, physical states are found by solving the Hamiltonian constraint in the operator form (the DeWitt equation) for the system wave function Ψ. It also requires that Ψ is an eigenfunction of the operators of charge and total mass. For the symmetric of the mass operator the corresponding ordering of operators is carried out. Since the total mass operator commutes with the Hamiltonian in the weak sense, its eigenfunctions must be constructed in conjunction with the solution of the DeWitt equation. The consistency condition leads to the ansatz, with the help of which the solution of the DeWitt equation for the state Ψ em with a defined total mass and charge is constructed, taking into account the regularity condition on the horizon. The mass and charge spectra of the con guration in this approach turn out to be continuous. It is interesting that formal quantization in the R-region with a space evolutionary coordinate leads to a similar result.

Asymptotically flat scalar, Dirac and Proca stars: Discrete vs. continuous families of solutions

The existence of localized, approximately stationary, lumps of the classical gravitational and electromagnetic field – geons – was conjectured more than half a century ago. If one insists on exact stationarity, topologically trivial configurations in electro-vacuum are ruled out by no-go theorems for solitons. But stationary, asymptotically flat geons found a realization in scalar-vacuum, where everywhere non-singular, localized field lumps exist, known as (scalar) boson stars. Similar geons have subsequently been found in Einstein–Dirac theory and, more recently, in Einstein–Proca theory. We identify the common conditions that allow these solutions, which may also exist for other spin fields. Moreover, we present a comparison of spherically symmetric geons for the spin 0,1/2 and 1, emphasizing the mathematical similarities and clarifying the physical differences, particularly between the bosonic and fermionic cases. We clarify that for the fermionic case, Pauli's exclusion principle prevents a continuous family of solutions for a fixed field mass; rather only a discrete set exists, in contrast with the bosonic case.

Quantum preservation of the measurements precision using ultra-short strong pulses in exact analytical solution

Various schemes have been proposed to improve the parameter-estimation precision. In the present work, we suggest an alternative method to preserve the estimation precision by considering a model that closely describes a realistic experimental scenario. We explore this active way to control and enhance the measurements precision for a two-level quantum system interacting with classical electromagnetic field using ultra-short strong pulses with an exact analytical solution, i.e. beyond the rotating wave approximation. In particular, we investigate the variation of the precision with a few cycles pulse and a smooth phase jump over a finite time interval. We show that by acting on the shape of the phase transient and other parameters of the considered system, the amount of information may be increased and has smaller decay rate in the long time. These features make two-level systems incorporated in ultra-short, of-resonant and gradually changing phase good candidates for implementation of schemes for the quantum computation and the coherent information processing.

Quark and gluon production from a boost-invariantly expanding color electric field

Particle production from an expanding classical color electromagnetic field is extensively studied, motivated by the early stage dynamics of ultra-relativistic heavy ion collisions. We develop a formalism at one-loop order to compute the particle spectra by canonically quantizing quark, gluon and ghost fluctuations under the presence of such an expanding classical color background field; the canonical quantization is done in the $\tau$-$\eta$ coordinates in order to take into account manifestly the expanding geometry. As a demonstration, we model the expanding classical color background field by a boost-invariantly expanding homogeneous color electric field with lifetime $T$, for which we obtain analytically the quark and gluon production spectra by solving the equations of motion of QCD non-perturbatively with respect to the color electric field. In this paper we study (i) finite lifetime effect which is found to modify significantly the particle spectra from those expected from the Schwinger formula; (ii) the difference between the quark and gluon production; and (iii) the quark mass dependence of the production spectra. Implications of these results to ultra-relativistic heavy ion collisions are also discussed.