Formulation Of Electrodynamics Research Articles

(Invited) A Quantum Electrodynamics Formulation of Energy Transfer Via Electric Dipole-Magnetic Dipole and Magnetic Dipole-Magnetic Dipole Interaction of Two Optically Active Ions

The nonradiative electron transfer process between optically active ions in luminescent materials via electric dipole (ED)-magnetic dipole (MD) and magnetic dipole-magnetic dipole interaction has been investigated using a molecular quantum electrodynamics (QED) approach. The QED approach provides an intuitively simple but rigorous method of calculating the energy transfer probability through multipolar interactions such as the ED-MD and MD-MD interactions considered in this work. More details of this approach and its application to resonant energy transfer between molecules through the ED-ED interaction can be obtained from Craig and Thirunamachandran [1] and references therein. The energy transfer process between two ions in the present study is shown schematically in Figure 1. While the energy levels have been considered to be discrete within the QED formulation for calculating the transition probabilities, the broadening of the energy levels in solids has been processed using the spectral line shape functions without using the special normalization in the energy space used by Dexter [2]. The transition probabilities have been simplified further using experimentally observable spectroscopic parameters such radiative lifetime and absorption cross section. The final expressions for transition probability includes additional periodic functions that are meaningful only in the short wavelength regime of the electromagnetic radiation. In this presentation, we will consider two classes of Feynman diagrams to calculate the transition rates for the energy transfer process through ED-MD and MD-MD interactions. In all the cases, the interaction between two ions is mediated by photons. In one class of diagrams, the photon is emitted first by ion A, and then absorbed by ion B at a later time. In other class of diagram, the photon is absorbed by ion B first and then emitted by ion A. The second class pertains to emission and absorption of a virtual photon. The theoretical details of calculating the transition probabilities and their significance will be presented. It will also be shown how this approach could be used in other luminescence processes to determine their plausibility and the transition rates. [1] D. P. Craig and T. Thirunamachandran, Molecular Quantum Electrodynamics, Dover Publications, Mineola, New York (1998). [2] D. L. Dexter, J. Chem. Phys. 21, 836 (1953). Figure 1. A schematic diagram of energy transfer from ion A to ion B. The associated eigenstates and eigenenergies for each of these ions are indicated. The wavy line indicates transfer of energy from the ion A and B while the solid arrows indicate the electronic transitions each ion is going through simultaneously. Figure 1

Editors' Choice—A Quantum Electrodynamics Formulation of Energy Transfer between Two Optically Active Ions

We have visited the nonradiative electron transfer process between optically active ions in luminescent materials. In contrast to the earlier formulations using multipolar expansion of instantaneous coulomb interaction between electrons, we have utilized a quantum electrodynamics (QED) approach to study the process of energy transfer from an excited ion to another. Such energy transfers occur in both sensitized luminescence and cross relaxations in the excited state. We have here investigated the nonradiative energy transfer processes specifically mediated by electric dipole moment-magnetic dipole moment and magnetic electric dipole moment-magnetic dipole moment interactions using a Feynman diagrammatic method. We have shown how experimentally relevant transfer rates could be obtained using a QED formulation involving discrete energy levels and spectral line shape function for emission and absorption profiles of interactive ions. Additional features of the dependence of the energy transfer rates on the interionic distance arising from retarded interaction potential have been pointed out.

Lagrangian and Hamiltonian formulation of classical electrodynamics without potentials

In the standard Lagrangian and Hamiltonian approach to Maxwell's theory the potentials $ A^{\mu}$ are taken as the dynamical variables. In this paper I take the electric field $ \overrightarrow{E}$ and the magnetic field $ \overrightarrow{B}$ as the dynamical variables. I find a Lagrangian that gives the dynamical Maxwell equations and include the constraint equations by using Lagrange multipliers. In passing to the Hamiltonian one finds that the canonical momenta $ \overrightarrow{\Pi}_{E}$ and $ \overrightarrow{\Pi}_{B}$ are constrained giving 6 second class constraints at each point in space. Gauss's law and $ \overrightarrow{\nabla}\cdot\overrightarrow{B}=0$ can than be added in as additional constraints. There are now 8 second class constraints, leaving 4 phase space degrees of freedom. The Dirac bracket is then introduced and is calculated for the field variables and their conjugate momenta.

Lagrangian formulation of Born-Infeld electrodynamics in fractional space

In this work, after a brief review of the Euler-Lagrange equations of motion in fractional space and Lagrangian formulation of Born-Infeld electrodynamics, we obtain the inhomogeneous and homogeneous Born-Infeld equations in fractional space. A fractional generalization of the Born-Infeld electrodynamics in vector form is found. Then, corresponding to fractal Born-Infeld equations we obtain the Laplace and Poisson equations in fractional space. Also, Faraday’s law and Amper’s law of Born-Infeld electrodynamics in fractional space are derived.

A reformulation of mechanics and electrodynamics.

Classical mechanics, as commonly taught in engineering and science, are confined to the conventional Newtonian theory. But classical mechanics has not really changed in substance since Newton formulation, describing simultaneous rotation and translation of objects with somewhat complicate drawbacks, risking interpretation of forces in non-inertial frames. In this work we introduce a new variational principle for out-of-equilibrium, rotating systems, obtaining a set of two first order differential equations that introduces a thermodynamic-mechanistic time into Newton's dynamical equation, and revealing the same formal symplectic structure shared by classical mechanics, fluid mechanics and thermodynamics. The results is a more consistent formulation of dynamics and electrodynamics, explaining natural phenomena as the outcome from a balance between energy and entropy, embedding translational with rotational motion into a single equation, showing centrifugal and Coriolis force as derivatives from the transport of angular momentum, and offering a natural method to handle variational problems, as shown with the brachistochrone problem. In consequence, a new force term appears, the topological torsion current, important for spacecraft dynamics. We describe a set of solved problems showing the potential of a competing technique, with significant interest to electrodynamics as well. We expect this new approach to have impact in a large class of scientific and technological problems.

Against fields

Using the example of classical electrodynamics, I argue that the concept of fields as mediators of particle interactions is fundamentally flawed and reflects a misguided attempt to retrieve Newtonian concepts in relativistic theories. This leads to various physical and metaphysical problems that are discussed in detail. In particular, I emphasize that physics has not found a satisfying solution to the self-interaction problem in the context of the classical field theory. To demonstrate the superiority of a pure particle ontology, I defend the direct interaction theory of Wheeler and Feynman against recent criticism and argue that it provides the most cogent formulation of classical electrodynamics.

Dispersive Properties of Mesoporous Gold: van der Waals and Near-Field Radiative Heat Interactions

We present a theoretical calculation of the dispersive interaction of mesoporous Au sponges. The ability to manipulate the dielectric function of the sponge by varying its porosity is applied to the calculation of the Hamaker constant using Lifshitz theory and the near radiative heat transfer properties. By using an effective medium approximation the dielectric function of the mesoporous sponge is calculated. As the porosity increases, our calculations show that the Hamaker constant decreases significantly. This is also used to calculate the van der Waals force between a gold nanoparticle and a gold mesoporous sponge as a function of the porosity. Also, using the fluctuating electrodynamics formalism, the change in the local electromagnetic density of states in the near field is calculated. As an application, the near field radiative heat absorbed by a SiC nanoparticle at a fixed distance from a Au sponge is calculated for different values of the porosity. The maximum heat transfer is achieved for high porosities near a metal–insulator percolation transition.

Numerical Computation of Dynamical Schwinger-like Pair Production in Graphene

The density of electron-hole pairs produced in a graphene sample immersed in a homogeneous time-dependent electrical field is evaluated. Because low energy charge carriers in graphene are described by relativistic quantum mechanics, the calculation is performed within the strong field quantum electrodynamics formalism, requiring a solution of the Dirac equation in momentum space. The latter is solved using a split-operator numerical scheme on parallel computers, allowing for the investigation of several field configurations. The strength of the method is illustrated by computing the electron momentum density generated from a realistic laser pulse model. We observe quantum interference patterns reminiscent of Landau-Zener-St\"{u}ckelberg interferometry.

Generalized noise terms for the quantized fluctuational electrodynamics

The quantization of optical fields in vacuum has been known for decades, but extending the field quantization to lossy and dispersive media in nonequilibrium conditions has proven to be complicated due to the position-dependent electric and magnetic responses of the media. In fact, consistent position-dependent quantum models for the photon number in resonant structures have only been formulated very recently and only for dielectric media. Here we present a general position-dependent quantized fluctuational electrodynamics (QFED) formalism that extends the consistent field quantization to describe the photon number also in the presence of magnetic field-matter interactions. It is shown that the magnetic fluctuations provide an additional degree of freedom in media where the magnetic coupling to the field is prominent. Therefore, the field quantization requires an additional independent noise operator that is commuting with the conventional bosonic noise operator describing the polarization current fluctuations in dielectric media. In addition to allowing the detailed description of field fluctuations, our methods provide practical tools for modeling optical energy transfer and the formation of thermal balance in general dielectric and magnetic nanodevices. We use QFED to investigate the magnetic properties of microcavity systems to demonstrate an example geometry in which it is possible to probe fields arising from the electric and magnetic source terms. We show that, as a consequence of the magnetic Purcell effect, the tuning of the position of an emitter layer placed inside a vacuum cavity can make the emissivity of a magnetic emitter to exceed the emissivity of a corresponding electric emitter.

A quantum transport model for atomic line radiation in plasmas*

Emission and absorption lines in plasmas are investigated theoretically using a phase space formulation of quantum electrodynamics. A transport equation for the one-photon Wigner function is derived and formulated in terms of the noncommutative Moyal product. This equation reduces to the standard radiative transfer equation at the large spectral band limit, when the characteristic spectral band of the emission and absorption coefficients is larger than the inverse photon absorption length and time. We examine deviations to this limit. An ideal slab geometry is considered. The Wigner function relative to hydrogen Lyman α in stellar atmospheric conditions is calculated.

Quantized fluctuational electrodynamics for three-dimensional plasmonic structures

We recently introduced a quantized fluctuational electrodynamics (QFED) formalism that provides a physically insightful definition of an effective position-dependent photon-number operator and the associated ladder operators. However, this far the formalism has been applicable only for the normal incidence of the electromagnetic field in planar structures. In this work, we overcome the main limitation of the one-dimensional QFED formalism by extending the model to three dimensions, allowing us to use the QFED method to study, e.g., plasmonic structures. To demonstrate the benefits of the developed formalism, we apply it to study the local steady-state photon numbers and field temperatures in a light-emitting near-surface InGaN quantum-well structure with a metallic coating supporting surface plasmons.

Bimetric QED

We study, as a model of Lorentz symmetry breaking, the quantisation and renormalisation of an extension of QED in a flat spacetime where the photons and electrons propagate differently and do not share the same lightcone. We will refer to this model as Bimetric QED (BIMQED). As a preliminary we discuss the formulation of electrodynamics in a pre-metric formalism showing nevertheless that there is, on the basis of a simple criteron, a preferred metric. Arising from this choice of metric is a Weyl-like tensor (WLT). The Petrov classification of the WLT gives rise to a corresponding classification of Lorentz symmetry breaking. We do not impose any constraint on the strength of the symmetry breaking and are able to obtain explicit dispersion relations for photon propagation in each of the Petrov classes. The associated birefringence appears in some cases as two distinct polarisation dependent lightcones and in other cases as a a more complicated structure that cannot be disentangled in a simple way. We show how in BIMQED the renormalisation procedure can, in addition to its effect on standard parameters such as charge and mass, force the renormalisation of the metrics and the WLT. Two particularly tractable cases are studied in detail for which we can obtain renormalisation group flows for the parameters of the model together with an analysis of fixed point structure. Of course these results are consistent with previous studies but we are not constrained to treat Lorentz symmetry breaking as necessarily weak. As we found in a previous study of a scalar field theory model an acceptable causal structure for the model imposes constraints on relationship between the various lightcones in BIMQED.

The influence of a weak magnetic field in the Renormalization-Group functions of (2 + 1)-dimensional Dirac systems

The experimental observation of the renormalization of the Fermi velocity $v_{F}$ as a function of doping has been a landmark for confirming the importance of electronic interactions in graphene. Although the experiments were performed in the presence of a perpendicular magnetic field $B$, the measurements are well described by a renormalization-group (RG) theory that did not include it. Here we clarify this issue, for both massive and massless Dirac systems, and show that for the weak magnetic fields at which the experiments are performed, there is no change in the renormalization-group functions. Our calculations are carried out in the framework of the Pseudo-quantum electrodynamics (PQED) formalism, which accounts for dynamical interactions. We include only the linear dependence in $B$, and solve the problem using two different parametrizations, the Feynman and the Schwinger one. We confirm the results obtained earlier within the RG procedure and show that, within linear order in the magnetic field, the only contribution to the renormalization of the Fermi velocity arises due to interactions. In addition, for gapped systems, we observe a running of the mass parameter.

Waveguide T-junctions with resonant coupling between sections of different dimensions

Electromagnetic characteristics of the E-plane T-junction for two rectangular waveguides using resonant coupling between the waveguide sections were studied by mathematical modeling. The problem of coupling between infinite and semi-infinite rectangular waveguides through a resonant slot in the end-wall of the semi-infinite waveguide in the presence of resonant monopole is solved in a strict electrodynamic formulation. The monopole with variable surface impedance is placed parallel to the narrow walls at an arbitrary position inside the infinite waveguide. The problem is solved analytically by the generalized method of induced electro-magneto-motive forces. Impedance vibrator inclusions with variable electro-physical parameters have been analyzed as control elements for waveguide junctions. To this purpose energy characteristics of the junction in the single-mode regime of the both waveguides, and also in multi-mode regime of the semi-infinite waveguide is investigated. The results may be useful for development of variety antennas and waveguide devices, which involves waveguide junctions.

Comment on "Gauge-invariant expectation values of the energy of a molecule in an electromagnetic field" [J. Chem. Phys. 144, 044109 (2016)

The 'problem' identified in the paper [J. Chem.Phys. 144, 044109 (2016)] does not arise in a properly formulated non-relativistic Hamiltonian formalism for both classical and quantum electrodynamics.

On the initial value formulation of classical electrodynamics

We describe a seemingly un-noticed feature of the text-book Maxwell–Lorentz system of classical electrodynamics which challenges its formulation in terms of an initial value problem. For point-charges, even after appropriate renormalization, we demonstrate that most of the generic initial data evolves to develop singularities in the electromagnetic fields along the light cones of the initial charge positions. We provide explicit formulas for the corresponding fields, demonstrate how this phenomenon renders the initial value problem ill-posed, and show how such bad initial data can be ruled out by extra conditions in addition to the Maxwell constraints. These extra conditions, however, require knowledge of the history of the solution and, as we discuss, effectively turn the Maxwell–Lorentz system into a system of delay equations much like the Fokker–Schwarzschild–Tetrode equations. For extended charges such singular light fronts persist in a smoothened form and, as we argue, yield physically doubtful solutions. Our results also apply to some extent to expectation values of field operators in quantum field theory.

On spacetime structure and electrodynamics

Electrodynamics is the most tested fundamental physical theory. Relativity arose from the completion of Maxwell–Lorentz electrodynamics. Introducing the metric [Formula: see text] as gravitational potential in 1913, versed in general (coordinate-)covariant formalism in 1914 and shortly after the completion of general relativity, Einstein put the Maxwell equations in general covariant form with only the constitutive relation between the excitation and the field dependent on and connected by the metric in 1916. Further clarification and developments by Weyl in 1918, Murnaghan in 1921, Kottler in 1922 and Cartan in 1923 together with the corresponding developments in electrodynamics of continuous media by Bateman in 1910, Tamm in 1924, Laue in 1952 and Post in 1962 established the premetric formalism of electrodynamics. Since almost all phenomena electrodynamics deal with have energy scales much lower than the Higgs mass energy and intermediate boson energy, electrodynamics of continuous media should be applicable and the constitutive relation of spacetime/vacuum should be local and linear. What is the key characteristic of the spacetime/vacuum? It is the Weak Equivalence Principle I (WEP I) for photons/wave packets of light which states that the spacetime trajectory of light in a gravitational field depends only on its initial position and direction of propagation, and does not depend on its frequency (energy) and polarization, i.e. nonbirefringence of light propagation in spacetime/vacuum. With this principle it is proved by the author in 1981 in the weak field limit, and by Lammerzahl and Hehl in 2004 together with Favaro and Bergamin in 2011 without assuming the weak-field condition that the constitutive tensor must be of the core metric form with only two additional degrees of freedom — the pseudoscalar (Abelian axion or EM axion) degree of freedom and the scalar (dilaton) degree of freedom (i.e. metric with axion and dilaton). In this paper, we review this connection and the ultrahigh precision empirical tests of nonbirefringence together with present status of tests of cosmic Abelian axion and dilaton. If the stronger version of WEP is assumed, i.e. WEP II for photons (wave packets of light) which states in addition to WEP I also that the polarization state of the light would not change (e.g. no polarization rotation for linear polarized light) and no amplification/attenuation of light, then no Abelian (EM) axion and no dilaton, and we have a pure metric theory.

Raman scattering mediated by neighboring molecules.

Raman scattering is most commonly associated with a change in vibrational state within individual molecules, the corresponding frequency shift in the scattered light affording a key way of identifying material structures. In theories where both matter and light are treated quantum mechanically, the fundamental scattering process is represented as the concurrent annihilation of a photon from one radiation mode and creation of another in a different mode. Developing this quantum electrodynamical formulation, the focus of the present work is on the spectroscopic consequences of electrodynamic coupling between neighboring molecules or other kinds of optical center. To encompass these nanoscale interactions, through which the molecular states evolve under the dual influence of the input light and local fields, this work identifies and determines two major mechanisms for each of which different selection rules apply. The constituent optical centers are considered to be chemically different and held in a fixed orientation with respect to each other, either as two components of a larger molecule or a molecular assembly that can undergo free rotation in a fluid medium or as parts of a larger, solid material. The two centers are considered to be separated beyond wavefunction overlap but close enough together to fall within an optical near-field limit, which leads to high inverse power dependences on their local separation. In this investigation, individual centers undergo a Stokes transition, whilst each neighbor of a different species remains in its original electronic and vibrational state. Analogous principles are applicable for the anti-Stokes case. The analysis concludes by considering the experimental consequences of applying this spectroscopic interpretation to fluid media; explicitly, the selection rules and the impact of pressure on the radiant intensity of this process.

Multiphoton resonant manipulation of qubits by train of pulses

We present a systematic approach based on Bloch vector's treatment and the Magnus quantum electrodynamical formalism to study qubit manipulation by a train of pulses. These investigations include one of the basic processes involved in quantum computation. The concrete calculations are performed for tunneling quantum dynamics, multiple resonance and off-resonance excitations of qubit driven by Gaussian pulses. In this way, the populations of qubit states due to multiple resonant interactions are investigated for various operational regimes including: single-pulse excitation, two-pulse excitation with phase shift between pulse envelopes being controlling parameter and for excitation with sequential pulses. In the last case, we demonstrate the formation of quasienergetic states and quasienergies of qubit driven by train of identical pulses. In this case the transition probability of qubit exhibits aperiodic oscillations, but also becomes periodically regular for definite values of the quasienergy.

Hertz potential formalism for force-free electrodynamics and its application to Brennan–Gralla–Jacobson solutions

The Hertz potential is a powerful tool for the source-free electrodynamics. Especially for the algebraically special spacetime background, the Hertz potential formalism simplifies the Maxwell equations quite much. In astrophysics, strong electric–magnetic field is very common. Force-free electrodynamics is a good approximation for strong enough electric–magnetic field compared to the inertial energy of the involved plasma. For example, the force-free model has been extensively used to describe the magnetosphere of stars in the universe. In this paper, we extend the Hertz potential formalism to the force-free electrodynamics. The Hertz potential formalism simplifies the force-free dynamical equations as much as that in the source-free case. As an application, we use the Hertz potential formalism to the Schwarzschild background. And the Brennan–Gralla–Jacobson solutions are recovered straightforwardly.