Electrodynamics of balanced charges

In this work we modify the wave-corpuscle mechanics for elementary charges introduced by us recently. This modification is designed to better describe electromagnetic (EM) phenomena at atomic scales. It includes a modification of the concept of the classical EM field and a new model for the elementary charge which we call a balanced charge (b-charge). A b-charge does not interact with itself electromagnetically, and every b-charge possesses its own elementary EM field. The EM energy is naturally partitioned as the interaction energy between pairs of different b-charges. We construct EM theory of b-charges (BEM) based on a relativistic Lagrangian with the following properties: (i) b-charges interact only through their elementary EM potentials and fields; (ii) the field equations for the elementary EM fields are exactly the Maxwell equations with proper currents; (iii) a free charge moves uniformly preserving up to the Lorentz contraction its shape; (iv) the Newton equations with the Lorentz forces hold approximately when charges are well separated and move with non-relativistic velocities. The BEM theory can be characterized as neoclassical one which covers the macroscopic as well as the atomic spatial scales, it describes EM phenomena at atomic scale differently than the classical EM theory. It yields in macroscopic regimes the Newton equations with Lorentz forces for centers of well separated charges moving with nonrelativistic velocities. Applied to atomic scales it yields a hydrogen atom model with a frequency spectrum matching the same for the Schrodinger model with any desired accuracy.Comment: Manuscript was edited to improve the exposition and to remove noticed typo

Attenuation and damping of electromagnetic fields: Influence of inertia and displacement current

New results for attenuation and damping of electromagnetic fields in rigid conducting media are derived under the conjugate influence of inertia due to charge carriers and displacement current. Inertial effects are described by a relaxation time for the current density in the realm of an extended Ohm's law. The classical notions of poor and good conductors are rediscussed on the basis of an effective electric conductivity, depending on both wave frequency and relaxation time. It is found that the attenuation for good conductors at high frequencies depends solely on the relaxation time. This means that the penetration depth saturates to a minimum value at sufficiently high frequencies. It is also shown that the actions of inertia and displacement current on damping of magnetic fields are opposite to each other. That could explain why the classical decay time of magnetic fields scales approximately as the diffusion time. At very small length scales, the decay time could be given either by the relaxation time or by a fraction of the diffusion time, depending whether inertia or displacement current, respectively, would prevail on magnetic diffusion.Comment: 21 pages, 1 figur

A derivation of Maxwell’s equations using the Heaviside notation

Maxwell's four differential equations describing electromagnetism are among the most famous equations in science. Feynman said that they provide four of the seven fundamental laws of classical physics. In this paper, we derive Maxwell's equations using a well-established approach for deriving time-dependent differential equations from static laws. The derivation uses the standard Heaviside notation. It assumes conservation of charge and that Coulomb's law of electrostatics and Ampere's law of magnetostatics are both correct as a function of time when they are limited to describing a local system. It is analogous to deriving the differential equation of motion for sound, assuming conservation of mass, Newton's second law of motion and that Hooke's static law of elasticity holds for a system in local equilibrium. This work demonstrates that it is the conservation of charge that couples time-varying E-fields and B-fields and that Faraday's Law can be derived without any relativistic assumptions about Lorentz invariance. It also widens the choice of axioms, or starting points, for understanding electromagnetism

Quantized Roentgen Effect in Bose-Einstein Condensates

A classical dielectric moving in a charged capacitor can create a magnetic field (Roentgen effect). A quantum dielectric, however, will not produce a magnetization, except at vortices. The magnetic field outside the quantum dielectric appears as the field of quantized monopoles

Gauge Theories with Cayley-Klein SO(2;j)SO(2;j) and SO(3;j)SO(3;j) Gauge Groups

Gauge theories with the orthogonal Cayley-Klein gauge groups $SO(2;j)$ and $SO(3;{\bf j})$ are regarded. For nilpotent values of the contraction parameters ${\bf j}$ these groups are isomorphic to the non-semisimple Euclid, Newton, Galilei groups and corresponding matter spaces are fiber spaces with degenerate metrics. It is shown that the contracted gauge field theories describe the same set of fields and particle mass as $SO(2), SO(3)$ gauge theories, if Lagrangians in the base and in the fibers all are taken into account. Such theories based on non-semisimple contracted group provide more simple field interactions as compared with the initial ones.Comment: 14 pages, 5 figure

Theory of Supercoupling, Squeezing Wave Energy, and Field Confinement in Narrow Channels and Tight Bends Using Epsilon-Near-Zero Metamaterials

In this work, we investigate the detailed theory of the supercoupling, anomalous tunneling effect, and field confinement originally identified in [M. Silveirinha, N. Engheta, Phys. Rev. Lett. 97, 157403, (2006)], where we demonstrated the possibility of using materials with permittivity near zero to drastically improve the transmission of electromagnetic energy through a narrow irregular channel with very subwavelength transverse cross-section. Here, we present additional physical insights, describe new applications of the tunneling effect in relevant waveguide scenarios (e.g., the "perfect" or "super" waveguide coupling), study the effect of metal losses in the metallic walls, and the possibility of using epsilon-near zero materials to confine energy in a subwavelength cavity with gigantic field enhancement. In addition, we systematically study the propagation of electromagnetic waves through narrow channels filled with anisotropic epsilon-near zero materials. It is demonstrated that these materials may have interesting potentials, and that for some particular geometries the reflectivity of the channel is independent of the specific dimensions or parameters of epsilon-near zero transition. We also describe several realistic metamaterial implementations of the studied problems, based on standard metallic waveguides, microstrip line configurations, and wire media.Comment: under revie

Differential Form Valued Forms and Distributional Electromagnetic Sources

Properties of a fundamental double-form of bi-degree $(p,p)$ for $p\ge 0$ are reviewed in order to establish a distributional framework for analysing equations of the form $$\Delta \Phi + \lambda^2 \Phi = {\cal S}$$ where $\Delta$ is the Hodge-de Rham operator on $p-$forms $\Phi$ on ${\bf R}^3$. Particular attention is devoted to singular distributional solutions that arise when the source ${\cal S}$ is a singular $p-$form distribution. A constructive approach to Dirac distributions on (moving) submanifolds embedded in ${\bf R}^3$ is developed in terms of (Leray) forms generated by the geometry of the embedding. This framework offers a useful tool in electromagnetic modeling where the possibly time dependent sources of certain physical attributes, such as electric charge, electric current and polarization or magnetization, are concentrated on localized regions in space.Comment: 40 page

A rigorous analysis of high order electromagnetic invisibility cloaks

There is currently a great deal of interest in the invisibility cloaks recently proposed by Pendry et al. that are based in the transformation approach. They obtained their results using first order transformations. In recent papers Hendi et al. and Cai et al. considered invisibility cloaks with high order transformations. In this paper we study high order electromagnetic invisibility cloaks in transformation media obtained by high order transformations from general anisotropic media. We consider the case where there is a finite number of spherical cloaks located in different points in space. We prove that for any incident plane wave, at any frequency, the scattered wave is identically zero. We also consider the scattering of finite energy wave packets. We prove that the scattering matrix is the identity, i.e., that for any incoming wave packet the outgoing wave packet is the same as the incoming one. This proves that the invisibility cloaks can not be detected in any scattering experiment with electromagnetic waves in high order transformation media, and in particular in the first order transformation media of Pendry et al. We also prove that the high order invisibility cloaks, as well as the first order ones, cloak passive and active devices. The cloaked objects completely decouple from the exterior. Actually, the cloaking outside is independent of what is inside the cloaked objects. The electromagnetic waves inside the cloaked objects can not leave the concealed regions and viceversa, the electromagnetic waves outside the cloaked objects can not go inside the concealed regions. As we prove our results for media that are obtained by transformation from general anisotropic materials, we prove that it is possible to cloak objects inside general crystals.Comment: The final version is now published in Journal of Physics A: Mathematical and Theoretical, vol 41 (2008) 065207 (21 pp). Included in IOP-Selec