273 research outputs found
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 and Gauge Groups
Gauge theories with the orthogonal Cayley-Klein gauge groups and
are regarded. For nilpotent values of the contraction
parameters 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 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
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
Differential Form Valued Forms and Distributional Electromagnetic Sources
Properties of a fundamental double-form of bi-degree for are
reviewed in order to establish a distributional framework for analysing
equations of the form where
is the Hodge-de Rham operator on forms on .
Particular attention is devoted to singular distributional solutions that arise
when the source is a singular form distribution. A constructive
approach to Dirac distributions on (moving) submanifolds embedded in 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
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