814 research outputs found
Longitudinal and transverse components of a vector field
A unified account, from a pedagogical perspective, is given of the
longitudinal and transverse projective delta functions proposed by Belinfante
and of their relation to the Helmholtz theorem for the decomposition of a
three-vector field into its longitudinal and transverse components. It is
argued that the results are applicable to fields that are time-dependent as
well as fields that are time-independent.Comment: 9 pages pdf format. Includes derivation and extension of the Frahm
relation and volume integrals of projector
Compact Lattice QED and the Coulomb Potential
The potential energy of a static charge distribution on a lattice is
rigorously computed in the standard compact quantum electrodynamic model. The
method used follows closely that of Weyl for ordinary quantum electrodynamics
in continuous space-time. The potential energy of the static charge
distribution is independent of temperature and can be calculated from the
lattice version of Poisson's equation. It is the usual Coulomb potential.Comment: 6 pages, includes one figure in Topdrawer, NUB 3054/9
Condensing Nielsen-Olesen strings and the vortex-boson duality in 3+1 and higher dimensions
The vortex-boson (or Abelian-Higgs, XY) duality in 2+1 dimensions
demonstrates that the quantum disordered superfluid is equivalent to an ordered
superconductor and the other way around. Such a duality structure should be
ubiquitous but in 3+1 (and higher) dimensions a precise formulation of the
duality is lacking. The problem is that the topological defects become extended
objects, strings in 3+1D. We argue how the condensate of such vortex strings
must behave from the known physics of the disordered superfluid, namely the
Bose-Mott insulator. A flaw in earlier proposals is repaired, and a more direct
viewpoint, avoiding gauge fields, in terms of the physical supercurrent is laid
out, that also easily generalizes to higher-dimensional and more complicated
systems. Furthermore topological defects are readily identified; we demonstrate
that the Bose-Mott insulator supports line defects, which may be seen in cold
atom experiments.Comment: LaTeX, 25 pages, 5 figures; several revisions and addition
An Asymptotic Preserving Maxwell Solver Resulting in the Darwin Limit of Electrodynamics
In plasma simulations, where the speed of light divided by a characteristic
length is at a much higher frequency than other relevant parameters in the
underlying system, such as the plasma frequency, implicit methods begin to play
an important role in generating efficient solutions in these multi-scale
problems. Under conditions of scale separation, one can rescale Maxwell's
equations in such a way as to give a magneto static limit known as the Darwin
approximation of electromagnetics. In this work, we present a new approach to
solve Maxwell's equations based on a Method of Lines Transpose (MOL)
formulation, combined with a fast summation method with computational
complexity , where is the number of grid points (particles).
Under appropriate scaling, we show that the proposed schemes result in
asymptotic preserving methods that can recover the Darwin limit of
electrodynamics
Conformal electromagnetic wave propagation using primal mimetic finite elements
Elektromagnetische Wellenausbreitung bildet die physikalische Grundlage fĂŒr unzĂ€hlige Anwendungen in verschiedenen Bereichen der heutigen Welt. Um rĂ€umliche Szenarien zu modellieren, muss der kontinuierliche Raum in geeigneter Weise in ein Rechengebiet umgewandelt werden. Ăblich diskretisierte Modelle â welche auf verschiedenen GröĂen beruhen â berĂŒcksichtigen die Beziehungen zwischen Feldvariablen mittels Relationen, welche durch partielle Differentialgleichungen reprĂ€sentiert werden. Um mathematische Beziehungen zwischen abhĂ€ngigen Variablen in zweckdienlicher Art nachzubilden, schaffen hyperkomplexe Zahlensysteme ein passendes alternatives Rahmenwerk. Dieser Ansatz bezweckt das Einbinden bestimmter Systemeigenschaften und umfasst zusĂ€tzlich zur Modellierung von Feldproblemen, bei denen alle Variablen vorkommen, auch vereinfachte Modelle. Um eine wettbewerbsfĂ€hige Alternative zur ĂŒblichen numerischen Behandlung elektromagnetischer Felder in beobachtungsorientierter Weise darzubieten, wird das elektrische und magnetische Feld elektromagnetischer Wellenfelder als eine zusammengefasste FeldgröĂe, eingebettet im Funktionenraum, verstanden. Dieses Vorgehen ist intuitiv, da beide Felder in der Elektrodynamik gemeinsam auftreten und direkt messbar sind. Der Schwerpunkt dieser Arbeit ist in zwei Ziele untergliedert. Auf der einen Seite wird ein umformuliertes Maxwell-System in einer metrikfreien Umgebung mittels dem sogenannten âbikomplexen Ansatzâ umfassend untersucht. Auf der anderen Seite wird eine mögliche numerische Implementierung hinsichtlich der Finite-Elemente-Methode auf modernem Wege durch Nutzung der diskreten Ă€uĂeren Analysis mit Fokus auf Genauigkeitsbelange bewertet. Hinsichtlich der numerischen Genauigkeitsbewertung wird demonstriert, dass der vorgelegte Ansatz grundsĂ€tzlich eine höhere Exaktheit zeigt, wenn man ihn mit Formulierungen vergleicht, welche auf der Helmholtz-Gleichung beruhen. Diese Dissertation trĂ€gt eine generalisierte hyperkomplexe alternative Darstellung von gewöhnlichen elektrodynamischen Ausdrucksweisen zum Themengebiet der Wellenausbreitung bei. Durch die Nutzung einer direkten Formulierung des elektrischen Feldes in Verbindung mit dem magnetischen Feld wird die Rechengenauigkeit von Randwertproblemen erhöht. Um diese Genauigkeitserhöhung zu erreichen, wird eine geeignete Erweiterung der de Rham-Kohomologie unterbreitet.Electromagnetic wave propagation provides the physical basis for countless applications in various subjects of todayâs world. In order to model spatial scenarios, the continuous space must be converted to an appropriate computational domain. Ordinarily discretized models â which are based on distinct quantities â consider the connection between field variables by relations which are represented by partial differential equations. To reproduce mathematical relationships between dependent variables in a convenient manner, hypercomplex number systems build a suitable alternative framework. This approach aims to incorporate certain system properties and covers, in addition to the modeling of field problems where all variables are present, also simplified models. To provide a competitive alternative to the ordinary numerical handling of electromagnetic fields in an observation-based way, the electric and magnetic field of electromagnetic wave fields is understood as only one combined field variable embedded in the function space. This procedure is intuitive since both fields occur together in electrodynamics and are directly measureable. The focus of this thesis is twofold. On the one side, a reformulated Maxwell system is broadly investigated in a metric-free environment by the use of the so-called âbicomplex approachâ. On the other side, a possible numerical implementation concerning the Finite Element Method is evaluated in a modern way by the use of discrete exterior calculus with focus on accuracy matters. Regarding the numerical accuracy evaluation, it is demonstrated that the presented approach yields a higher exactness in general when comparing it to formulations which are based on the Helmholtz equation. This thesis contributes generalized hypercomplex alternative representations of ordinary electrodynamic expressions to the topic of wave propagation. By the use of a direct formulation of the electric field in conjunction with the magnetic field, the computational accuracy of boundary value problems is improved. In order to achieve this increase of accuracy, an appropriate enhancement of the de Rham cohomology is proposed
The physics of angular momentum radio
Wireless communications, radio astronomy and other radio science applications
are predominantly implemented with techniques built on top of the
electromagnetic linear momentum (Poynting vector) physical layer. As a
supplement and/or alternative to this conventional approach, techniques rooted
in the electromagnetic angular momentum physical layer have been advocated, and
promising results from proof-of-concept radio communication experiments using
angular momentum were recently published. This sparingly exploited physical
observable describes the rotational (spinning and orbiting) physical properties
of the electromagnetic fields and the rotational dynamics of the pertinent
charge and current densities. In order to facilitate the exploitation of
angular momentum techniques in real-world implementations, we present a
systematic, comprehensive theoretical review of the fundamental physical
properties of electromagnetic angular momentum observable. Starting from an
overview that puts it into its physical context among the other Poincar\'e
invariants of the electromagnetic field, we describe the multi-mode quantized
character and other physical properties that sets electromagnetic angular
momentum apart from the electromagnetic linear momentum. These properties
allow, among other things, a more flexible and efficient utilization of the
radio frequency spectrum. Implementation aspects are discussed and illustrated
by examples based on analytic and numerical solutions.Comment: Fixed LaTeX rendering errors due to inconsistencies between arXiv's
LaTeX machine and texlive in OpenSuSE 13.
Quantum Information Propagation Preserving Computational Electromagnetics
We propose a new methodology, called numerical canonical quantization, to
solve quantum Maxwell's equations useful for mathematical modeling of quantum
optics physics, and numerical experiments on arbitrary passive and lossless
quantum-optical systems. It is based on: (1) the macroscopic (phenomenological)
electromagnetic theory on quantum electrodynamics (QED), and (2) concepts
borrowed from computational electromagnetics. It was shown that canonical
quantization in inhomogeneous dielectric media required definite and proper
normal modes. Here, instead of ad-hoc analytic normal modes, we numerically
construct complete and time-reversible normal modes in the form of traveling
waves to diagonalize the Hamiltonian. Specifically, we directly solve the
Helmholtz wave equations for a general linear, reciprocal, isotropic,
non-dispersive, and inhomogeneous dielectric media by using either
finite-element or finite-difference methods. To convert a scattering problem
with infinite number of modes into one with a finite number of modes, we impose
Bloch-periodic boundary conditions. This will sparsely sample the normal modes
with numerical Bloch-Floquet-like normal modes. Subsequent procedure of
numerical canonical quantization is straightforward using linear algebra. We
provide relevant numerical recipes in detail and show an important numerical
example of indistinguishable two-photon interference in quantum beam splitters,
exhibiting Hong-Ou-Mandel effect, which is purely a quantum effect. Also, the
present methodology provides a way of numerically investigating existing or new
macroscopic QED theories. It will eventually allow quantum-optical numerical
experiments of high fidelity to replace many real experiments as in classical
electromagnetics.Comment: 17 pages, 11 figures, journal article submitted to Physical review A
(under review
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