12,677 research outputs found
Can Maxwell's equations be obtained from the continuity equation?
We formulate an existence theorem that states that given localized scalar and
vector time-dependent sources satisfying the continuity equation, there exist
two retarded fields that satisfy a set of four field equations. If the theorem
is applied to the usual electromagnetic charge and current densities, the
retarded fields are identified with the electric and magnetic fields and the
associated field equations with Maxwell's equations. This application of the
theorem suggests that charge conservation can be considered to be the
fundamental assumption underlying Maxwell's equations.Comment: 14 pages. See the comment: "O. D. Jefimenko, Causal equations for
electric and magnetic fields and Maxwell's equations: comment on a paper by
Heras [Am. J. Phys. 76, 101 (2008)].
Delay Equations and Radiation Damping
Starting from delay equations that model field retardation effects, we study
the origin of runaway modes that appear in the solutions of the classical
equations of motion involving the radiation reaction force. When retardation
effects are small, we argue that the physically significant solutions belong to
the so-called slow manifold of the system and we identify this invariant
manifold with the attractor in the state space of the delay equation. We
demonstrate via an example that when retardation effects are no longer small,
the motion could exhibit bifurcation phenomena that are not contained in the
local equations of motion.Comment: 15 pages, 1 figure, a paragraph added on page 5; 3 references adde
Replacing Leads by Self-Energies Using Nonequilibrium Green's Functions
An open quantum system consists of leads connected to a device of interest.
Within the nonequilibrium Green's function technique, we examine the
replacement of leads by self-energies in continuum calculations. Our starting
point is a formulation of the problem for continuum systems by T.E. Feuchtwang.
In this approach there is considerable flexibility in the choice of unperturbed
Green's functions. We examine the consequences of this freedom on the treatment
of leads. For any choice the leads can be replaced by coupling self-energies
which are simple functions of energy. We find that the retarded self-energy
depends on the details of the choice of unperturbed Green's function, and can
take any value. However, the nonequilibrum self-energy or scattering function
can be taken to be independent of this choice. Expressed in terms of these
self-energies, nonequilibrium transport calculations take a particularly simple
form.Comment: 14 pages, 0 figure
Quantum-classical crossover in electrodynamics
A classical field theory is proposed for the electric current and the
electromagnetic field interpolating between microscopic and macroscopic
domains. It represents a generalization of the density functional for the
dynamics of the current and the electromagnetic field in the quantum side of
the crossover and reproduces standard classical electrodynamics on the other
side. The effective action derived in the closed time path formalism and the
equations of motion follow from the variational principle. The polarization of
the Dirac-see can be taken into account in the quadratic approximation of the
action by the introduction of the deplacement field strengths as in
conventional classical electrodynamics. Decoherence appears naturally as a
simple one-loop effect in this formalism. It is argued that the radiation time
arrow is generated from the quantum boundary conditions in time by decoherence
at the quantum-classical crossover and the Abraham-Lorentz force arises from
the accelerating charge or from other charges in the macroscopic or the
microscopic side, respectively. The functional form of quantum renormalization
group, the generalization of the renormalization group method for the density
matrix, is proposed to follow the scale dependence through the
quantum-classical crossover in a systematical manner.Comment: new references added, few sign errors fixed, to appear in Physical
Review
Controversies in the History of the Radiation Reaction problem in General Relativity
This paper examines the historical controversy over whether gravitationally
bound systems, such as binary stars, experienced orbital damping due to the
emission of gravitational radiation, focusing especially on the period of the
1950s, but also discussing the work of Einstein and Rosen in the 1930s on
cylindrical gravitational waves and the later quadrupole formula controversy.Comment: 33 pages, Late
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