444 research outputs found
Interference in the radiation of two point-like charges
Energy-momentum and angular momentum carried by electromagnetic field of two
point-like charged particles arbitrarily moving in flat spacetime are
presented. Apart from usual contributions to the Noether quantities produced
separately by particles 1 and 2, the conservation laws contain also joint
contribution due to the fields of both particles. The mixed part of Maxwell
energy-momentum density is decomposed into bound and radiative components which
are separately conserved off the world lines of particles. The former describes
the deformation of electromagnetic clouds of ``bare'' charges due to mutual
interaction while the latter defines the radiation which escapes to infinity.
The bound terms contribute to particles' individual 4-momenta while the
radiative ones exert the radiation reaction. Analysis of energy-momentum and
angular momentum balance equations results the Lorentz-Dirac equation as an
equation of motion for a pointed charge under the influence of its own
electromagnetic field as well as field produced by another charge.Comment: 46 pages, 8 figure
Causal Classical Theory of Radiation Damping
It is shown how initial conditions can be appropriately defined for the
integration of Lorentz-Dirac equations of motion. The integration is performed
\QTR{it}{forward} in time. The theory is applied to the case of the motion of
an electron in an intense laser pulse, relevant to nonlinear Compton
scattering.Comment: 8 pages, 2 figure
Regulator constants and the parity conjecture
The p-parity conjecture for twists of elliptic curves relates multiplicities
of Artin representations in p-infinity Selmer groups to root numbers. In this
paper we prove this conjecture for a class of such twists. For example, if E/Q
is semistable at 2 and 3, K/Q is abelian and K^\infty is its maximal pro-p
extension, then the p-parity conjecture holds for twists of E by all orthogonal
Artin representations of Gal(K^\infty/Q). We also give analogous results when
K/Q is non-abelian, the base field is not Q and E is replaced by an abelian
variety. The heart of the paper is a study of relations between permutation
representations of finite groups, their "regulator constants", and
compatibility between local root numbers and local Tamagawa numbers of abelian
varieties in such relations.Comment: 50 pages; minor corrections; final version, to appear in Invent. Mat
Controlled Dephasing of a Quantum Dot: From Coherent to Sequential Tunneling
Resonant tunneling through identical potential barriers is a textbook problem
in quantum mechanics. Its solution yields total transparency (100% tunneling)
at discrete energies. This dramatic phenomenon results from coherent
interference among many trajectories, and it is the basis of transport through
periodic structures. Resonant tunneling of electrons is commonly seen in
semiconducting 'quantum dots'. Here we demonstrate that detecting
(distinguishing) electron trajectories in a quantum dot (QD) renders the QD
nearly insulating. We couple trajectories in the QD to a 'detector' by
employing edge channels in the integer quantum Hall regime. That is, we couple
electrons tunneling through an inner channel to electrons in the neighboring
outer, 'detector' channel. A small bias applied to the detector channel
suffices to dephase (quench) the resonant tunneling completely. We derive a
formula for dephasing that agrees well with our data and implies that just a
few electrons passing through the detector channel suffice to dephase the QD
completely. This basic experiment shows how path detection in a QD induces a
transition from delocalization (due to coherent tunneling) to localization
(sequential tunneling)
Radiation from a charged particle and radiation reaction -- revisited
We study the electromagnetic fields of an arbitrarily moving charged particle
and the radiation reaction on the charged particle using a novel approach. We
first show that the fields of an arbitrarily moving charged particle in an
inertial frame can be related in a simple manner to the fields of a uniformly
accelerated charged particle in its rest frame. Since the latter field is
static and easily obtainable, it is possible to derive the fields of an
arbitrarily moving charged particle by a coordinate transformation. More
importantly, this formalism allows us to calculate the self-force on a charged
particle in a remarkably simple manner. We show that the original expression
for this force, obtained by Dirac, can be rederived with much less computation
and in an intuitively simple manner using our formalism.Comment: Submitted to Physical Review
On the Green-Functions of the classical offshell electrodynamics under the manifestly covariant relativistic dynamics of Stueckelberg
In previous paper derivations of the Green function have been given for 5D
off-shell electrodynamics in the framework of the manifestly covariant
relativistic dynamics of Stueckelberg (with invariant evolution parameter
). In this paper, we reconcile these derivations resulting in different
explicit forms, and relate our results to the conventional fundamental
solutions of linear 5D wave equations published in the mathematical literature.
We give physical arguments for the choice of the Green function retarded in the
fifth variable .Comment: 16 pages, 1 figur
One-mirror Fabry-Perot and one-slit Young interferometry
We describe a new and distinctive interferometry in which a probe particle
scatters off a superposition of locations of a single free target particle. In
one dimension, probe particles incident on superposed locations of a single
"mirror" can interfere as if in a Fabry-Perot interferometer; in two
dimensions, probe particles scattering off superposed locations of a single
"slit" can interfere as if in a two-slit Young interferometer. The condition
for interference is loss of orthogonality of the target states and reduces, in
simple examples, to transfer of orthogonality from target to probe states. We
analyze experimental parameters and conditions necessary for interference to be
observed.Comment: 5 pages, 2 figures, RevTeX, submitted to PR
Singularity-Free Electrodynamics for Point Charges and Dipoles: Classical Model for Electron Self-Energy and Spin
It is shown how point charges and point dipoles with finite self-energies can
be accomodated into classical electrodynamics. The key idea is the introduction
of constitutive relations for the electromagnetic vacuum, which actually
mirrors the physical reality of vacuum polarization. Our results reduce to
conventional electrodynamics for scales large compared to the classical
electron radius cm. A classical simulation for a
structureless electron is proposed, with the appropriate values of mass, spin
and magnetic moment.Comment: 3 page
Self force in 2+1 electrodynamics
The radiation reaction problem for an electric charge moving in flat
space-time of three dimensions is discussed. The divergences stemming from the
pointness of the particle are studied. A consistent regularization procedure is
proposed, which exploits the Poincar\'e invariance of the theory. Effective
equation of motion of radiating charge in an external electromagnetic field is
obtained via the consideration of energy-momentum and angular momentum
conservation. This equation includes the effect of the particle's own field.
The radiation reaction is determined by the Lorentz force of point-like charge
acting upon itself plus a non-local term which provides finiteness of the
self-action.Comment: 20 pages, 3 figure
Radiation reaction on charged particles in three-dimensional motion in classical and quantum electrodynamics
We extend our previous work (see arXiv:quant-ph/0501026), which compared the
predictions of quantum electrodynamics concerning radiation reaction with those
of the Abraham-Lorentz-Dirac theory for a charged particle in linear motion.
Specifically, we calculate the predictions for the change in position of a
charged scalar particle, moving in three-dimensional space, due to the effect
of radiation reaction in the one-photon-emission process in quantum
electrodynamics. The scalar particle is assumed to be accelerated for a finite
period of time by a three-dimensional electromagnetic potential dependent only
on one of the spacetime coordinates. We perform this calculation in the
limit and show that the change in position agrees with that
obtained in classical electrodynamics with the Lorentz-Dirac force treated as a
perturbation. We also show for a time-dependent but space-independent
electromagnetic potential that the forward-scattering amplitude at order
does not contribute to the position change in the limit after the
mass renormalization is taken into account.Comment: Latex, 20page
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