301 research outputs found
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
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
On the Electromagnetic Properties of Matter in Collapse Models
We discuss the electromagnetic properties of both a charged free particle,
and a charged particle bounded by an harmonic potential, within collapse
models. By choosing a particularly simple, yet physically relevant, collapse
model, and under only the dipole approximation, we are able to solve the
equation of motion exactly. In this way, both the finite time and large time
behavior can be analyzed accurately. We discovered new features, which did not
appear in previous works on the same subject. Since, so far, the spontaneous
photon emission process places the strongest upper bounds on the collapse
parameters, our results call for a further analysis of this process for those
atomic systems which can be employed in experimental tests of collapse models,
as well as of quantum mechanics.Comment: 17 pages, LaTeX, updated version with minor change
Spin superfluidity and spin-orbit gauge symmetry fixing
The Hamiltonian describing 2D electron gas, in a spin-orbit active medium,
can be cast into a consistent non-Abelian gauge field theory leading to a
proper definition of the spin current. The generally advocated gauge symmetric
version of the theory results in current densities that are gauge covariant, a
fact that poses severe concerns on their physical nature. We show that in fact
the problem demands gauge fixing, leaving no room to ambiguity in the
definition of physical spin currents. Gauge fixing also allows for polarized
edge excitations not present in the gauge symmetric case. The scenario here is
analogous to that of superconductivity gauge theory. We develop a variational
formulation that accounts for the constraints between U(1) physical fields and
SU(2) gauge fields and show that gauge fixing renders a physical matter and
radiation currents and derive the particular consequences for the Rashba SO
interaction.Comment: to appear in EP
Exact solution of the EM radiation-reaction problem for classical finite-size and Lorentzian charged particles
An exact solution is given to the classical electromagnetic (EM)
radiation-reaction (RR) problem, originally posed by Lorentz. This refers to
the dynamics of classical non-rotating and quasi-rigid finite size particles
subject to an external prescribed EM field. A variational formulation of the
problem is presented. It is shown that a covariant representation for the EM
potential of the self-field generated by the extended charge can be uniquely
determined, consistent with the principles of classical electrodynamics and
relativity. By construction, the retarded self 4-potential does not possess any
divergence, contrary to the case of point charges. As a fundamental
consequence, based on Hamilton variational principle, an exact representation
is obtained for the relativistic equation describing the dynamics of a
finite-size charged particle (RR equation), which is shown to be realized by a
second-order delay-type ODE. Such equation is proved to apply also to the
treatment of Lorentzian particles, i.e., point-masses with finite-size charge
distributions, and to recover the usual LAD equation in a suitable asymptotic
approximation. Remarkably, the RR equation admits both standard Lagrangian and
conservative forms, expressed respectively in terms of a non-local effective
Lagrangian and a stress-energy tensor. Finally, consistent with the Newton
principle of determinacy, it is proved that the corresponding initial-value
problem admits a local existence and uniqueness theorem, namely it defines a
classical dynamical system
On the Solutions of the Lorentz-Dirac Equation
We discuss the unstable character of the solutions of the Lorentz-Dirac
equation and stress the need of methods like order reduction to derive a
physically acceptable equation of motion. The discussion is illustrated with
the paradigmatic example of the non-relativistic harmonic oscillator with
radiation reaction. We also illustrate removal of the noncasual
pre-acceleration with the introduction of a small correction in the
Lorentz-Dirac equation.Comment: 4 eps figs. to be published in GR
Accelerated Detector - Quantum Field Correlations: From Vacuum Fluctuations to Radiation Flux
In this paper we analyze the interaction of a uniformly accelerated detector
with a quantum field in (3+1)D spacetime, aiming at the issue of how kinematics
can render vacuum fluctuations the appearance of thermal radiance in the
detector (Unruh effect) and how they engender flux of radiation for observers
afar. Two basic questions are addressed in this study: a) How are vacuum
fluctuations related to the emitted radiation? b) Is there emitted radiation
with energy flux in the Unruh effect? We adopt a method which places the
detector and the field on an equal footing and derive the two-point correlation
functions of the detector and of the field separately with full account of
their interplay. From the exact solutions, we are able to study the complete
process from the initial transient to the final steady state, keeping track of
all activities they engage in and the physical effects manifested. We derive a
quantum radiation formula for a Minkowski observer. We find that there does
exist a positive radiated power of quantum nature emitted by the detector, with
a hint of certain features of the Unruh effect. We further verify that the
total energy of the dressed detector and a part of the radiated energy from the
detector is conserved. However, this part of the radiation ceases in steady
state. So the hint of the Unruh effect in radiated power is actually not
directly from the energy flux that the detector experiences in Unruh effect.
Since all the relevant quantum and statistical information about the detector
(atom) and the field can be obtained from the results presented here, they are
expected to be useful, when appropriately generalized, for addressing issues of
quantum information processing in atomic and optical systems, such as quantum
decoherence, entanglement and teleportation.Comment: 24 pages, 11 figures, new results and comments added in Secs.VI and
VII, with other corresponding change
New Insights into Uniformly Accelerated Detector in a Quantum Field
We obtained an exact solution for a uniformly accelerated Unruh-DeWitt
detector interacting with a massless scalar field in (3+1) dimensions which
enables us to study the entire evolution of the total system, from the initial
transient to late-time steady state. We find that the Unruh effect as derived
from time-dependent perturbation theory is valid only in the transient stage
and is totally invalid for cases with proper acceleration smaller than the
damping constant. We also found that, unlike in (1+1)D results, the (3+1)D
uniformly accelerated Unruh-DeWitt detector in a steady state does emit a
positive radiated power of quantum nature at late-times, but it is not
connected to the thermal radiance experienced by the detector in the Unruh
effect proper.Comment: 6 pages, invited talk given by SYL at the conference of International
Association for Relativistic Dynamics (IARD), June 2006, Storrs, Connecticut,
US
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