5,056 research outputs found
Coulomb field of an accelerated charge: physical and mathematical aspects
The Maxwell field equations relative to a uniformly accelerated frame, and
the variational principle from which they are obtained, are formulated in terms
of the technique of geometrical gauge invariant potentials. They refer to the
transverse magnetic (TM) and the transeverse electric (TE) modes. This gauge
invariant "2+2" decomposition is used to see how the Coulomb field of a charge,
static in an accelerated frame, has properties that suggest features of
electromagnetism which are different from those in an inertial frame. In
particular, (1) an illustrative calculation shows that the Larmor radiation
reaction equals the electrostatic attraction between the accelerated charge and
the charge induced on the surface whose history is the event horizon, and (2) a
spectral decomposition of the Coulomb potential in the accelerated frame
suggests the possibility that the distortive effects of this charge on the
Rindler vacuum are akin to those of a charge on a crystal lattice.Comment: 27 pages, PlainTex. Related papers available at
http://www.math.ohio-state.edu/~gerlac
Radiation from Violently Accelerated Bodies
A determination is made of the radiation emitted by a linearly uniformly
accelerated uncharged dipole transmitter. It is found that, first of all, the
radiation rate is given by the familiar Larmor formula, but it is augmented by
an amount which becomes dominant for sufficiently high acceleration. For an
accelerated dipole oscillator, the criterion is that the center of mass motion
become relativistic within one oscillation period. The augmented formula and
the measurements which it summarizes presuppose an expanding inertial
observation frame. A static inertial reference frame will not do. Secondly, it
is found that the radiation measured in the expanding inertial frame is
received with 100% fidelity. There is no blueshift or redshift due to the
accelerative motion of the transmitter. Finally, it is found that a pair of
coherently radiating oscillators accelerating (into opposite directions) in
their respective causally disjoint Rindler-coordinatized sectors produces an
interference pattern in the expanding inertial frame. Like the pattern of a
Young double slit interferometer, this Rindler interferometer pattern has a
fringe spacing which is inversely proportional to the proper separation and the
proper frequency of the accelerated sources. The interferometer, as well as the
augmented Larmor formula, provide a unifying perspective. It joins adjacent
Rindler-coordinatized neighborhoods into a single spacetime arena for
scattering and radiation from accelerated bodies.Comment: 29 pages, 1 figure, Revte
Quantum Mechanical Carrier of the Imprints of Gravitation
We exhibit a purely quantum mechanical carrier of the imprints of gravitation
by identifying for a relativistic system a property which (i) is independent of
its mass and (ii) expresses the Poincare invariance of spacetime in the absence
of gravitation. This carrier consists of the phase and amplitude correlations
of waves in oppositely accelerating frames. These correlations are expressed as
a Klein-Gordon-equation-determined vector field whose components are the
``Planckian power'' and the ``r.m.s. thermal fluctuation'' spectra. The
imprints themselves are deviations away from this vector field.Comment: 8 pages, RevTex. Html version of this and related papers on
accelerated frames available at http://www.math.ohio-state.edu/~gerlac
Test Beam Results of Geometry Optimized Hybrid Pixel Detectors
The Multi-Chip-Module-Deposited (MCM-D) technique has been used to build
hybrid pixel detector assemblies. This paper summarises the results of an
analysis of data obtained in a test beam campaign at CERN. Here, single chip
hybrids made of ATLAS pixel prototype read-out electronics and special sensor
tiles were used. They were prepared by the Fraunhofer Institut fuer
Zuverlaessigkeit und Mikrointegration, IZM, Berlin, Germany. The sensors
feature an optimized sensor geometry called equal sized bricked. This design
enhances the spatial resolution for double hits in the long direction of the
sensor cells.Comment: Contribution to Proceedings of Pixel2005 Workshop, Bonn Germany 200
Bubble wall perturbations coupled with gravitational waves
We study a coupled system of gravitational waves and a domain wall which is
the boundary of a vacuum bubble in de Sitter spacetime. To treat the system, we
use the metric junction formalism of Israel. We show that the dynamical degree
of the bubble wall is lost and the bubble wall can oscillate only while the
gravitational waves go across it. It means that the gravitational backreaction
on the motion of the bubble wall can not be ignored.Comment: 23 pages with 3 eps figure
Probing the local dynamics of periodic orbits by the generalized alignment index (GALI) method
As originally formulated, the Generalized Alignment Index (GALI) method of
chaos detection has so far been applied to distinguish quasiperiodic from
chaotic motion in conservative nonlinear dynamical systems. In this paper we
extend its realm of applicability by using it to investigate the local dynamics
of periodic orbits. We show theoretically and verify numerically that for
stable periodic orbits the GALIs tend to zero following particular power laws
for Hamiltonian flows, while they fluctuate around non-zero values for
symplectic maps. By comparison, the GALIs of unstable periodic orbits tend
exponentially to zero, both for flows and maps. We also apply the GALIs for
investigating the dynamics in the neighborhood of periodic orbits, and show
that for chaotic solutions influenced by the homoclinic tangle of unstable
periodic orbits, the GALIs can exhibit a remarkable oscillatory behavior during
which their amplitudes change by many orders of magnitude. Finally, we use the
GALI method to elucidate further the connection between the dynamics of
Hamiltonian flows and symplectic maps. In particular, we show that, using for
the computation of GALIs the components of deviation vectors orthogonal to the
direction of motion, the indices of stable periodic orbits behave for flows as
they do for maps.Comment: 17 pages, 9 figures (accepted for publication in Int. J. of
Bifurcation and Chaos
The generalization of the Regge-Wheeler equation for self-gravitating matter fields
It is shown that the dynamical evolution of perturbations on a static
spacetime is governed by a standard pulsation equation for the extrinsic
curvature tensor. The centerpiece of the pulsation equation is a wave operator
whose spatial part is manifestly self-adjoint. In contrast to metric
formulations, the curvature-based approach to gravitational perturbation theory
generalizes in a natural way to self-gravitating matter fields. For a certain
relevant subspace of perturbations the pulsation operator is symmetric with
respect to a positive inner product and therefore allows spectral theory to be
applied. In particular, this is the case for odd-parity perturbations of
spherically symmetric background configurations. As an example, the pulsation
equations for self-gravitating, non-Abelian gauge fields are explicitly shown
to be symmetric in the gravitational, the Yang Mills, and the off-diagonal
sector.Comment: 4 pages, revtex, no figure
Numerical integration of variational equations
We present and compare different numerical schemes for the integration of the
variational equations of autonomous Hamiltonian systems whose kinetic energy is
quadratic in the generalized momenta and whose potential is a function of the
generalized positions. We apply these techniques to Hamiltonian systems of
various degrees of freedom, and investigate their efficiency in accurately
reproducing well-known properties of chaos indicators like the Lyapunov
Characteristic Exponents (LCEs) and the Generalized Alignment Indices (GALIs).
We find that the best numerical performance is exhibited by the
\textit{`tangent map (TM) method'}, a scheme based on symplectic integration
techniques which proves to be optimal in speed and accuracy. According to this
method, a symplectic integrator is used to approximate the solution of the
Hamilton's equations of motion by the repeated action of a symplectic map ,
while the corresponding tangent map , is used for the integration of the
variational equations. A simple and systematic technique to construct is
also presented.Comment: 27 pages, 11 figures, to appear in Phys. Rev.
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