3,258 research outputs found
The quantum metrology triangle and the re-definition of the SI ampere and kilogram; Analysis of a reduced set of observational equations
We have developed a set of seven observational equations that include all of
the physics necessary to relate the most important of the fundamental constants
to the definitions of the SI kilogram and ampere. We have used these to
determine the influence of alternative definitions being considered for the SI
kilogram and ampere on the uncertainty of three of the fundamental constants
(h, e and mu). We have also reviewed the experimental evidence for the
exactness of the quantum metrology triangle resulting from experiments
combining the quantum Hall effect, the Josephson effects and single-electron
tunnelling.Comment: 16 pages, 3 figures & 5 table
Resonance between Noise and Delay
We propose here a stochastic binary element whose transition rate depends on
its state at a fixed interval in the past. With this delayed stochastic
transition this is one of the simplest dynamical models under the influence of
``noise'' and ``delay''. We demonstrate numerically and analytically that we
can observe resonant phenomena between the oscillatory behavior due to noise
and that due to delay.Comment: 4 pages, 5 figures, submitted to Phys.Rev.Lett Expanded and Added
Reference
Casimir Force on a Micrometer Sphere in a Dip: Proposal of an Experiment
The attractive Casimir force acting on a micrometer-sphere suspended in a
spherical dip, close to the wall, is discussed. This setup is in principle
directly accessible to experiment. The sphere and the substrate are assumed to
be made of the same perfectly conducting material.Comment: 11 pages, 1 figure; to appear in J. Phys. A: Math. Ge
Multiple Scattering: Dispersion, Temperature Dependence, and Annular Pistons
We review various applications of the multiple scattering approach to the
calculation of Casimir forces between separate bodies, including dispersion,
wedge geometries, annular pistons, and temperature dependence. Exact results
are obtained in many cases.Comment: 15 pages, 12 figures, contributed to the Festschrift for Emilio
Elizald
Casimir Energy of a Spherical Shell
The Casimir energy for a conducting spherical shell of radius is computed
using a direct mode summation approach. An essential ingredient is the
implementation of a recently proposed method based on Cauchy's theorem for an
evaluation of the eigenfrequencies of the system. It is shown, however, that
this earlier calculation uses an improper set of modes to describe the waves
exterior to the sphere. Upon making the necessary corrections and taking care
to ensure that no mathematically ill-defined expressions occur, the technique
is shown to leave numerical results unaltered while avoiding a longstanding
criticism raised against earlier calculations of the Casimir energy.Comment: LaTeX, 14 pages, 1 figur
Identity of the van der Waals Force and the Casimir Effect and the Irrelevance of these Phenomena to Sonoluminescence
We show that the Casimir, or zero-point, energy of a dilute dielectric ball,
or of a spherical bubble in a dielectric medium, coincides with the sum of the
van der Waals energies between the molecules that make up the medium. That
energy, which is finite and repulsive when self-energy and surface effects are
removed, may be unambiguously calculated by either dimensional continuation or
by zeta function regularization. This physical interpretation of the Casimir
energy seems unambiguous evidence that the bulk self-energy cannot be relevant
to sonoluminescence.Comment: 7 pages, no figures, REVTe
Casimir Forces: An Exact Approach for Periodically Deformed Objects
A novel approach for calculating Casimir forces between periodically deformed
objects is developed. This approach allows, for the first time, a rigorous
non-perturbative treatment of the Casimir effect for disconnected objects
beyond Casimir's original two-plate configuration. The approach takes into
account the collective nature of fluctuation induced forces, going beyond the
commonly used pairwise summation of two-body van der Waals forces. As an
application of the method, we exactly calculate the Casimir force due to scalar
field fluctuations between a flat and a rectangular corrugated plate. In the
latter case, the force is found to be always attractive.Comment: 4 pages, 3 figure
Vector Casimir effect for a D-dimensional sphere
The Casimir energy or stress due to modes in a D-dimensional volume subject
to TM (mixed) boundary conditions on a bounding spherical surface is
calculated. Both interior and exterior modes are included. Together with
earlier results found for scalar modes (TE modes), this gives the Casimir
effect for fluctuating ``electromagnetic'' (vector) fields inside and outside a
spherical shell. Known results for three dimensions, first found by Boyer, are
reproduced. Qualitatively, the results for TM modes are similar to those for
scalar modes: Poles occur in the stress at positive even dimensions, and cusps
(logarithmic singularities) occur for integer dimensions . Particular
attention is given the interesting case of D=2.Comment: 20 pages, 1 figure, REVTe
Casimir Energy for Spherical boundaries
Calculations of the Casimir energy for spherical geometries which are based
on integrations of the stress tensor are critically examined. It is shown that
despite their apparent agreement with numerical results obtained from mode
summation methods, they contain a number of serious errors. Specifically, these
include (1) an improper application of the stress tensor to spherical
boundaries, (2) the neglect of pole terms in contour integrations, and (3) the
imposition of inappropriate boundary conditions upon the relevant propagators.
A calculation which is based on the stress tensor and which avoids such
problems is shown to be possible. It is, however, equivalent to the mode
summation method and does not therefore constitute an independent calculation
of the Casimir energy.Comment: Revtex, 7 pages, Appendix added providing details of failure of
stress tensor metho
Direct mode summation for the Casimir energy of a solid ball
The Casimir energy of a solid ball placed in an infinite medium is calculated
by a direct frequency summation using the contour integration. It is assumed
that the permittivity and permeability of the ball and medium satisfy the
condition . Upon deriving the general
expression for the Casimir energy, a dilute compact ball is considered
. In this case the
calculations are carried out which are of the first order in and take
account of the five terms in the Debye expansion of the Bessel functions
involved. The implication of the obtained results to the attempts of explaining
the sonoluminescence via the Casimir effect is shortly discussed.Comment: REVTeX, 7 pages, no figures and tables, treatment of a dilute
dielectric ball is revised, new references are adde
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