30 research outputs found
Comment on ``Consistency, amplitudes and probabilities in quantum theory'' by A. Caticha
A carefully written paper by A. Caticha [Phys. Rev. A57, 1572 (1998)] applies
consistency arguments to derive the quantum mechanical rules for compounding
probability amplitudes in much the same way as earlier work by the present
author [J. Math. Phys. 29, 398 (1988) and Int. J. Theor. Phys. 27, 543 (1998)].
These works are examined together to find the minimal assumptions needed to
obtain the most general results
Casimir Force between a Dielectric Sphere and a Wall: A Model for Amplification of Vacuum Fluctuations
The interaction between a polarizable particle and a reflecting wall is
examined. A macroscopic approach is adopted in which the averaged force is
computed from the Maxwell stress tensor. The particular case of a perfectly
reflecting wall and a sphere with a dielectric function given by the Drude
model is examined in detail. It is found that the force can be expressed as the
sum of a monotonically decaying function of position and of an oscillatory
piece. At large separations, the oscillatory piece is the dominant
contribution, and is much larger than the Casimir-Polder interaction that
arises in the limit that the sphere is a perfect conductor. It is argued that
this enhancement of the force can be interpreted in terms of the frequency
spectrum of vacuum fluctuations. In the limit of a perfectly conducting sphere,
there are cancellations between different parts of the spectrum which no longer
occur as completely in the case of a sphere with frequency dependent
polarizability. Estimates of the magnitude of the oscillatory component of the
force suggest that it may be large enough to be observable.Comment: 18pp, LaTex, 7 figures, uses epsf. Several minor errors corrected,
additional comments added in the final two sections, and references update
Casimir-Polder interaction of atoms with magnetodielectric bodies
A general theory of the Casimir-Polder interaction of single atoms with
dispersing and absorbing magnetodielectric bodies is presented, which is based
on QED in linear, causal media. Both ground-state and excited atoms are
considered. Whereas the Casimir-Polder force acting on a ground-state atom can
conveniently be derived from a perturbative calculation of the atom-field
coupling energy, an atom in an excited state is subject to transient force
components that can only be fully understood by a dynamical treatment based on
the body-assisted vacuum Lorentz force. The results show that the
Casimir-Polder force can be influenced by the body-induced broadening and
shifting of atomic transitions - an effect that is not accounted for within
lowest-order perturbation theory. The theory is used to study the
Casimir-Polder force of a ground-state atom placed within a magnetodielectric
multilayer system, with special emphasis on thick and thin plates as well as a
planar cavity consisting of two thick plates. It is shown how the competing
attractive and repulsive force components related to the electric and magnetic
properties of the medium, respectively, can - for sufficiently strong magnetic
properties - lead to the formation of potential walls and wells.Comment: 16 pages, 6 figures, minor additions and correction
Retarded long-range potentials for the alkali-metal atoms and a perfectly conducting wall
The retarded long-range potentials for hydrogen and alkali-metal atoms in
their ground states and a perfectly conducting wall are calculated. The
potentials are given over a wide range of atom-wall distances and the validity
of the approximations used is established.Comment: RevTeX, epsf, 11 pages, 2 fig
Using atomic interference to probe atom-surface interaction
We show that atomic interference in the reflection from two suitably
polarized evanescent waves is sensitive to retardation effects in the
atom-surface interaction for specific experimental parameters. We study the
limit of short and long atomic de Broglie wavelength. The former case is
analyzed in the semiclassical approximation (Landau-Zener model). The latter
represents a quantum regime and is analyzed by solving numerically the
associated coupled Schroedinger equations. We consider a specific experimental
scheme and show the results for rubidium (short wavelength) and the much
lighter meta-stable helium atom (long wavelength). The merits of each case are
then discussed.Comment: 11 pages, including 6 figures, submitted to Phys. Rev. A, RevTeX
sourc
Long-range interactions of metastable helium atoms
Polarizabilities, dispersion coefficients, and long-range atom-surface
interaction potentials are calculated for the n=2 triplet and singlet states of
helium using highly accurate, variationally determined, wave functions.Comment: RevTeX, epsf, 4 fig
Quantum Integrals of Motion for Variable Quadratic Hamiltonians
We construct the integrals of motion for several models of the quantum damped
oscillators in nonrelativistic quantum mechanics in a framework of a general
approach to the time-dependent Schroedinger equation with variable quadratic
Hamiltonians. An extension of Lewis-Riesenfeld dynamical invariant is given.
The time-evolution of the expectation values of the energy related positive
operators is determined for the oscillators under consideration. A proof of
uniqueness of the corresponding Cauchy initial value problem is discussed as an
application.Comment: 32 pages, no figure
On Born approximation in black hole scattering
A massless field propagating on spherically symmetric black hole metrics such
as the Schwarzschild, Reissner-Nordstr\"{o}m and Reissner-Nordstr\"{o}m-de
Sitter backgrounds is considered. In particular, explicit formulae in terms of
transcendental functions for the scattering of massless scalar particles off
black holes are derived within a Born approximation. It is shown that the
conditions on the existence of the Born integral forbid a straightforward
extraction of the quasi normal modes using the Born approximation for the
scattering amplitude. Such a method has been used in literature. We suggest a
novel, well defined method, to extract the large imaginary part of quasinormal
modes via the Coulomb-like phase shift. Furthermore, we compare the numerically
evaluated exact scattering amplitude with the Born one to find that the
approximation is not very useful for the scattering of massless scalar,
electromagnetic as well as gravitational waves from black holes