1,005 research outputs found
Sonoluminescence as a QED vacuum effect. II: Finite Volume Effects
In a companion paper [quant-ph/9904013] we have investigated several
variations of Schwinger's proposed mechanism for sonoluminescence. We
demonstrated that any realistic version of Schwinger's mechanism must depend on
extremely rapid (femtosecond) changes in refractive index, and discussed ways
in which this might be physically plausible. To keep that discussion tractable,
the technical computations in that paper were limited to the case of a
homogeneous dielectric medium. In this paper we investigate the additional
complications introduced by finite-volume effects. The basic physical scenario
remains the same, but we now deal with finite spherical bubbles, and so must
decompose the electromagnetic field into Spherical Harmonics and Bessel
functions. We demonstrate how to set up the formalism for calculating Bogolubov
coefficients in the sudden approximation, and show that we qualitatively retain
the results previously obtained using the homogeneous-dielectric (infinite
volume) approximation.Comment: 23 pages, LaTeX 209, ReV-TeX 3.2, five figure
Analysis of Fourier transform valuation formulas and applications
The aim of this article is to provide a systematic analysis of the conditions
such that Fourier transform valuation formulas are valid in a general
framework; i.e. when the option has an arbitrary payoff function and depends on
the path of the asset price process. An interplay between the conditions on the
payoff function and the process arises naturally. We also extend these results
to the multi-dimensional case, and discuss the calculation of Greeks by Fourier
transform methods. As an application, we price options on the minimum of two
assets in L\'evy and stochastic volatility models.Comment: 26 pages, 3 figures, to appear in Appl. Math. Financ
Vortex in a trapped Bose-Einstein condensate with dipole-dipole interactions
We calculate the critical rotation frequency at which a vortex state becomes
energetically favorable over the vortex-free ground state in a harmonically
trapped Bose-Einstein condensate whose atoms have dipole-dipole interactions as
well as the usual s-wave contact interactions. In the Thomas-Fermi
(hydrodynamic) regime, dipolar condensates in oblate cylindrical traps (with
the dipoles aligned along the axis of symmetry of the trap) tend to have lower
critical rotation frequencies than their purely s-wave contact interaction
counterparts. The converse is true for dipolar condensates in prolate traps.
Quadrupole excitations and centre of mass motion are also briefly discussed as
possible competing mechanisms to a vortex as means by which superfluids with
partially attractive interactions might carry angular momentumComment: 12 pages, 12 figure
Gauge Theories with Cayley-Klein and Gauge Groups
Gauge theories with the orthogonal Cayley-Klein gauge groups and
are regarded. For nilpotent values of the contraction
parameters these groups are isomorphic to the non-semisimple Euclid,
Newton, Galilei groups and corresponding matter spaces are fiber spaces with
degenerate metrics. It is shown that the contracted gauge field theories
describe the same set of fields and particle mass as gauge
theories, if Lagrangians in the base and in the fibers all are taken into
account. Such theories based on non-semisimple contracted group provide more
simple field interactions as compared with the initial ones.Comment: 14 pages, 5 figure
Connecting geodesics and security of configurations in compact locally symmetric spaces
A pair of points in a riemannian manifold makes a secure configuration if the
totality of geodesics connecting them can be blocked by a finite set. The
manifold is secure if every configuration is secure. We investigate the
security of compact, locally symmetric spaces.Comment: 27 pages, 2 figure
Sonoluminescence as Quantum Vaccum Radiation
We argue that the available experimental data is not compatible with models
of sonoluminescence which invoke dynamical properties of the interface without
regard to the compositional properties of the trapped gas inside the bubble.Comment: 2 pages,Revtex,No figures,Submitted to PRL(comments
Force on a neutral atom near conducting microstructures
We derive the non-retarded energy shift of a neutral atom for two different
geometries. For an atom close to a cylindrical wire we find an integral
representation for the energy shift, give asymptotic expressions, and
interpolate numerically. For an atom close to a semi-infinite halfplane we
determine the exact Green's function of the Laplace equation and use it derive
the exact energy shift for an arbitrary position of the atom. These results can
be used to estimate the energy shift of an atom close to etched microstructures
that protrude from substrates.Comment: 7 pages, 5 figure
Entropy of semiclassical measures for nonpositively curved surfaces
We study the asymptotic properties of eigenfunctions of the Laplacian in the
case of a compact Riemannian surface of nonpositive sectional curvature. We
show that the Kolmogorov-Sinai entropy of a semiclassical measure for the
geodesic flow is bounded from below by half of the Ruelle upper bound. We
follow the same main strategy as in the Anosov case (arXiv:0809.0230). We focus
on the main differences and refer the reader to (arXiv:0809.0230) for the
details of analogous lemmas.Comment: 20 pages. This note provides a detailed proof of a result announced
in appendix A of a previous work (arXiv:0809.0230, version 2
All metrics have curvature tensors characterised by its invariants as a limit: the \epsilon-property
We prove a generalisation of the -property, namely that for any
dimension and signature, a metric which is not characterised by its polynomial
scalar curvature invariants, there is a frame such that the components of the
curvature tensors can be arbitrary close to a certain "background". This
"background" is defined by its curvature tensors: it is characterised by its
curvature tensors and has the same polynomial curvature invariants as the
original metric.Comment: 6 page
On an exact solution of the Thomas-Fermi equation for a trapped Bose-Einstein condensate with dipole-dipole interactions
We derive an exact solution to the Thomas-Fermi equation for a Bose-Einstein
condensate which has dipole-dipole interactions as well as the usual s-wave
contact interaction, in a harmonic trap. Remarkably, despite the non-local
anisotropic nature of the dipolar interaction the solution is an inverted
parabola, as in the pure s-wave case, but with a different aspect ratio.
Various properties such as electrostriction and stability are discussed.Comment: 11 pages, 5 figure
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