1,014 research outputs found
Exact hydrodynamics of a trapped dipolar Bose-Einstein condensate
We derive the exact density profile of a harmonically trapped Bose-Einstein
condensate (BEC) which has dipole-dipole interactions as well as the usual
s-wave contact interaction, in the Thomas-Fermi limit. Remarkably, despite the
non-local anisotropic nature of the dipolar interaction, the density turns out
to be an inverted parabola, just as in the pure s-wave case, but with a
modified aspect ratio. The ``scaling'' solution approach of Kagan, Surkov, and
Shlyapnikov [Phys. Rev. A 54, 1753 (1996)] and Castin and Dum [Phys. Rev. Lett.
77}, 5315 (1996)] for a BEC in a time-dependent trap can therefore be applied
to a dipolar BEC, and we use it to obtain the exact monopole and quadrupole
shape oscillation frequencies.Comment: 5 pages, 3 figure
Exact Casimir-Polder potentials: interaction of an atom with a conductor-patched dielectric surface
We study the interaction between a neutral atom or molecule and a
conductor-patched dielectric surface. We model this system by a perfectly
reflecting disc lying atop of a non-dispersive dielectric half-space, both
interacting with the neutral atom or molecule. We assume the interaction to be
non-retarded and at zero temperature. We find an exact solution to this
problem. In addition we generate a number of other useful results. For the case
of no substrate we obtain the exact formula for the van der Waals interaction
energy of an atom near a perfectly conducting disc. We show that the
Casimir-Polder force acting on an atom that is polarized in the direction
normal to the surface of the disc displays intricate behaviour. This part of
our results is directly relevant to recent matter-wave experiments in which
cold molecules are scattered by a radially symmetric object in order to study
diffraction patterns and the so-called Poisson spot. Furthermore, we give an
exact expression for the non-retarded limit of the Casimir-Polder interaction
between an atom and a perfectly-conducting bowl.Comment: 9 pages, 9 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
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
Sonoluminescence as a QED vacuum effect: Probing Schwinger's proposal
Several years ago Schwinger proposed a physical mechanism for
sonoluminescence in terms of photon production due to changes in the properties
of the quantum-electrodynamic (QED) vacuum arising from a collapsing dielectric
bubble. This mechanism can be re-phrased in terms of the Casimir effect and has
recently been the subject of considerable controversy. The present paper probes
Schwinger's suggestion in detail: Using the sudden approximation we calculate
Bogolubov coefficients relating the QED vacuum in the presence of the expanded
bubble to that in the presence of the collapsed bubble. In this way we derive
an estimate for the spectrum and total energy emitted. We verify that in the
sudden approximation there is an efficient production of photons, and further
that the main contribution to this dynamic Casimir effect comes from a volume
term, as per Schwinger's original calculation. However, we also demonstrate
that the timescales required to implement Schwinger's original suggestion are
not physically relevant to sonoluminescence. Although Schwinger was correct in
his assertion that changes in the zero-point energy lead to photon production,
nevertheless his original model is not appropriate for sonoluminescence. In
other works (see quant-ph/9805023, quant-ph/9904013, quant-ph/9904018,
quant-ph/9905034) we have developed a variant of Schwinger's model that is
compatible with the physically required timescales.Comment: 18 pages, ReV_TeX 3.2, 9 figures. Major revisions: This document is
now limited to providing a probe of Schwinger's original suggestion for
sonoluminescence. For details on our own variant of Schwinger's ideas see
quant-ph/9805023, quant-ph/9904013, quant-ph/9904018, quant-ph/990503
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
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
Stochastic Spacetime and Brownian Motion of Test Particles
The operational meaning of spacetime fluctuations is discussed. Classical
spacetime geometry can be viewed as encoding the relations between the motions
of test particles in the geometry. By analogy, quantum fluctuations of
spacetime geometry can be interpreted in terms of the fluctuations of these
motions. Thus one can give meaning to spacetime fluctuations in terms of
observables which describe the Brownian motion of test particles. We will first
discuss some electromagnetic analogies, where quantum fluctuations of the
electromagnetic field induce Brownian motion of test particles. We next discuss
several explicit examples of Brownian motion caused by a fluctuating
gravitational field. These examples include lightcone fluctuations, variations
in the flight times of photons through the fluctuating geometry, and
fluctuations in the expansion parameter given by a Langevin version of the
Raychaudhuri equation. The fluctuations in this parameter lead to variations in
the luminosity of sources. Other phenomena which can be linked to spacetime
fluctuations are spectral line broadening and angular blurring of distant
sources.Comment: 15 pages, 3 figures. Talk given at the 9th Peyresq workshop, June
200
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
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