440 research outputs found
Rapidly Rotating Bose-Einstein Condensates in Homogeneous Traps
We extend the results of a previous paper on the Gross-Pitaevskii description
of rotating Bose-Einstein condensates in two-dimensional traps to confining
potentials of the form V(r) = r^s, . Writing the coupling constant
as we study the limit . We derive rigorously the
leading asymptotics of the ground state energy and the density profile when the
rotation velocity \Omega tends to infinity as a power of . The case
of asymptotically homogeneous potentials is also discussed.Comment: LaTex2e, 16 page
Rapidly Rotating Bose-Einstein Condensates in Strongly Anharmonic Traps
We study a rotating Bose-Einstein Condensate in a strongly anharmonic trap
(flat trap with a finite radius) in the framework of 2D Gross-Pitaevskii
theory. We write the coupling constant for the interactions between the gas
atoms as and we are interested in the limit (TF
limit) with the angular velocity depending on . We derive
rigorously the leading asymptotics of the ground state energy and the density
profile when tends to infinity as a power of . If
a ``hole'' (i.e., a region where the
density becomes exponentially small as ) develops for
above a certain critical value. If
the hole essentially exhausts the container and a ``giant vortex'' develops
with the density concentrated in a thin layer at the boundary. While we do not
analyse the detailed vortex structure we prove that rotational symmetry is
broken in the ground state for .Comment: LaTex2e, 28 pages, revised version to be published in Journal of
Mathematical Physic
Importance of an Astrophysical Perspective for Textbook Relativity
The importance of a teaching a clear definition of the ``observer'' in
special relativity is highlighted using a simple astrophysical example from the
exciting current research area of ``Gamma-Ray Burst'' astrophysics. The example
shows that a source moving relativistically toward a single observer at rest
exhibits a time ``contraction'' rather than a ``dilation'' because the light
travel time between the source and observer decreases with time. Astrophysical
applications of special relativity complement idealized examples with real
applications and very effectively exemplify the role of a finite light travel
time.Comment: 5 pages TeX, European Journal of Physics, in pres
A New Independent Limit on the Cosmological Constant/Dark Energy from the Relativistic Bending of Light by Galaxies and Clusters of Galaxies
We derive new limits on the value of the cosmological constant, ,
based on the Einstein bending of light by systems where the lens is a distant
galaxy or a cluster of galaxies. We use an amended lens equation in which the
contribution of to the Einstein deflection angle is taken into
account and use observations of Einstein radii around several lens systems. We
use in our calculations a Schwarzschild-de Sitter vacuole exactly matched into
a Friedmann-Robertson-Walker background and show that a -contribution
term appears in the deflection angle within the lens equation. We find that the
contribution of the -term to the bending angle is larger than the
second-order term for many lens systems. Using these observations of bending
angles, we derive new limits on the value of . These limits constitute
the best observational upper bound on after cosmological constraints
and are only two orders of magnitude away from the value determined by those
cosmological constraints.Comment: 5 pages, 1 figure, matches version published in MNRA
Multiple Photonic Shells Around a Line Singularity
Line singularities including cosmic strings may be screened by photonic
shells until they appear as a planar wall.Comment: 6 page
More on Lensing by a Cosmological Constant
The question of whether or not the cosmological constant affects the bending
of light around a concentrated mass has been the subject of some recent papers.
We present here a simple, specific and transparent example where
bending clearly takes place, and where it is clearly neither a coordinate
effect nor an aberration effect. We then show that in some recent works using
perturbation theory the contribution was missed because of initial
too-stringent smallness assumptions. Namely: Our method has been to insert a
Kottler (Schwarzschild with ) vacuole into a Friedmann universe, and
to calculate the total bending within the vacuole. We assume that no more
bending occurs outside. It is important to observe that while the mass
contribution to the bending takes place mainly quite near the lens, the
bending continues throughout the vacuole. Thus if one deliberately
restricts one's search for bending to the immediate neighborhood of
the lens, one will not find it. Lastly, we show that the bending also
follows from standard Weyl focusing, and so again, it cannot be a coordinate
effect.Comment: 5 pages, matches MNRAS accepted versio
Considerations on the Unruh Effect: Causality and Regularization
This article is motivated by the observation, that calculations of the Unruh
effect based on idealized particle detectors are usually made in a way that
involves integrations along the {\em entire} detector trajectory up to the
infinitely remote {\em future}. We derive an expression which allows
time-dependence of the detector response in the case of a non-stationary
trajectory and conforms more explicitely to the principle of causality, namely
that the response at a given instant of time depends only on the detectors {\em
past} movements. On trying to reproduce the thermal Unruh spectrum we are led
to an unphysical result, which we trace down to the use of the standard
regularization t\to t-i\eps of the correlation function. By consistently
employing a rigid detector of finite extension, we are led to a different
regularization which works fine with our causal response function.Comment: 19 pages, 2 figures, v2: some minor change
The Schwarzschild-de Sitter solution in five-dimensional general relativity briefly revisited
We briefly revisit the Schwarzschild-de Sitter solution in the context of
five-dimensional general relativity. We obtain a class of five-dimensional
solutions of Einstein vacuum field equations into which the four-dimensional
Schwarzschild-de Sitter space can be locally and isometrically embedded. We
show that this class of solutions is well-behaved in the limit of lambda
approaching zero. Applying the same procedure to the de Sitter cosmological
model in five dimensions we obtain a class of embedding spaces which are
similarly well-behaved in this limit. These examples demonstrate that the
presence of a non-zero cosmological constant does not in general impose a rigid
relation between the (3+1) and (4+1)-dimensional spacetimes, with degenerate
limiting behaviour.Comment: 7 page
Scattering of scalar perturbations with cosmological constant in low-energy and high-energy regimes
We study the absorption and scattering of massless scalar waves propagating
in spherically symmetric spacetimes with dynamical cosmological constant both
in low-energy and high-energy zones. In the former low-energy regime, we solve
analytically the Regge-Wheeler wave equation and obtain an analytic absorption
probability expression which varies with , where is the
central mass and is cosmological constant. The low-energy absorption
probability, which is in the range of , increases monotonically
with increase in . In the latter high-energy regime, the scalar
particles adopt their geometric optics limit value. The trajectory equation
with effective potential emerges and the analytic high-energy greybody factor,
which is relevant with the area of classically accessible regime, also
increases monotonically with increase in , as long is less
than or of the order of . In this high-energy case, the null cosmological
constant result reduces to the Schwarzschild value .Comment: 12 pages, 6 figure
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