348 research outputs found
K\"{a}hler-Einstein metrics on strictly pseudoconvex domains
The metrics of S. Y. Cheng and S.-T. Yau are considered on a strictly
pseudoconvex domains in a complex manifold. Such a manifold carries a complete
K\"{a}hler-Einstein metric if and only if its canonical bundle is positive. We
consider the restricted case in which the CR structure on is
normal. In this case M must be a domain in a resolution of the Sasaki cone over
. We give a condition on a normal CR manifold which it cannot
satisfy if it is a CR infinity of a K\"{a}hler-Einstein manifold. We are able
to mostly determine those normal CR 3-manifolds which can be CR infinities.
Many examples are given of K\"{a}hler-Einstein strictly pseudoconvex manifolds
on bundles and resolutions.Comment: 30 pages, 1 figure, couple corrections, improved a couple example
Calculating Casimir Energies in Renormalizable Quantum Field Theory
Quantum vacuum energy has been known to have observable consequences since
1948 when Casimir calculated the force of attraction between parallel uncharged
plates, a phenomenon confirmed experimentally with ever increasing precision.
Casimir himself suggested that a similar attractive self-stress existed for a
conducting spherical shell, but Boyer obtained a repulsive stress. Other
geometries and higher dimensions have been considered over the years. Local
effects, and divergences associated with surfaces and edges have been studied
by several authors. Quite recently, Graham et al. have re-examined such
calculations, using conventional techniques of perturbative quantum field
theory to remove divergences, and have suggested that previous self-stress
results may be suspect. Here we show that the examples considered in their work
are misleading; in particular, it is well-known that in two dimensions a
circular boundary has a divergence in the Casimir energy for massless fields,
while for general dimension not equal to an even integer the corresponding
Casimir energy arising from massless fields interior and exterior to a
hyperspherical shell is finite. It has also long been recognized that the
Casimir energy for massive fields is divergent for . These conclusions
are reinforced by a calculation of the relevant leading Feynman diagram in
and three dimensions. There is therefore no doubt of the validity of the
conventional finite Casimir calculations.Comment: 25 pages, REVTeX4, 1 ps figure. Revision includes new subsection 4B
and Appendix, and other minor correction
Local and Global Casimir Energies: Divergences, Renormalization, and the Coupling to Gravity
From the beginning of the subject, calculations of quantum vacuum energies or
Casimir energies have been plagued with two types of divergences: The total
energy, which may be thought of as some sort of regularization of the
zero-point energy, , seems manifestly divergent. And
local energy densities, obtained from the vacuum expectation value of the
energy-momentum tensor, , typically diverge near
boundaries. The energy of interaction between distinct rigid bodies of whatever
type is finite, corresponding to observable forces and torques between the
bodies, which can be unambiguously calculated. The self-energy of a body is
less well-defined, and suffers divergences which may or may not be removable.
Some examples where a unique total self-stress may be evaluated include the
perfectly conducting spherical shell first considered by Boyer, a perfectly
conducting cylindrical shell, and dilute dielectric balls and cylinders. In
these cases the finite part is unique, yet there are divergent contributions
which may be subsumed in some sort of renormalization of physical parameters.
The divergences that occur in the local energy-momentum tensor near surfaces
are distinct from the divergences in the total energy, which are often
associated with energy located exactly on the surfaces. However, the local
energy-momentum tensor couples to gravity, so what is the significance of
infinite quantities here? For the classic situation of parallel plates there
are indications that the divergences in the local energy density are consistent
with divergences in Einstein's equations; correspondingly, it has been shown
that divergences in the total Casimir energy serve to precisely renormalize the
masses of the plates, in accordance with the equivalence principle.Comment: 53 pages, 1 figure, invited review paper to Lecture Notes in Physics
volume in Casimir physics edited by Diego Dalvit, Peter Milonni, David
Roberts, and Felipe da Ros
Casimir interaction between two concentric cylinders: exact versus semiclassical results
The Casimir interaction between two perfectly conducting, infinite,
concentric cylinders is computed using a semiclassical approximation that takes
into account families of classical periodic orbits that reflect off both
cylinders. It is then compared with the exact result obtained by the
mode-by-mode summation technique. We analyze the validity of the semiclassical
approximation and show that it improves the results obtained through the
proximity theorem.Comment: 28 pages, 5 figures include
The Effect of Leg Muscle Activation State and Localized Muscle Fatigue on Tibial Response during Impact
Photon-Photon and Pomeron-Pomeron Processes in Peripheral Heavy Ion Collisions
We estimate the cross sections for the production of resonances, pion pairs
and a central cluster of hadrons in peripheral heavy-ion collisions through
two-photon and double-pomeron exchange, at energies that will be available at
RHIC and LHC. The effect of the impact parameter in the diffractive reactions
is introduced, and imposing the condition for realistic peripheral collisions
we verify that in the case of very heavy ions the pomeron-pomeron contribution
is indeed smaller than the electromagnetic one. However, they give a
non-negligible background in the collision of light ions. This diffractive
background will be more important at RHIC than at LHC.Comment: 22 pages, 1 Postscript figures, 4 tables, to appear in Phys. Rev.
Normal and Lateral Casimir Forces between Deformed Plates
The Casimir force between macroscopic bodies depends strongly on their shape
and orientation. To study this geometry dependence in the case of two deformed
metal plates, we use a path integral quantization of the electromagnetic field
which properly treats the many-body nature of the interaction, going beyond the
commonly used pairwise summation (PWS) of van der Waals forces. For arbitrary
deformations we provide an analytical result for the deformation induced change
in Casimir energy, which is exact to second order in the deformation amplitude.
For the specific case of sinusoidally corrugated plates, we calculate both the
normal and the lateral Casimir forces. The deformation induced change in the
Casimir interaction of a flat and a corrugated plate shows an interesting
crossover as a function of the ratio of the mean platedistance H to the
corrugation length \lambda: For \lambda \ll H we find a slower decay \sim
H^{-4}, compared to the H^{-5} behavior predicted by PWS which we show to be
valid only for \lambda \gg H. The amplitude of the lateral force between two
corrugated plates which are out of registry is shown to have a maximum at an
optimal wavelength of \lambda \approx 2.5 H. With increasing H/\lambda \gtrsim
0.3 the PWS approach becomes a progressively worse description of the lateral
force due to many-body effects. These results may be of relevance for the
design and operation of novel microelectromechanical systems (MEMS) and other
nanoscale devices.Comment: 20 pages, 5 figure
Non-monotonic variation with salt concentration of the second virial coefficient in protein solutions
The osmotic virial coefficient of globular protein solutions is
calculated as a function of added salt concentration at fixed pH by computer
simulations of the ``primitive model''. The salt and counter-ions as well as a
discrete charge pattern on the protein surface are explicitly incorporated. For
parameters roughly corresponding to lysozyme, we find that first
decreases with added salt concentration up to a threshold concentration, then
increases to a maximum, and then decreases again upon further raising the ionic
strength. Our studies demonstrate that the existence of a discrete charge
pattern on the protein surface profoundly influences the effective interactions
and that non-linear Poisson Boltzmann and Derjaguin-Landau-Verwey-Overbeek
(DLVO) theory fail for large ionic strength. The observed non-monotonicity of
is compared to experiments. Implications for protein crystallization are
discussed.Comment: 43 pages, including 17 figure
Atomic X-ray Spectroscopy of Accreting Black Holes
Current astrophysical research suggests that the most persistently luminous
objects in the Universe are powered by the flow of matter through accretion
disks onto black holes. Accretion disk systems are observed to emit copious
radiation across the electromagnetic spectrum, each energy band providing
access to rather distinct regimes of physical conditions and geometric scale.
X-ray emission probes the innermost regions of the accretion disk, where
relativistic effects prevail. While this has been known for decades, it also
has been acknowledged that inferring physical conditions in the relativistic
regime from the behavior of the X-ray continuum is problematic and not
satisfactorily constraining. With the discovery in the 1990s of iron X-ray
lines bearing signatures of relativistic distortion came the hope that such
emission would more firmly constrain models of disk accretion near black holes,
as well as provide observational criteria by which to test general relativity
in the strong field limit. Here we provide an introduction to this phenomenon.
While the presentation is intended to be primarily tutorial in nature, we aim
also to acquaint the reader with trends in current research. To achieve these
ends, we present the basic applications of general relativity that pertain to
X-ray spectroscopic observations of black hole accretion disk systems, focusing
on the Schwarzschild and Kerr solutions to the Einstein field equations. To
this we add treatments of the fundamental concepts associated with the
theoretical and modeling aspects of accretion disks, as well as relevant topics
from observational and theoretical X-ray spectroscopy.Comment: 63 pages, 21 figures, Einstein Centennial Review Article, Canadian
Journal of Physics, in pres
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