21,341 research outputs found
Residue currents associated with weakly holomorphic functions
We construct Coleff-Herrera products and Bochner-Martinelli type residue
currents associated with a tuple of weakly holomorphic functions, and show
that these currents satisfy basic properties from the (strongly) holomorphic
case, as the transformation law, the Poincar\'e-Lelong formula and the
equivalence of the Coleff-Herrera product and the Bochner-Martinelli type
residue current associated with when defines a complete intersection.Comment: 28 pages. Updated with some corrections from the revision process. In
particular, corrected and clarified some things in Section 5 and 6 regarding
products of weakly holomorphic functions and currents, and the definition of
the Bochner-Martinelli type current
Optimal minimum-cost quantum measurements for imperfect detection
Knowledge of optimal quantum measurements is important for a wide range of
situations, including quantum communication and quantum metrology. Quantum
measurements are usually optimised with an ideal experimental realisation in
mind. Real devices and detectors are, however, imperfect. This has to be taken
into account when optimising quantum measurements. In this paper, we derive the
optimal minimum-cost and minimum-error measurements for a general model of
imperfect detection.Comment: 5 page
Gravitational-wave astronomy: the high-frequency window
This contribution is divided in two parts. The first part provides a
text-book level introduction to gravitational radiation. The key concepts
required for a discussion of gravitational-wave physics are introduced. In
particular, the quadrupole formula is applied to the anticipated
``bread-and-butter'' source for detectors like LIGO, GEO600, EGO and TAMA300:
inspiralling compact binaries. The second part provides a brief review of high
frequency gravitational waves. In the frequency range above (say) 100Hz,
gravitational collapse, rotational instabilities and oscillations of the
remnant compact objects are potentially important sources of gravitational
waves. Significant and unique information concerning the various stages of
collapse, the evolution of protoneutron stars and the details of the
supranuclear equation of state of such objects can be drawn from careful study
of the gravitational-wave signal. As the amount of exciting physics one may be
able to study via the detections of gravitational waves from these sources is
truly inspiring, there is strong motivation for the development of future
generations of ground based detectors sensitive in the range from hundreds of
Hz to several kHz.Comment: 21 pages, 5 figures, Lectures presented at the 2nd Aegean Summer
School on the Early Universe, Syros, Greece, September 200
Nonexistence of Generalized Apparent Horizons in Minkowski Space
We establish a Positive Mass Theorem for initial data sets of the Einstein
equations having generalized trapped surface boundary. In particular we answer
a question posed by R. Wald concerning the existence of generalized apparent
horizons in Minkowski space
Gas identification based on bias induced hysteresis of a gas-sensitive SiC field effect transistor
In this work dynamic variation of gate bias is used on a gas-sensitive SiC
field effect transistor ("GasFET") to optimize its sensitivity and
increase its selectivity. Gate bias ramps introduce strong hysteresis in the
sensor signal. The shape of this hysteresis is shown to be an appropriate
feature both for the discrimination of various gases (ammonia, carbon
monoxide, nitrogen monoxide and methane) as well as for different gas
concentrations (250 and 500 ppm). The shape is very sensitive to ambient
conditions as well as to the bias sweep rate. Thus, the influences of oxygen
concentration, relative humidity, sensor temperature and cycle duration,
i.e., sweep rate, are investigated and reasons for the observed signal
changes, most importantly the existence of at least two different and
competing processes taking place simultaneously, are discussed. Furthermore,
it is shown that even for very fast cycles, in the range of seconds, the
gas-induced shape change in the signal is strong enough to achieve a
reliable separation of gases using gate bias cycled operation and linear
discriminant analysis (LDA) making this approach suitable for practical
application
Asymptotically Hyperbolic Non Constant Mean Curvature Solutions of the Einstein Constraint Equations
We describe how the iterative technique used by Isenberg and Moncrief to
verify the existence of large sets of non constant mean curvature solutions of
the Einstein constraints on closed manifolds can be adapted to verify the
existence of large sets of asymptotically hyperbolic non constant mean
curvature solutions of the Einstein constraints.Comment: 19 pages, TeX, no figure
Maximum Confidence Quantum Measurements
We consider the problem of discriminating between states of a specified set
with maximum confidence. For a set of linearly independent states unambiguous
discrimination is possible if we allow for the possibility of an inconclusive
result. For linearly dependent sets an analogous measurement is one which
allows us to be as confident as possible that when a given state is identified
on the basis of the measurement result, it is indeed the correct state.Comment: 4 pages, 2 figure
The Tolman VII solution, trapped null orbits and w - modes
The Tolman VII solution is an exact static spherically symmetric perfect
fluid solution of Einstein's equations that exhibits a surprisingly good
approximation to a neutron star. We show that this solution exhibits trapped
null orbits in a causal region even for a tenuity (total radius to mass ratio)
. In this region the dynamical part of the potential for axial w - modes
dominates over the centrifugal part.Comment: 5 pages revtex. 10 figures png. Further information at
http://grtensor.phy.queensu.ca/tolmanvii
Entanglement of distant optomechanical systems
We theoretically investigate the possibility to generate non-classical states
of optical and mechanical modes of optical cavities, distant from each other. A
setup comprised of two identical cavities, each with one fixed and one movable
mirror and coupled by an optical fiber, is studied in detail. We show that with
such a setup there is potential to generate entanglement between the distant
cavities, involving both optical and mechanical modes. The scheme is robust
with respect to dissipation, and nonlocal correlations are found to exist in
the steady state at finite temperatures.Comment: 12 pages (published with minor modifications
Where are the trapped surfaces?
We discuss the boundary of the spacetime region through each point of which a
trapped surface passes, first in some simple soluble examples, and then in the
self-similar Vaidya solution. For the latter the boundary must lie strictly
inside the event horizon. We present a class of closed trapped surfaces
extending strictly outside the apparent horizon.Comment: 6 pages, 1 figure; talk at the Spanish Relativity Meeting ERE09 in
Bilba
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