17,038 research outputs found

    Geometric quantization of Hamiltonian actions of Lie algebroids and Lie groupoids

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    We construct Hermitian representations of Lie algebroids and associated unitary representations of Lie groupoids by a geometric quantization procedure. For this purpose we introduce a new notion of Hamiltonian Lie algebroid actions. The first step of our procedure consists of the construction of a prequantization line bundle. Next, we discuss a version of K\"{a}hler quantization suitable for this setting. We proceed by defining a Marsden-Weinstein quotient for our setting and prove a ``quantization commutes with reduction'' theorem. We explain how our geometric quantization procedure relates to a possible orbit method for Lie groupoids. Our theory encompasses the geometric quantization of symplectic manifolds, Hamiltonian Lie algebra actions, actions of families of Lie groups, foliations, as well as some general constructions from differential geometry.Comment: 40 pages, corrected version 11-01-200

    Measurement of turbulent correlations in a coaxial flow of dissimilar fluids

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    Axial turbulence measurements in coaxial flow of dissimilar gase

    Observing Gravitational Waves with a Single Detector

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    A major challenge of any search for gravitational waves is to distinguish true astrophysical signals from those of terrestrial origin. Gravitational-wave experiments therefore make use of multiple detectors, considering only those signals which appear in coincidence in two or more instruments. It is unclear, however, how to interpret loud gravitational-wave candidates observed when only one detector is operational. In this paper, we demonstrate that the observed rate of binary black hole mergers can be leveraged in order to make confident detections of gravitational-wave signals with one detector alone. We quantify detection confidences in terms of the probability P(S)P(S) that a signal candidate is of astrophysical origin. We find that, at current levels of instrumental sensitivity, loud signal candidates observed with a single Advanced LIGO detector can be assigned P(S)0.4P(S)\gtrsim0.4. In the future, Advanced LIGO may be able to observe single-detector events with confidences exceeding P(S)90%P(S)\sim90\%.Comment: 8 pages, 4 figures; published in CQG; minor updates to match published versio

    Observation of B_s Production at the Y(5S) Resonance

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    Using the CLEO detector at the Cornell Electron Storage Ring, we have observed the B_s meson in e^+e^- annihilation at the Υ(5S) resonance. We find 14 candidates consistent with B_s decays into final states with a J/ψ or a D_s^((*)-). The probability that we have observed a background fluctuation is less than 8×10^(-10). We have established that at the energy of the Υ(5S) resonance B_s production proceeds predominantly through the creation of B_s^*B̅ _s^* pairs. We find σ(e^+e^-→B^s^*B̅ ^*)=[0.11_(-0.03)^(+0.04)(stat)±0.02(syst)]  nb, and set the following limits: σ(e^+e^-→B_sB̅ _s)/σ(e^+e^-→B_s^*B̅ _s^*)<0.16 and [σ(e^+e^-→B_sB̅ _s^*)+σ(e^+e^-→B_s*B̅ _s)]/σ(e^+e^-→B_s*B̅ _s^*)<0.16 (90% C.L.). The mass of the B_s^* meson is measured to be M_(B_s^*=[5.414±0.001(stat)±0.003(syst)]  GeV/c^2

    Two-photon width of the charmonium state X_(c2)

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    The two-photon width of X_(c2)^3P_2 state of charmonium has been measured using 14.4 fb^(-1) of e^+e^-data taken at √s =9.46–11.30 GeV with the CLEO III detector. The yy-fusion reaction studied is e^+e^- → e^+e^-yy, → yy X_(c2) → yJ/Ψ → ye^+e^-(µ^+µ^-). We measure Г_(yy) (X_(c2))B(X_(c2)) → y J/Ψ)B(J/Ψ → e^+e^- + µ^+µ^-)= 13.2 ± 1.4(stat)± 1.1(syst) eV, and obtain Г yy(Xc2)= 559 ± 57(stat) ± 48(syst) ± 36(br) eV. This result is in excellent agreement with the result of -fusion measurement by Belle and is consistent with that of the pp → X_(c2) → yy measurement, when they are both reevaluated using the recent CLEO result for the radiative decay X_(c2) → J/Ψ

    Charged Rotating Black Holes in Equilibrium

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    Axially symmetric, stationary solutions of the Einstein-Maxwell equations with disconnected event horizon are studied by developing a method of explicit integration of the corresponding boundary-value problem. This problem is reduced to non-leaner system of algebraic equations which gives relations between the masses, the angular momenta, the angular velocities, the charges, the distance parameters, the values of the electromagnetic field potential at the horizon and at the symmetry axis. A found solution of this system for the case of two charged non-rotating black holes shows that in general the total mass depends on the distance between black holes. Two-Killing reduction procedure of the Einstein-Maxwell equations is also discussed.Comment: LaTeX 2.09, no figures, 15 pages, v2, references added, introduction section slightly modified; v3, grammar errors correcte

    An effectual template bank for the detection of gravitational waves from inspiralling compact binaries with generic spins

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    We report the construction of a three-dimensional template bank for the search for gravitational waves from inspiralling binaries consisting of spinning compact objects. The parameter space consists of two dimensions describing the mass parameters and one "reduced-spin" parameter, which describes the secular (non-precessing) spin effects in the waveform. The template placement is based on an efficient stochastic algorithm and makes use of the semi-analytical computation of a metric in the parameter space. We demonstrate that for "low-mass" (m1+m212Mm_1 + m_2 \lesssim 12\,M_\odot) binaries, this template bank achieves effective fitting factors 0.92\sim0.92--0.990.99 towards signals from generic spinning binaries in the advanced detector era over the entire parameter space of interest (including binary neutron stars, binary black holes, and black hole-neutron star binaries). This provides a powerful and viable method for searching for gravitational waves from generic spinning low-mass compact binaries. Under the assumption that spin magnitudes of black-holes [neutron-stars] are uniformly distributed between 0--0.98 [0 -- 0.4] and spin angles are isotropically distributed, the expected improvement in the average detection volume (at a fixed signal-to-noise-ratio threshold) of a search using this reduced-spin bank is 2052%\sim20-52\%, as compared to a search using a non-spinning bank.Comment: Minor changes, version appeared in Phys. Rev.
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