246 research outputs found

    Properties of low-lying states in some high-nuclearity Mn, Fe and V clusters: Exact studies of Heisenberg models

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    Using an efficient numerical scheme that exploits spatial symmetries and spin parity, we have obtained the exact low-lying eigenstates of exchange Hamiltonians for the high nuclearity spin clusters, Mn_{12}, Fe_8 and V_{15}. The largest calculation involves the Mn_{12} cluster which spans a Fock space of a hundred million. Our results show that the earlier estimates of the exchange constants need to be revised for the Mn_{12} cluster to explain the level ordering of low-lying eigenstates. In the case of the Fe_8 cluster, correct level ordering can be obtained which is consistent with the exchange constants for the already known clusters with butterfly structure. In the V_{15} cluster, we obtain an effective Hamiltonian that reproduces exactly, the eight low-lying eigenvalues of the full Hamiltonian.Comment: Revtex, 12 pages, 16 eps figures; this is the final published versio

    An optimal gap theorem

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    By solving the Cauchy problem for the Hodge-Laplace heat equation for dd-closed, positive (1,1)(1, 1)-forms, we prove an optimal gap theorem for K\"ahler manifolds with nonnegative bisectional curvature which asserts that the manifold is flat if the average of the scalar curvature over balls of radius rr centered at any fixed point oo is a function of o(r2)o(r^{-2}). Furthermore via a relative monotonicity estimate we obtain a stronger statement, namely a `positive mass' type result, asserting that if (M,g)(M, g) is not flat, then lim infrr2Vo(r)Bo(r)S(y)dμ(y)>0\liminf_{r\to \infty} \frac{r^2}{V_o(r)}\int_{B_o(r)}\mathcal{S}(y)\, d\mu(y)>0 for any oMo\in M

    Gravitational-wave astronomy: the high-frequency window

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    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

    Neutron charge form factor at large q2q^2

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    The neutron charge form factor GEn(q)G_{En}(q) is determined from an analysis of the deuteron quadrupole form factor FC2F_{C2} data. Recent calculations, based on a variety of different model interactions and currents, indicate that the contributions associated with the uncertain two-body operators of shorter range are relatively small for FC2F_{C2}, even at large momentum transfer qq. Hence, GEn(q)G_{En}(q) can be extracted from FC2F_{C2} at large q2q^2 without undue systematic uncertainties from theory.Comment: 8 pages, 3 figure

    Young and Intermediate-age Distance Indicators

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    Distance measurements beyond geometrical and semi-geometrical methods, rely mainly on standard candles. As the name suggests, these objects have known luminosities by virtue of their intrinsic proprieties and play a major role in our understanding of modern cosmology. The main caveats associated with standard candles are their absolute calibration, contamination of the sample from other sources and systematic uncertainties. The absolute calibration mainly depends on their chemical composition and age. To understand the impact of these effects on the distance scale, it is essential to develop methods based on different sample of standard candles. Here we review the fundamental properties of young and intermediate-age distance indicators such as Cepheids, Mira variables and Red Clump stars and the recent developments in their application as distance indicators.Comment: Review article, 63 pages (28 figures), Accepted for publication in Space Science Reviews (Chapter 3 of a special collection resulting from the May 2016 ISSI-BJ workshop on Astronomical Distance Determination in the Space Age

    On the EPR-type Entanglement in the Experiments of Scully et Al. I. The Micromaser Case and Delayed-choice Quantum Erasure

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    Delayed-choice erasure is investigated in two-photon two-slit experiments that are generalizations of the micromaser experiment of Scully et al. [Scully, M. O. et al. Nature 351, 111-116 (1991)]. Applying quantum mechanics to the localization detector, it is shown that erasure with delayed choice in the sense of Scully, has an analogous structure as simple erasure. The description goes beyond probabilities. The EPR-type disentanglement, consisting in two mutually incompatible distant measurements, is used as a general framework in both parts of this study. Two simple coherence cases are shown to emerge naturally, and they are precisely the two experiments of Scully et al. The treatment seems to require the relative-reality-of-unitarily-evolving-state (RRUES) approach. Besides insight in the exoeriments, this study has also the goal of insight in quantum mechanics. The question is if it can be more than just a "book-keeping device" for calculating probabilities as Scully et al. modestly and cautiously claim.Comment: Latex2e, no figures, this manuscript is the first part of a study in two part

    Empirically-grounded development of legal ontologies: a socio-legal perspective

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    This paper shows the multiple relationships between empirical data and semantic content in the legal field. One of the well-known problems of ontology construction is the "knowledge acquisition bottleneck problem" pointed out by Edward Feigenbaum and others, many years ago. In the next generation of Semantic Web developments this problem has not been completely solved. It is our con-tention that an accurate description of the legal environment, and well-grounded previous sociological studies may help to face it in a more satisfactory way. This means adopting a user-centered approach for legal ontologies, in what we will call an "iterative and integrated pragmatic circle" involving legal theorists, socio-legal researchers, professional people (lawyers, magistrates, prosecutors…) and com-puter scientists. We put the example of how the ontology of IURISERVICE was built up
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