7,887 research outputs found

    Static, massive fields and vacuum polarization potential in Rindler space

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    In Rindler space, we determine in terms of special functions the expression of the static, massive scalar or vector field generated by a point source. We find also an explicit integral expression of the induced electrostatic potential resulting from the vacuum polarization due to an electric charge at rest in the Rindler coordinates. For a weak acceleration, we give then an approximate expression in the Fermi coordinates associated with the uniformly accelerated observer.Comment: 11 pages, latex, no figure

    Flow Equations for Uplifting Half-Flat to Spin(7) Manifolds

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    In this short supplement to [1], we discuss the uplift of half-flat six-folds to Spin(7) eight-folds by fibration of the former over a product of two intervals. We show that the same can be done in two ways - one, such that the required Spin(7) eight-fold is a double G_2 seven-fold fibration over an interval, the G_2 seven-fold itself being the half-flat six-fold fibered over the other interval, and second, by simply considering the fibration of the half-flat six-fold over a product of two intervals. The flow equations one gets are an obvious generalization of the Hitchin's flow equations (to obtain seven-folds of G_2 holonomy from half-flat six-folds [2]). We explicitly show the uplift of the Iwasawa using both methods, thereby proposing the form of the new Spin(7) metrics. We give a plausibility argument ruling out the uplift of the Iwasawa manifold to a Spin(7) eight fold at the "edge", using the second method. For Spin(7)Spin(7) eight-folds of the type X7Ă—S1X_7\times S^1, X7X_7 being a seven-fold of SU(3) structure, we motivate the possibility of including elliptic functions into the "shape deformation" functions of seven-folds of SU(3) structure of [1] via some connections between elliptic functions, the Heisenberg group, theta functions, the already known D7D7-brane metric [3] and hyper-K\"{a}hler metrics obtained in twistor spaces by deformations of Atiyah-Hitchin manifolds by a Legendre transform in [4].Comment: 12 pages, LaTeX; v3: (JMP) journal version which includes clarifying remarks related to connection between Spin(7)-folds and SU(3)structur

    Belief, Practice, and Grammatical Understanding

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    Kierkegaard and Existence Communications

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    A precise description of the p-adic valuation of the number of alternating sign matrices

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    Following Sun and Moll, we study v_p(T(N)), the p-adic valuation of the counting function of the alternating sign matrices. We find an exact analytic expression for it that exhibits the fluctuating behaviour, by means of Fourier coefficients. The method is the Mellin-Perron technique, which is familiar in the analysis of the sum-of-digits function and related quantities

    MAGNITUDE ESTIMATION: AN APPLICATION TO FARMERS' RISK-INCOME PREFERENCES

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    Magnitude estimation, a technique developed by psychology for obtaining ratio scaled values, was used to derive risk-income preferences of ninety-one central Indiana farmers. Both variability-income and bankruptcy-income measures were developed and related to farmers' socio-economic attributes. Wealth and education had limited effects compared with off-farm employment, percent debt and expected levels of income, percent debt and net worth growth. Magnitude estimation provided reliable estimates of preferences. Farmers gave greater importance to the bankruptcy-income measure of risk-income preferences, but only a small portion of the variation of either measure could be explained.Farm Management, Risk and Uncertainty,

    Nonexistence of an integral of the 6th degree in momenta for the Zipoy-Voorhees metric

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    We prove nonexistence of a nontrivial integral that is polynomial in momenta of degree less than 7 for the Zipoy-Voorhees spacetime with the parameter δ=2\delta=2Comment: 7 pages, no figure

    Coherence properties of the microcavity polariton condensate

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    A theoretical model is presented which explains the dominant decoherence process in a microcavity polariton condensate. The mechanism which is invoked is the effect of self-phase modulation, whereby interactions transform polariton number fluctuations into random energy variations. The model shows that the phase coherence decay, g1(t), has a Kubo form, which can be Gaussian or exponential, depending on whether the number fluctuations are slow or fast. This fluctuation rate also determines the decay time of the intensity correlation function, g2(t), so it can be directly determined experimentally. The model explains recent experimental measurements of a relatively fast Gaussian decay for g1(t), but also predicts a regime, further above threshold, where the decay is much slower.Comment: 5 pages, 1 figur

    Adiabatic-Impulse approximation for avoided level crossings: from phase transition dynamics to Landau-Zener evolutions and back again

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    We show that a simple approximation based on concepts underlying the Kibble-Zurek theory of second order phase transition dynamics can be used to treat avoided level crossing problems. The approach discussed in this paper provides an intuitive insight into quantum dynamics of two level systems, and may serve as a link between the theory of dynamics of classical and quantum phase transitions. To illustrate these ideas we analyze dynamics of a paramagnet-ferromagnet quantum phase transition in the Ising model. We also present exact unpublished solutions of the Landau-Zener like problems.Comment: 12 pages & 6 figures, minor corrections, version accepted in Phys. Rev.
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