228,525 research outputs found

    On universal decoherence under gravity: a perspective through the Equivalence Principle

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    In Nature Phys. 11, 668 (2015) (Ref. [1]), a composite particle prepared in a pure initial quantum state and propagated in a uniform gravitational field is shown to undergo a decoherence process at a rate determined by the gravitational acceleration. By assuming Einstein's Equivalence Principle to be valid, we demonstrate, first in a Lorentz frame with accelerating detectors, and then directly in the Lab frame with uniform gravity, that the dephasing between the different internal states arise not from gravity but rather from differences in their rest mass, and the mass dependence of the de Broglie wave's dispersion relation. We provide an alternative view to the situation considered by Ref. [1], where we propose that gravity plays a kinematic role in the loss of fringe visibility by giving the detector a transverse velocity relative to the particle beam; visibility can be easily recovered by giving the screen an appropriate uniform velocity. We finally propose that dephasing due to gravity may in fact take place for certain modifications to the gravitational potential where the Equivalence Principle is violated.Comment: 5 pages, 3 figure

    Marginally Trapped Surfaces in the Nonsymmetric Gravitational Theory

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    We consider a simple, physical approach to the problem of marginally trapped surfaces in the Nonsymmetric Gravitational Theory (NGT). We apply this approach to a particular spherically symmetric, Wyman sector gravitational field, consisting of a pulse in the antisymmetric field variable. We demonstrate that marginally trapped surfaces do exist for this choice of initial data.Comment: REVTeX 3.0 with epsf macros and AMS symbols, 3 pages, 1 figur

    Eigenvalues of Ruijsenaars-Schneider models associated with An−1A_{n-1} root system in Bethe ansatz formalism

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    Ruijsenaars-Schneider models associated with An−1A_{n-1} root system with a discrete coupling constant are studied. The eigenvalues of the Hamiltonian are givein in terms of the Bethe ansatz formulas. Taking the "non-relativistic" limit, we obtain the spectrum of the corresponding Calogero-Moser systems in the third formulas of Felder et al [20].Comment: Latex file, 25 page

    The Cauchy Operator for Basic Hypergeometric Series

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    We introduce the Cauchy augmentation operator for basic hypergeometric series. Heine's 2Ï•1{}_2\phi_1 transformation formula and Sears' 3Ï•2{}_3\phi_2 transformation formula can be easily obtained by the symmetric property of some parameters in operator identities. The Cauchy operator involves two parameters, and it can be considered as a generalization of the operator T(bDq)T(bD_q). Using this operator, we obtain extensions of the Askey-Wilson integral, the Askey-Roy integral, Sears' two-term summation formula, as well as the qq-analogues of Barnes' lemmas. Finally, we find that the Cauchy operator is also suitable for the study of the bivariate Rogers-Szeg\"o polynomials, or the continuous big qq-Hermite polynomials.Comment: 21 pages, to appear in Advances in Applied Mathematic
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