335,395 research outputs found

    Quasinormal modes of a black hole in the deformed Ho\v{r}ava-Lifshitz gravity

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    We study the quasinormal modes of the massless scalar perturbation in the background of a deformed black hole in the Ho\v{r}ava-Lifshitz gravity with coupling constant λ=1\lambda=1. Our results show that the quasinormal frequencies depend on the parameter in the Ho\v{r}ava-Lifshitz gravity and the behavior of the quasinormal modes is different from those in the Reissner-Norstr\"{om} and Einstein-Born-Infeld black hole spacetimes. The absolute value of imaginary parts is smaller and the scalar perturbations decay more slowly in the deformed Ho\v{r}ava-Lifshitz black hole spacetime. This information can help us understand more about the Ho\v{r}ava-Lifshitz gravity.Comment: 9 pages, 3 figures and 4 table

    Propagations of massive graviton in the deformed Ho\v{r}ava-Lifshitz gravity

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    We study massive graviton propagations of scalar, vector, and tensor modes in the deformed Ho\v{r}ava-Lifshitz gravity by introducing Lorentz-violating mass term. It turns out that vector and tensor modes are massively propagating on the Minkowski spacetime background. However, adding the mass term does not cure a ghost instability in the Ho\v{r}ava scalar.Comment: 17 pages, version with projectability requirement, to appear in PR

    Spontaneous symmetry breaking of fundamental states, vortices, and dipoles in two- and one-dimensional linearly coupled traps with cubic self-attraction

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    We introduce two- and one-dimensional (2D and 1D) systems of two linearly-coupled Gross-Pitaevskii equations (GPEs) with the cubic self-attraction and harmonic-oscillator (HO) trapping potential in each GPE. The system models a Bose-Einstein condensate with a negative scattering length, loaded in a double-pancake trap, combined with the in-plane HO potential. In addition to that, the 1D version applies to the light transmission in a dual-core waveguide with the Kerr nonlinearity and in-core confinement represented by the HO potential. The subject of the analysis is spontaneous symmetry breaking in 2D and 1D ground-state (GS, alias fundamental) modes, as well as in 2D vortices and 1D dipole modes (the latter ones do not exist without the HO potential). By means of the variational approximation and numerical analysis, it is found that both the 2D and 1D systems give rise to a symmetry-breaking bifurcation (SBB) of the supercrtical type. Stability of symmetric states and asymmetric ones, produced by the SBB, is analyzed through the computation of eigenvalues for perturbation modes, and verified by direct simulations. The asymmetric GSs are always stable, while the stability region for vortices shrinks and eventually disappears with the increase of the linear-coupling constant, κ \kappa . The SBB in the 2D system does not occur if κ\kappa is too large (at κ>κmax\kappa >\kappa_{\max }); in that case, the two-component system behaves, essentially, as its single-component counterpart. In the 1D system, both asymmetric and symmetric dipole modes feature an additional oscillatory instability, unrelated to the symmetry breaking. This instability occurs in several regions, which expand with the increase of κ\kappa .Comment: 22 pages, 19 figures, Phys. Rev. A, in pres

    Empirical Evaluation of Four Tensor Decomposition Algorithms

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    Higher-order tensor decompositions are analogous to the familiar Singular Value Decomposition (SVD), but they transcend the limitations of matrices (second-order tensors). SVD is a powerful tool that has achieved impressive results in information retrieval, collaborative filtering, computational linguistics, computational vision, and other fields. However, SVD is limited to two-dimensional arrays of data (two modes), and many potential applications have three or more modes, which require higher-order tensor decompositions. This paper evaluates four algorithms for higher-order tensor decomposition: Higher-Order Singular Value Decomposition (HO-SVD), Higher-Order Orthogonal Iteration (HOOI), Slice Projection (SP), and Multislice Projection (MP). We measure the time (elapsed run time), space (RAM and disk space requirements), and fit (tensor reconstruction accuracy) of the four algorithms, under a variety of conditions. We find that standard implementations of HO-SVD and HOOI do not scale up to larger tensors, due to increasing RAM requirements. We recommend HOOI for tensors that are small enough for the available RAM and MP for larger tensors

    Massive graviton propagation of the deformed Ho\v{r}ava-Lifshitz gravity without projectability condition

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    We study graviton propagations of scalar, vector, and tensor modes in the deformed Ho\v{r}ava-Lifshitz gravity (λR\lambda R-model) without projectability condition. The quadratic Lagrangian is invariant under diffeomorphism only for λ=1\lambda=1 case, which contradicts to the fact that λ\lambda is irrelevant to a consistent Hamiltonian approach to the λR\lambda R model. In this case, as far as scalar propagations are concerned, there is no essential difference between deformed Ho\v{r}ava-Lifshitz gravity (λR\lambda R-model) and general relativity. This implies that there are two degrees of freedom for a massless graviton without Ho\v{r}ava scalar, and five degrees of freedom appear for a massive graviton when introducing Lorentz-violating and Fierz-Pauli mass terms. Finally, it is shown that for λ=1\lambda=1, the vDVZ discontinuity is absent in the massless limit of Lorentz-violating mass terms by considering external source terms.Comment: 21 pages, no figure, version to appear in PL

    Fermionic quasinormal modes for two-dimensional Ho\v{r}ava-Lifshitz black holes

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    To obtain fermionic quasinormal modes, the Dirac equation for two types of black holes is investigated. For the first type of black hole, the quasinormal modes have continuous spectrum with negative imaginary part that provides the stability of black hole geometry. For the second type of the black hole, the quasinormal modes have discrete spectrum and are completely imaginary. This type of the black hole appears to be stable for arbitrary masses of fermion field perturbations.Comment: 13 pages, no figure

    Vibrational assignments and line shapes in inelastic tunnelling spectroscopy: H on Cu(100)

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    We have carried out a computational study of the inelastic electron tunneling spectrum (IETS) of the two vibrational modes of a single hydrogen atom on a Cu(100) surface in a scanning tunneling microscopy (STM) junction. This study addresses key issues about vibrational assignment and line shape of observed peaks in IETS within the framework of density functional theory calculations and the Lorente-Persson theory for STM-IETS. We argue that the observation of only a single, broad peak in the STM-IETS [L.J. Lauhon and W. Ho, Phys. Rev. Lett. 85, 4566 (2000)] is not caused by any symmetry restrictions or any cancellation between inelastic and elastic vibrational contributions for one of the two modes but is due to strongly overlapping superposition of the contributions from the two modes caused by the rather large instrumental broadening and the narrow vibrational energy separation between the modes. In particular, we find that this broadening and the large asymmetry of the vibrational line shapes gives rise to substantial apparent vibrational energy shifts of the two modes and decrease their apparent energy separation
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