10,885 research outputs found

    Magnetic dipole-dipole interaction induced by the electromagnetic field

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    We give a derivation for the indirect interaction between two magnetic dipoles induced by the quantized electromagnetic field. It turns out that the interaction between permanent dipoles directly returns to the classical form; the interaction between transition dipoles does not directly return to the classical result, yet returns in the short-distance limit. In a finite volume, the field modes are highly discrete, and both the permanent and transition dipole-dipole interactions are changed. For transition dipoles, the changing mechanism is similar with the Purcell effect, since only a few number of nearly resonant modes take effect in the interaction mediation; for permanent dipoles, the correction comes from the boundary effect: if the dipoles are placed close to the boundary, the influence is strong, otherwise, their interaction does not change too much from the free space case.Comment: 8 pages, 2 figure

    Tensor effects on gap evolution of N=40 from non-relativistic and relativistic mean-field theory

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    Tensor effects on the N=40 gap evolution of N=40 isotones are studied by employing the Skyrme-Hartree-Fock-Bogoliubov (SHFB) and relativistic Hartree-Fock-Bogoliubov (RHFB) theories. The results with and without the inclusion of the tensor component are compared with the experimental data. When the tensor force is included, both of the two different approaches are found to give the same trend and agree with the experimental one, which indicates the necessity of introducing the tensor force in the evolution of N=40 subshell and on the other hand the reliability of the methods. Furthermore, it is shown that the gap evolution is primarily determined by the corresponding tensor contributions from π\pi and ρ\rho-tensor coupling in the relativistic framework.Comment: 4 pages, 3 figure

    Invariance of Quantum Rings under Ordinary Flops I: Quantum corrections and reduction to local models

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    This is the first of a sequence of papers proving the quantum invariance under ordinary flops over an arbitrary smooth base. In this first part, we determine the defect of the cup product under the canonical correspondence and show that it is corrected by the small quantum product attached to the extremal ray. We then perform various reductions to reduce the problem to the local models. In Part II, we develop a quantum Leray--Hirsch theorem and use it to show that the big quantum cohomology ring is invariant under analytic continuations in the K\"ahler moduli space for ordinary flops of splitting type. In Part III, together with F. Qu, we remove the splitting condition by developing a quantum splitting principle, and hence solve the problem completely.Comment: 38 pages, the final version to appear in Algebraic Geometr

    Quantum Cohomology under Birational Maps and Transitions

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    This is an expanded version of the third author's lecture in String-Math 2015 at Sanya. It summarizes some of our works in quantum cohomology. After reviewing the quantum Lefschetz and quantum Leray--Hirsch, we discuss their applications to the functoriality properties under special smooth flops, flips and blow-ups. Finally, for conifold transitions of Calabi--Yau 3-folds, formulations for small resolutions (blow-ups along Weil divisors) are sketched.Comment: 20 pages. A contribution to "Proceedings of the String-Math 2015 Conference" to be published in AMS Proceedings of Symposia in Pure Mathematic

    Shadows of Kerr-like black holes in a modified gravity theory

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    In this paper, the shadows cast by non-rotating and rotating modified gravity black holes are investigated. In addition to the black hole spin parameter aa and the inclination angle θ\theta of observer, another parameter α\alpha measuring the deviation of gravitational constant from the Newton one is also found to affect the shape of the black hole shadow. The result shows that, for fixed values of a/Ma/M and θ\theta, the size and perimeter of the shadows cast by the non-rotating and rotating black holes significantly increase with the parameter α\alpha, while the distortions decrease with α\alpha. Moreover, the energy emission rate of the black hole in high energy case is also investigated, and the result shows that the peak of the emission rate decreases with the parameter α\alpha.Comment: 14 pages, 8 figure

    Flops, motives and invariance of quantum rings

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    For ordinary flops, the correspondence defined by the graph closure is shown to give equivalence of Chow motives and to preserve the Poincar\'e pairing. In the case of simple ordinary flops, this correspondence preserves the big quantum cohomology ring after an analytic continuation over the extended K\"ahler moduli space. For Mukai flops, it is shown that the birational map for the local models is deformation equivalent to isomorphisms. This implies that the birational map induces isomorphisms on the full quantum rings and all the quantum corrections attached to the extremal ray vanish.Comment: 51 pages, 2 figures, final version to appear in Annals of Mathematic

    Base Station Cooperation in Millimeter Wave Cellular Networks: Performance Enhancement of Cell-Edge Users

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    Millimeter wave (mmWave) signals are much more sensitive to blockage, which results in a significant increase of the outage probability, especially for the users at the edge of the cells. In this paper, we exploit the technique of base station (BS) cooperation to improve the performance of the cell-edge users in the downlink transmission of mmWave cellular networks. We design two cooperative schemes, which are referred to as fixed-number BS cooperation (FNC) scheme and fixed-region BS cooperation (FRC) scheme, respectively. In FNC scheme, the cooperative BSs consist of the M nearest BSs around the served cell-edge users, and in FRC scheme, the cooperative BSs include all the BSs located within a given region. We derive the expressions for the average rate and outage probability of a typical cell-edge user located at the origin based on the stochastic geometry framework. To reduce the computational complexity of our analytical results for the outage probability, we further propose a Gamma approximation based method to provide approximations with satisfying accuracy. Our analytical results incorporate the critical characteristics of mmWave channels, i.e., the blockage effects, the different path loss of LOS and NLOS links and the highly directional antenna arrays. Simulation results show that the performance of the cell-edge users is greatly improved when mmWave networks are combined with the technique of BS cooperation.Comment: To be published in IEEE Transactions on Communication

    Towards A+BA + B theory in conifold transitions for Calabi-Yau threefolds

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    For projective conifold transitions between Calabi-Yau threefolds XX and YY, with XX close to YY in the moduli, we show that the combined information provided by the AA model (Gromov--Witten theory in all genera) and BB model (variation of Hodge structures) on XX, linked along the vanishing cycles, determines the corresponding combined information on YY. Similar result holds in the reverse direction when linked with the exceptional curves.Comment: 47 pages, references updated. To appear in J. Diff. Geometr

    Invariance of Quantum Rings under Ordinary Flops II: A quantum Leray--Hirsch theorem

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    This is the second of a sequence of papers proving the quantum invariance for ordinary flops over an arbitrary smooth base. In this paper, we complete the proof of the invariance of the big quantum rings under ordinary flops of splitting type. To achieve that, several new ingredients are introduced. One is a quantum Leray--Hirsch theorem for the local model (a certain toric bundle) which extends the quantum D module of Dubrovin connection on the base by a Picard--Fuchs system of the toric fibers. Nonsplit flops as well as further applications of the quantum Leray--Hirsch theorem will be discussed in subsequent papers. In particular, a quantum splitting principle is developed in Part III which reduces the general ordinary flops to the split case solved here.Comment: 39 pages, the final version to appear in Algebraic Geometr

    Vortex states and spin textures of rotating spin-orbit-coupled Bose-Einstein condensates in a toroidal trap

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    We consider the ground-state properties of Rashba spin-orbit-coupled pseudo-spin-1/2 Bose-Einstein condensates (BECs) in a rotating two-dimensional (2D) toroidal trap. In the absence of spin-orbit coupling (SOC), the increasing rotation frequency enhances the creation of giant vortices for the initially miscible BECs, while it can lead to the formation of semiring density patterns with irregular hidden vortex structures for the initially immiscible BECs. Without rotation, strong 2D isotropic SOC yields a heliciform-stripe phase for the initially immiscible BECs. Combined effects of rotation, SOC, and interatomic interactions on the vortex structures and typical spin textures of the ground state of the system are discussed systematically. In particular, for fixed rotation frequency above the critical value, the increasing isotropic SOC favors a visible vortex ring in each component which is accompanied by a hidden giant vortex plus a (several) hidden vortex ring(s) in the central region. In the case of 1D anisotropic SOC, large SOC strength results in the generation of hidden linear vortex string and the transition from initial phase separation (phase mixing) to phase mixing (phase separation). Furthermore, the peculiar spin textures including skyrmion lattice, skyrmion pair and skyrmion string are revealed in this system.Comment: 11pages,8figure
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