46,260 research outputs found

    Renormalization of the Sigma-Omega model within the framework of U(1) gauge symmetry

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    It is shown that the Sigma-Omega model which is widely used in the study of nuclear relativistic many-body problem can exactly be treated as an Abelian massive gauge field theory. The quantization of this theory can perfectly be performed by means of the general methods described in the quantum gauge field theory. Especially, the local U(1) gauge symmetry of the theory leads to a series of Ward-Takahashi identities satisfied by Green's functions and proper vertices. These identities form an uniquely correct basis for the renormalization of the theory. The renormalization is carried out in the mass-dependent momentum space subtraction scheme and by the renormalization group approach. With the aid of the renormalization boundary conditions, the solutions to the renormalization group equations are given in definite expressions without any ambiguity and renormalized S-matrix elememts are exactly formulated in forms as given in a series of tree diagrams provided that the physical parameters are replaced by the running ones. As an illustration of the renormalization procedure, the one-loop renormalization is concretely carried out and the results are given in rigorous forms which are suitable in the whole energy region. The effect of the one-loop renormalization is examined by the two-nucleon elastic scattering.Comment: 32 pages, 17 figure

    Blowing Carbon Nanotubes to Carbon Nanobulbs

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    Stochastic Language Generation in Dialogue using Recurrent Neural Networks with Convolutional Sentence Reranking

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    The natural language generation (NLG) component of a spoken dialogue system (SDS) usually needs a substantial amount of handcrafting or a well-labeled dataset to be trained on. These limitations add significantly to development costs and make cross-domain, multi-lingual dialogue systems intractable. Moreover, human languages are context-aware. The most natural response should be directly learned from data rather than depending on predefined syntaxes or rules. This paper presents a statistical language generator based on a joint recurrent and convolutional neural network structure which can be trained on dialogue act-utterance pairs without any semantic alignments or predefined grammar trees. Objective metrics suggest that this new model outperforms previous methods under the same experimental conditions. Results of an evaluation by human judges indicate that it produces not only high quality but linguistically varied utterances which are preferred compared to n-gram and rule-based systems.Comment: To be appear in SigDial 201

    Generation of GHZ entangled states of photons in multiple cavities via a superconducting qutrit or an atom through resonant interaction

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    We propose an efficient method to generate a GHZ entangled state of n photons in n microwave cavities (or resonators) via resonant interaction to a single superconducting qutrit. The deployment of a qutrit, instead of a qubit, as the coupler enables us to use resonant interactions exclusively for all qutrit-cavity and qutrit-pulse operations. This unique approach significantly shortens the time of operation which is advantageous to reducing the adverse effects of qutrit decoherence and cavity decay on fidelity of the protocol. Furthermore, the protocol involves no measurement on either the state of qutrit or cavity photons. We also show that the protocol can be generalized to other systems by replacing the superconducting qutrit coupler with different types of physical qutrit, such as an atom in the case of cavity QED, to accomplish the same task.Comment: 11 pages, 5 figures, accepted by Phys. Rev.

    Dirac-Schr\"odinger equation for quark-antiquark bound states and derivation of its interaction kerne

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    The four-dimensional Dirac-Schr\"odinger equation satisfied by quark-antiquark bound states is derived from Quantum Chromodynamics. Different from the Bethe-Salpeter equation, the equation derived is a kind of first-order differential equations of Schr\"odinger-type in the position space. Especially, the interaction kernel in the equation is given by two different closed expressions. One expression which contains only a few types of Green's functions is derived with the aid of the equations of motion satisfied by some kinds of Green's functions. Another expression which is represented in terms of the quark, antiquark and gluon propagators and some kinds of proper vertices is derived by means of the technique of irreducible decomposition of Green's functions. The kernel derived not only can easily be calculated by the perturbation method, but also provides a suitable basis for nonperturbative investigations. Furthermore, it is shown that the four-dimensinal Dirac-Schr\"odinger equation and its kernel can directly be reduced to rigorous three-dimensional forms in the equal-time Lorentz frame and the Dirac-Schr\"odinger equation can be reduced to an equivalent Pauli-Schr\"odinger equation which is represented in the Pauli spinor space. To show the applicability of the closed expressions derived and to demonstrate the equivalence between the two different expressions of the kernel, the t-channel and s-channel one gluon exchange kernels are chosen as an example to show how they are derived from the closed expressions. In addition, the connection of the Dirac-Schr\"odinger equation with the Bethe-Salpeter equation is discussed

    Lie bialgebras of generalized Witt type

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    In a paper by Michaelis a class of infinite-dimensional Lie bialgebras containing the Virasoro algebra was presented. This type of Lie bialgebras was classified by Ng and Taft. In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are classified. It is proved that, for any Lie algebra WW of generalized Witt type, all Lie bialgebras on WW are coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H1(W,W⊗W)H^1(W,W \otimes W) is trivial.Comment: 14 page

    Stretched exponential relaxation in the mode-coupling theory for the Kardar-Parisi-Zhang equation

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    We study the mode-coupling theory for the Kardar-Parisi-Zhang equation in the strong-coupling regime, focusing on the long time properties. By a saddle point analysis of the mode-coupling equations, we derive exact results for the correlation function in the long time limit - a limit which is hard to study using simulations. The correlation function at wavevector k in dimension d is found to behave asymptotically at time t as C(k,t)\simeq 1/k^{d+4-2z} (Btk^z)^{\gamma/z} e^{-(Btk^z)^{1/z}}, with \gamma=(d-1)/2, A a determined constant and B a scale factor.Comment: RevTex, 4 pages, 1 figur
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