3,643 research outputs found

    Constructing quantum vertex algebras

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    This is a sequel to \cite{li-qva}. In this paper, we focus on the construction of quantum vertex algebras over \C, whose notion was formulated in \cite{li-qva} with Etingof and Kazhdan's notion of quantum vertex operator algebra (over \C[[h]]) as one of the main motivations. As one of the main steps in constructing quantum vertex algebras, we prove that every countable-dimensional nonlocal (namely noncommutative) vertex algebra over \C, which either is irreducible or has a basis of PBW type, is nondegenerate in the sense of Etingof and Kazhdan. Using this result, we establish the nondegeneracy of better known vertex operator algebras and some nonlocal vertex algebras. We then construct a family of quantum vertex algebras closely related to Zamolodchikov-Faddeev algebras.Comment: 37 page

    Devil's staircase of incompressible electron states in a nanotube

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    It is shown that a periodic potential applied to a nanotube can lock electrons into incompressible states. Depending on whether electrons are weakly or tightly bound to the potential, excitation gaps open up either due to the Bragg diffraction enhanced by the Tomonaga - Luttinger correlations, or via pinning of the Wigner crystal. Incompressible states can be detected in a Thouless pump setup, in which a slowly moving periodic potential induces quantized current, with a possibility to pump on average a fraction of an electron per cycle as a result of interactions.Comment: 4 pages, 1 figure, published versio

    The Dirac Sea

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    We give an alternate definition of the free Dirac field featuring an explicit construction of the Dirac sea. The treatment employs a semi-infinite wedge product of Hilbert spaces. We also show that the construction is equivalent to the standard Fock space construction.Comment: 7 page

    The Integrals of Motion for the Deformed W-Algebra Wqt(slN)W_{qt}(sl_N^) II: Proof of the commutation relations

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    We explicitly construct two classes of infinitly many commutative operators in terms of the deformed W-algebra Wqt(slN)W_{qt}(sl_N^), and give proofs of the commutation relations of these operators. We call one of them local integrals of motion and the other nonlocal one, since they can be regarded as elliptic deformation of local and nonlocal integrals of motion for the WNW_N algebra.Comment: Dedicated to Professor Tetsuji Miwa on the occasion on the 60th birthda

    The structure of the hard sphere solid

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    We show that near densest-packing the perturbations of the HCP structure yield higher entropy than perturbations of any other densest packing. The difference between the various structures shows up in the correlations between motions of nearest neighbors. In the HCP structure random motion of each sphere impinges slightly less on the motion of its nearest neighbors than in the other structures.Comment: For related papers see: http://www.ma.utexas.edu/users/radin/papers.htm

    Mutually Penetrating Motion of Self-Organized 2D Patterns of Soliton-Like Structures

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    Results of numerical simulations of a recently derived most general dissipative-dispersive PDE describing evolution of a film flowing down an inclined plane are presented. They indicate that a novel complex type of spatiotemporal patterns can exist for strange attractors of nonequilibrium systems. It is suggested that real-life experiments satisfying the validity conditions of the theory are possible: the required sufficiently viscous liquids are readily available.Comment: minor corrections, 4 pages, LaTeX, 6 figures, mpeg simulations available upon or reques

    Effective actions at finite temperature

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    This is a more detailed version of our recent paper where we proposed, from first principles, a direct method for evaluating the exact fermion propagator in the presence of a general background field at finite temperature. This can, in turn, be used to determine the finite temperature effective action for the system. As applications, we discuss the complete one loop finite temperature effective actions for 0+1 dimensional QED as well as for the Schwinger model in detail. These effective actions, which are derived in the real time (closed time path) formalism, generate systematically all the Feynman amplitudes calculated in thermal perturbation theory and also show that the retarded (advanced) amplitudes vanish in these theories. Various other aspects of the problem are also discussed in detail.Comment: 9 pages, revtex, 1 figure, references adde

    Heat capacity at the glass transition

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    A fundamental problem of glass transition is to explain the jump of heat capacity at the glass transition temperature TgT_g without asserting the existence of a distinct solid glass phase. This problem is also common to other disordered systems, including spin glasses. We propose that if TgT_g is defined as the temperature at which the liquid stops relaxing at the experimental time scale, the jump of heat capacity at TgT_g follows as a necessary consequence due to the change of system's elastic, vibrational and thermal properties. In this picture, we discuss time-dependent effects of glass transition, and identify three distinct regimes of relaxation. Our approach explains widely observed logarithmic increase of TgT_g with the quench rate and the correlation of heat capacity jump with liquid fragility

    The thickness of a liquid layer on the free surface of ice as obtained from computer simulation

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    Molecular dynamic simulations were performed for ice Ih with a free surface by using four water models, SPC/E, TIP4P, TIP4P/Ice and TIP4P/2005. The behavior of the basal plane, the primary prismatic plane and of the secondary prismatic plane when exposed to vacuum was analyzed. We observe the formation of a thin liquid layer at the ice surface at temperatures below the melting point for all models and the three planes considered. For a given plane it was found that the thickness of a liquid layer was similar for different water models, when the comparison is made at the same undercooling with respect to the melting point of the model. The liquid layer thickness is found to increase with temperature. For a fixed temperature it was found that the thickness of the liquid layer decreases in the following order: the basal plane, the primary prismatic plane, and the secondary prismatic plane. For the TIP4P/Ice model, a model reproducing the experimental value of the melting temperature of ice, the first clear indication of the formation of a liquid layer appears at about -100 Celsius for the basal plane, at about -80 Celsius for the primary prismatic plane and at about -70 Celsius for the secondary prismatic plane.Comment: 41 pages and 13 figure

    A central extension of \cD Y_{\hbar}(\gtgl_2) and its vertex representations

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    A central extension of \cD Y_{\hbar}(\gtgl_2) is proposed. The bosonization of level 11 module and vertex operators are also given.Comment: 10 pages, AmsLatex, to appear in Lett. in Math. Phy
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