68,470 research outputs found

    The number of ramified coverings of the sphere by the double torus, and a general form for higher genera

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    An explicit expression is obtained for the generating series for the number of ramified coverings of the sphere by the double torus, with elementary branch points and prescribed ramification type over infinity. Thus we are able to prove a conjecture of Graber and Pandharipande, giving a linear recurrence equation for the number of these coverings with no ramification over infinity. The general form of the series is conjectured for the number of these coverings by a surface of arbitrary genus that is at least two.Comment: 14pp.; revised version has two additional results in Section

    A proof of a conjecture for the number of ramified coverings of the sphere by the torus

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    An explicit expression is obtained for the generating series for the number of ramified coverings of the sphere by the torus, with elementary branch points and prescribed ramification type over infinity. This proves a conjecture of Goulden, Jackson and Vainshtein for the explicit number of such coverings.Comment: 10 page

    Vortices in Bose-Einstein condensates with anharmonic confinement

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    We examine an effectively repulsive Bose-Einstein condensate of atoms, that rotates in a quadratic-plus-quartic trapping potential. We investigate the phase diagram of the system as a function of the angular frequency of rotation and of the coupling constant, demonstrating that there are phase transitions between multiply- and singly-quantized vortex states. The derived phase diagram is shown to be universal and exact in the limits of small anharmonicity and weak coupling constant.Comment: 4 pages, 2 ps figures, RevTe

    Transitive factorizations of permutations and geometry

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    We give an account of our work on transitive factorizations of permutations. The work has had impact upon other areas of mathematics such as the enumeration of graph embeddings, random matrices, branched covers, and the moduli spaces of curves. Aspects of these seemingly unrelated areas are seen to be related in a unifying view from the perspective of algebraic combinatorics. At several points this work has intertwined with Richard Stanley's in significant ways.Comment: 12 pages, dedicated to Richard Stanley on the occasion of his 70th birthda

    Propagation of exciton pulses in semiconductors

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    Using a toy model, we examine the propagation of excitons in Cu2_2O, which form localized pulses under certain experimental conditions. The formation of these waves is attributed to the effect of dispersion, non-linearity and the coupling of the excitons to phonons, which acts as a dissipative mechanism.Comment: 5 pages, 4 ps figures, RevTe

    Finding the Pion in the Chiral Random Matrix Vacuum

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    The existence of a Goldstone boson is demonstrated in chiral random matrix theory. After determining the effective coupling and calculating the scalar and pseudoscalar propagators, a random phase approximation summation reveals the massless pion and massive sigma modes expected whenever chiral symmetry is spontaneously broken.Comment: 3 pages, 1 figure, revte

    Quantization and 2π2\pi Periodicity of the Axion Action in Topological Insulators

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    The Lagrangian describing the bulk electromagnetic response of a three-dimensional strong topological insulator contains a topological `axion' term of the form '\theta E dot B'. It is often stated (without proof) that the corresponding action is quantized on periodic space-time and therefore invariant under '\theta -> \theta +2\pi'. Here we provide a simple, physically motivated proof of the axion action quantization on the periodic space-time, assuming only that the vector potential is consistent with single-valuedness of the electron wavefunctions in the underlying insulator.Comment: 4 pages, 1 figure, version2 (section on axion action quantization of non-periodic systems added

    Wind tunnel model and method

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    The design and development of a wind tunnel model equipped with pressure measuring devices are discussed. The pressure measuring orifices are integrally constructed in the wind tunnel model and do not contribute to distortions of the aerodynamic surface. The construction of a typical model is described and a drawing of the device is included

    Tasting edge effects

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    We show that the baking of potato wedges constitutes a crunchy example of edge effects, which are usually demonstrated in electrostatics. A simple model of the diffusive transport of water vapor around the potato wedges shows that the water vapor flux diverges at the sharp edges in analogy with its electrostatic counterpart. This increased evaporation at the edges leads to the crispy taste of these parts of the potatoes.Comment: to appear in American Journal of Physic
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