231 research outputs found

    simplicial cohomology of orbifolds

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    For any orbifold M, we explicitly construct a simplicial complex S(M) from a given triangulation of the `coarse' underlying space together with the local isotropy groups of M. We prove that, for any local system on M, this complex S(M) has the same cohomology as M. The use of S(M) in explicit calculations is illustrated in the example of the `teardrop' orbifold.Comment: 23 pages, 4 figures, 6 diagram

    Algebroid Yang-Mills Theories

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    A framework for constructing new kinds of gauge theories is suggested. Essentially it consists in replacing Lie algebras by Lie or Courant algebroids. Besides presenting novel topological theories defined in arbitrary spacetime dimensions, we show that equipping Lie algebroids E with a fiber metric having sufficiently many E-Killing vectors leads to an astonishingly mild deformation of ordinary Yang-Mills theories: Additional fields turn out to carry no propagating modes. Instead they serve as moduli parameters gluing together in part different Yang-Mills theories. This leads to a symmetry enhancement at critical points of these fields, as is also typical for String effective field theories.Comment: 4 pages; v3: Minor rewording of v1, version to appear in Phys. Rev. Let

    Higher Descent Data as a Homotopy Limit

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    We define the 2-groupoid of descent data assigned to a cosimplicial 2-groupoid and present it as the homotopy limit of the cosimplicial space gotten after applying the 2-nerve in each cosimplicial degree. This can be applied also to the case of nn-groupoids thus providing an analogous presentation of "descent data" in higher dimensions.Comment: Appeared in JHR

    Strongly enhanced inelastic collisions in a Bose-Einstein condensate near Feshbach resonances

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    The properties of Bose-Einstein condensed gases can be strongly altered by tuning the external magnetic field near a Feshbach resonance. Feshbach resonances affect elastic collisions and lead to the observed modification of the scattering length. However, as we report here, this is accompanied by a strong increase in the rate of inelastic collisions. The observed three-body loss rate in a sodium Bose-Einstein condensation increased when the scattering length was tuned to both larger or smaller values than the off-resonant value. This observation and the maximum measured increase of the loss rate by several orders of magnitude are not accounted for by theoretical treatments. The strong losses impose severe limitations for using Feshbach resonances to tune the properties of Bose-Einstein condensates. A new Feshbach resonance in sodium at 1195 G was observed.Comment: 4 pages, 3 figure

    Quantum Computing with Atomic Josephson Junction Arrays

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    We present a quantum computing scheme with atomic Josephson junction arrays. The system consists of a small number of atoms with three internal states and trapped in a far-off resonant optical lattice. Raman lasers provide the "Josephson" tunneling, and the collision interaction between atoms represent the "capacitive" couplings between the modes. The qubit states are collective states of the atoms with opposite persistent currents. This system is closely analogous to the superconducting flux qubit. Single qubit quantum logic gates are performed by modulating the Raman couplings, while two-qubit gates result from a tunnel coupling between neighboring wells. Readout is achieved by tuning the Raman coupling adiabatically between the Josephson regime to the Rabi regime, followed by a detection of atoms in internal electronic states. Decoherence mechanisms are studied in detail promising a high ratio between the decoherence time and the gate operation time.Comment: 7 figure

    Poisson algebras for non-linear field theories in the Cahiers topos

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    We develop an approach to construct Poisson algebras for non-linear scalar field theories that is based on the Cahiers topos model for synthetic differential geometry. In this framework the solution space of the field equation carries a natural smooth structure and, following Zuckerman's ideas, we can endow it with a presymplectic current. We formulate the Hamiltonian vector field equation in this setting and show that it selects a family of observables which forms a Poisson algebra. Our approach provides a clean splitting between geometric and algebraic aspects of the construction of a Poisson algebra, which are sufficient to guarantee existence, and analytical aspects that are crucial to analyze its properties

    Three-body recombination of ultra-cold atoms to a weakly bound ss level

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    We discuss three-body recombination of ultra-cold atoms to a weakly bound ss level. In this case, characterized by large and positive scattering length aa for pair interaction, we find a repulsive effective potential for three-body collisions, which strongly reduces the recombination probability and makes simple Jastrow-like approaches absolutely inadequate. In the zero temperature limit we obtain a universal relation, independent of the detailed shape of the interaction potential, for the (event) rate constant of three-body recombination: αrec=3.9a4/m\alpha_{\rm rec}=3.9\hbar a^4/m, where mm is the atom mass.Comment: 10 pages, 3 Postscript figure

    Local Spin-Gauge Symmetry of the Bose-Einstein Condensates in Atomic Gases

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    The Bose-Einstein condensates of alkali atomic gases are spinor fields with local ``spin-gauge" symmetry. This symmetry is manifested by a superfluid velocity us{\bf u}_{s} (or gauge field) generated by the Berry phase of the spin field. In ``static" traps, us{\bf u}_{s} splits the degeneracy of the harmonic energy levels, breaks the inversion symmetry of the vortex nucleation frequency Ωc1{\bf \Omega}_{c1}, and can lead to {\em vortex ground states}. The inversion symmetry of Ωc1{\bf \Omega}_{c1}, however, is not broken in ``dynamic" traps. Rotations of the atom cloud can be generated by adiabatic effects without physically rotating the entire trap.Comment: Typos in the previous version corrected, thanks to the careful reading of Daniel L. Cox. 13 pages + 2 Figures in uuencode + gzip for

    Three-body recombination in Bose gases with large scattering length

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    An effective field theory for the three-body system with large scattering length is applied to three-body recombination to a weakly-bound s-wave state in a Bose gas. Our model independent analysis demonstrates that the three-body recombination constant alpha is not universal, but can take any value between zero and 67.9 \hbar a^4/m, where a is the scattering length. Other low-energy three-body observables can be predicted in terms of a and alpha. Near a Feshbach resonance, alpha should oscillate between those limits as the magnetic field B approaches the point where a -> infinity. In any interval of B over which a increases by a factor of 22.7, alpha should have a zero.Comment: 8 pages, RevTex, 3 postscript figures, uses epsf.sty, rotate.sty, references added, discussion improve

    Atom loss from Bose-Einstein condensates due to Feshbach resonance

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    In recent experiments on Na Bose-Einstein condensates [S. Inouye et al, Nature 392, 151 (1998); J. Stenger et al, Phys. Rev. Lett. 82, 2422 (1999)], large loss rates were observed when a time-varying magnetic field was used to tune a molecular Feshbach resonance state near the state of pairs of atoms belonging to the condensate many-body wavefunction. A mechanism is offered here to account for the observed losses, based on the deactivation of the resonant molecular state by interaction with a third condensate atom.Comment: LaTeX, 4 pages, 4 PostScript figures, uses REVTeX and psfig, submitted to Physical Review A, Rapid Communication
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