57 research outputs found

    The determination of the electron-phonon interaction from tunneling data in the two-band superconductor MgB2

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    We calculate the tunneling density of states (DOS) of MgB2 for different tunneling directions, by directly solving the real-axis, two-band Eliashberg equations (EE). Then we show that the numeric inversion of the standard single-band EE, if applied to the DOS of the two-band superconductor MgB2, may lead to wrong estimates of the strength of certain phonon branches (e.g. the E_2g) in the extracted electron-phonon spectral function alpha^(2)F(omega). The fine structures produced by the two-band interaction turn out to be clearly observable only for tunneling along the ab planes in high-quality single crystals. The results are compared to recent experimental data.Comment: 2 pages, 2 figures, proceedings of M2S-HTSC-VII conference, Rio de Janeiro (May 2003

    Non Abelian Differentiable Gerbes

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    We study non-abelian differentiable gerbes over stacks using the theory of Lie groupoids. More precisely, we develop the theory of connections on Lie groupoid GG-extensions, which we call "connections on gerbes", and study the induced connections on various associated bundles. We also prove analogues of the Bianchi identities. In particular, we develop a cohomology theory which measures the existence of connections and curvings for GG-gerbes over stacks. We also introduce GG-central extensions of groupoids, generalizing the standard groupoid S1S^1-central extensions. As an example, we apply our theory to study the differential geometry of GG-gerbes over a manifold.Comment: 67 pages, references added and updated, final version to appear in Adv. Mat

    Multivariable calculus and differential geometry

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    This text is a modern in-depth study of the subject that includes all the material needed from linear algebra. It then goes on to investigate topics in differential geometry, such as manifolds in Euclidean space, curvature, and the generalization of the fundamental theorem of calculus known as Stokes' theorem

    Metric structures in differential geometry

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