58 research outputs found
The determination of the electron-phonon interaction from tunneling data in the two-band superconductor MgB2
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
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 -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 -gerbes over stacks.
We also introduce -central extensions of groupoids, generalizing the
standard groupoid -central extensions.
As an example, we apply our theory to study the differential geometry of
-gerbes over a manifold.Comment: 67 pages, references added and updated, final version to appear in
Adv. Mat
Multivariable calculus and differential geometry
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
Multivariable Calculus and Differential Geometry
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
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