459 research outputs found

    Contact orderability up to conjugation

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    We study in this paper the remnants of the contact partial order on the orbits of the adjoint action of contactomorphism groups on their Lie algebras. Our main interest is a class of non-compact contact manifolds, called convex at infinity.Comment: 28 pages, 1 figur

    Spin-triplet pairing instability of the spinon Fermi surface in a U(1) spin liquid

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    Recent experiments on the organic compound \kappa-(ET)_2Cu_2(CN)_3 have provided a promising example of a two dimensional spin liquid state. This phase is described by a two-dimensional spinon Fermi sea coupled to a U(1) gauge field. We study Kohn-Luttinger-like pairing instabilities of the spinon Fermi surface due to singular interaction processes with twice-the-Fermi-momentum transfer. We find that under certain circumstances the pairing instability occurs in odd-orbital-angular-momentum/spin-triplet channels. Implications to experiments are discussed.Comment: 4 pages, 1 figur

    Partial Isometries of a Sub-Riemannian Manifold

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    In this paper, we obtain the following generalisation of isometric C1C^1-immersion theorem of Nash and Kuiper. Let MM be a smooth manifold of dimension mm and HH a rank kk subbundle of the tangent bundle TMTM with a Riemannian metric gHg_H. Then the pair (H,gH)(H,g_H) defines a sub-Riemannian structure on MM. We call a C1C^1-map f:(M,H,gH)(N,h)f:(M,H,g_H)\to (N,h) into a Riemannian manifold (N,h)(N,h) a {\em partial isometry} if the derivative map dfdf restricted to HH is isometric; in other words, fhH=gHf^*h|_H=g_H. The main result states that if dimN>k\dim N>k then a smooth HH-immersion f0:MNf_0:M\to N satisfying fhH<gHf^*h|_H<g_H can be homotoped to a partial isometry f:(M,gH)(N,h)f:(M,g_H)\to (N,h) which is C0C^0-close to f0f_0. In particular we prove that every sub-Riemannian manifold (M,H,gH)(M,H,g_H) admits a partial isometry in Rn\R^n provided nm+kn\geq m+k.Comment: 13 pages. This is a revised version of an earlier submission (minor revision

    Compactness results in Symplectic Field Theory

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    This is one in a series of papers devoted to the foundations of Symplectic Field Theory sketched in [Y Eliashberg, A Givental and H Hofer, Introduction to Symplectic Field Theory, Geom. Funct. Anal. Special Volume, Part II (2000) 560--673]. We prove compactness results for moduli spaces of holomorphic curves arising in Symplectic Field Theory. The theorems generalize Gromov's compactness theorem in [M Gromov, Pseudo-holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307--347] as well as compactness theorems in Floer homology theory, [A Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math. 41 (1988) 775--813 and Morse theory for Lagrangian intersections, J. Diff. Geom. 28 (1988) 513--547], and in contact geometry, [H Hofer, Pseudo-holomorphic curves and Weinstein conjecture in dimension three, Invent. Math. 114 (1993) 307--347 and H Hofer, K Wysocki and E Zehnder, Foliations of the Tight Three Sphere, Annals of Mathematics, 157 (2003) 125--255].Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper25.abs.htm

    Weak and strong fillability of higher dimensional contact manifolds

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    For contact manifolds in dimension three, the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent. We extend these facts to higher dimensions: in particular, we define a natural generalization of weak fillings and prove that it is indeed weaker (at least in dimension five),while also being obstructed by all known manifestations of "overtwistedness". We also find the first examples of contact manifolds in all dimensions that are not symplectically fillable but also cannot be called overtwisted in any reasonable sense. These depend on a higher-dimensional analogue of Giroux torsion, which we define via the existence in all dimensions of exact symplectic manifolds with disconnected contact boundary.Comment: 68 pages, 5 figures. v2: Some attributions clarified, and other minor edits. v3: exposition improved using referee's comments. Published by Invent. Mat

    Spin fluctuations and superconductivity in noncentrosymmetric heavy fermion systems CeRhSi3_3 and CeIrSi3_3

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    We study the normal and the superconducting properties in noncentrosymmetric heavy fermion superconductors CeRhSi3_3 and CeIrSi3_3. For the normal state, we show that experimentally observed linear temperature dependence of the resistivity is understood through the antiferromagnetic spin fluctuations near the quantum critical point (QCP) in three dimensions. For the superconducting state, we derive a general formula to calculate the upper critical field Hc2H_{c2}, with which we can treat the Pauli and the orbital depairing effect on an equal footing. The strong coupling effect for general electronic structures is also taken into account. We show that the experimentally observed features in Hc2z^H_{c2}\parallel \hat{z}, the huge value up to 30(T), the downward curvatures, and the strong pressure dependence, are naturally understood as an interplay of the Rashba spin-orbit interaction due to the lack of inversion symmetry and the spin fluctuations near the QCP. The large anisotropy between Hc2z^H_{c2}\parallel \hat{z} and Hc2z^H_{c2}\perp \hat{z} is explained in terms of the spin-orbit interaction. Furthermore, a possible realization of the Fulde-Ferrell- Larkin-Ovchinnikov state for Hz^H\perp \hat{z} is studied. We also examine effects of spin-flip scattering processes in the pairing interaction and those of the applied magnetic field on the spin fluctuations. We find that the above mentioned results are robust against these effects. The consistency of our results strongly supports the scenario that the superconductivity in CeRhSi3_3 and CeIrSi3_3 is mediated by the spin fluctuations near the QCP.Comment: 21pages, 13figures, to be published in Phys. Rev.

    Imaging the essential role of spin-fluctuations in high-Tc superconductivity

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    We have used scanning tunneling spectroscopy to investigate short-length electronic correlations in three-layer Bi2Sr2Ca2Cu3O(10+d) (Bi-2223). We show that the superconducting gap and the energy Omega_dip, defined as the difference between the dip minimum and the gap, are both modulated in space following the lattice superstructure, and are locally anti-correlated. Based on fits of our data to a microscopic strong-coupling model we show that Omega_dip is an accurate measure of the collective mode energy in Bi-2223. We conclude that the collective mode responsible for the dip is a local excitation with a doping dependent energy, and is most likely the (pi,pi) spin resonance.Comment: 4 pages, 4 figure

    Theory of SIS tunnelling in cuprates

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    We show that the single-particle polaron Green's function describes SIS tunnelling in cuprates, including the absence of Ohm's law at high voltages, the dip/hump features in the first derivative of the current, a substantial incoherent spectral weight beyond quasiparticle peaks and unusual shape of the peaks. The theory allows us to determine the characteristic phonon frequencies, normal and superconducting gaps, impurity scattering rate, and the electron-phonon coupling from the tunnelling data.Comment: 10 pages, 2 figure
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