459 research outputs found
Contact orderability up to conjugation
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
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
In this paper, we obtain the following generalisation of isometric
-immersion theorem of Nash and Kuiper. Let be a smooth manifold of
dimension and a rank subbundle of the tangent bundle with a
Riemannian metric . Then the pair defines a sub-Riemannian
structure on . We call a -map into a Riemannian
manifold a {\em partial isometry} if the derivative map restricted
to is isometric; in other words, . The main result states that
if then a smooth -immersion satisfying
can be homotoped to a partial isometry which is
-close to . In particular we prove that every sub-Riemannian manifold
admits a partial isometry in provided .Comment: 13 pages. This is a revised version of an earlier submission (minor
revision
Compactness results in Symplectic Field Theory
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
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 CeRhSi and CeIrSi
We study the normal and the superconducting properties in noncentrosymmetric
heavy fermion superconductors CeRhSi and CeIrSi. 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
, 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 , 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
and is explained in terms of
the spin-orbit interaction. Furthermore, a possible realization of the
Fulde-Ferrell- Larkin-Ovchinnikov state for 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 CeRhSi and CeIrSi 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
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
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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