10,644 research outputs found
Multiple scattering of matter waves: an analytic model of the refractive index for atomic and molecular gases
We present an analytic model of the refractive index for matter waves
propagating through atomic or molecular gases. The model, which combines a WKB
treatment of the long range attraction with the Fraunhofer model treatment of
the short range repulsion, furnishes a refractive index in compelling agreement
with recent experiments of Jacquey et al. [Phys. Rev. Lett. 98, 240405 (2007)]
on Li atom matter waves passing through dilute noble gases. We show that the
diffractive contribution, which arises from scattering by a two dimensional
"hard core" of the potential, is essential for obtaining a correct imaginary
part of the refractive index.Comment: 5 pages, 1 figure, 2 table
On transversally elliptic operators and the quantization of manifolds with -structure
An -structure on a manifold is an endomorphism field
\phi\in\Gamma(M,\End(TM)) such that . Any -structure
determines an almost CR structure E_{1,0}\subset T_\C M given by the
-eigenbundle of . Using a compatible metric and connection
on , we construct an odd first-order differential operator ,
acting on sections of , whose principal symbol is of the
type considered in arXiv:0810.0338. In the special case of a CR-integrable
almost -structure, we show that when is the generalized
Tanaka-Webster connection of Lotta and Pastore, the operator is given by D
= \sqrt{2}(\dbbar+\dbbar^*), where \dbbar is the tangential Cauchy-Riemann
operator.
We then describe two "quantizations" of manifolds with -structure that
reduce to familiar methods in symplectic geometry in the case that is a
compatible almost complex structure, and to the contact quantization defined in
\cite{F4} when comes from a contact metric structure. The first is an
index-theoretic approach involving the operator ; for certain group actions
will be transversally elliptic, and using the results in arXiv:0810.0338,
we can give a Riemann-Roch type formula for its index. The second approach uses
an analogue of the polarized sections of a prequantum line bundle, with a CR
structure playing the role of a complex polarization.Comment: 31 page
Cyclic and ruled Lagrangian surfaces in complex Euclidean space
We study those Lagrangian surfaces in complex Euclidean space which are
foliated by circles or by straight lines. The former, which we call cyclic,
come in three types, each one being described by means of, respectively, a
planar curve, a Legendrian curve of the 3-sphere or a Legendrian curve of the
anti de Sitter 3-space. We also describe ruled Lagrangian surfaces. Finally we
characterize those cyclic and ruled Lagrangian surfaces which are solutions to
the self-similar equation of the Mean Curvature Flow. Finally, we give a
partial result in the case of Hamiltonian stationary cyclic surfaces
A Note on Doubly Warped Product Contact CR-Submanifolds in trans-Sasakian Manifolds
Warped product CR-submanifolds in Kaehlerian manifolds were intensively
studied only since 2001 after the impulse given by B.Y. Chen. Immediately
after, another line of research, similar to that concerning Sasakian geometry
as the odd dimensional version of Kaehlerian geometry, was developed, namely
warped product contact CR-submanifolds in Sasakian manifolds. In this note we
proved that there exists no proper doubly warped product contact
CR-submanifolds in trans-Sasakian manifolds.Comment: 5 Latex page
Hidden symmetries and Killing tensors on curved spaces
Higher order symmetries corresponding to Killing tensors are investigated.
The intimate relation between Killing-Yano tensors and non-standard
supersymmetries is pointed out. In the Dirac theory on curved spaces,
Killing-Yano tensors generate Dirac type operators involved in interesting
algebraic structures as dynamical algebras or even infinite dimensional
algebras or superalgebras. The general results are applied to space-times which
appear in modern studies. One presents the infinite dimensional superalgebra of
Dirac type operators on the 4-dimensional Euclidean Taub-NUT space that can be
seen as a twisted loop algebra. The existence of the conformal Killing-Yano
tensors is investigated for some spaces with mixed Sasakian structures.Comment: 12 pages; talk presented at Group 27 Colloquium, Yerevan, Armenia,
August 200
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