2,428 research outputs found
The family of quaternionic quasi-unitary Lie algebras and their central extensions
The family of quaternionic quasi-unitary (or quaternionic unitary
Cayley--Klein algebras) is described in a unified setting. This family includes
the simple algebras sp(N+1) and sp(p,q) in the Cartan series C_{N+1}, as well
as many non-semisimple real Lie algebras which can be obtained from these
simple algebras by particular contractions. The algebras in this family are
realized here in relation with the groups of isometries of quaternionic
hermitian spaces of constant holomorphic curvature. This common framework
allows to perform the study of many properties for all these Lie algebras
simultaneously. In this paper the central extensions for all quasi-simple Lie
algebras of the quaternionic unitary Cayley--Klein family are completely
determined in arbitrary dimension. It is shown that the second cohomology group
is trivial for any Lie algebra of this family no matter of its dimension.Comment: 17 pages, LaTe
Central extensions of the families of quasi-unitary Lie algebras
The most general possible central extensions of two whole families of Lie
algebras, which can be obtained by contracting the special pseudo-unitary
algebras su(p,q) of the Cartan series A_l and the pseudo-unitary algebras
u(p,q), are completely determined and classified for arbitrary p,q. In addition
to the su(p,q) and u({p,q}) algebras, whose second cohomology group is well
known to be trivial, each family includes many non-semisimple algebras; their
central extensions, which are explicitly given, can be classified into three
types as far as their properties under contraction are involved. A closed
expression for the dimension of the second cohomology group of any member of
these families of algebras is given.Comment: 23 pages. Latex2e fil
Superintegrability on sl(2)-coalgebra spaces
We review a recently introduced set of N-dimensional quasi-maximally
superintegrable Hamiltonian systems describing geodesic motions, that can be
used to generate "dynamically" a large family of curved spaces. From an
algebraic viewpoint, such spaces are obtained through kinetic energy
Hamiltonians defined on either the sl(2) Poisson coalgebra or a quantum
deformation of it. Certain potentials on these spaces and endowed with the same
underlying coalgebra symmetry have been also introduced in such a way that the
superintegrability properties of the full system are preserved. Several new N=2
examples of this construction are explicitly given, and specific Hamiltonians
leading to spaces of non-constant curvature are emphasized.Comment: 12 pages. Based on the contribution presented at the "XII
International Conference on Symmetry Methods in Physics", Yerevan (Armenia),
July 2006. To appear in Physics of Atomic Nucle
Superintegrability on N-dimensional spaces of constant curvature from so(N+1) and its contractions
The Lie-Poisson algebra so(N+1) and some of its contractions are used to
construct a family of superintegrable Hamiltonians on the ND spherical,
Euclidean, hyperbolic, Minkowskian and (anti-)de Sitter spaces. We firstly
present a Hamiltonian which is a superposition of an arbitrary central
potential with N arbitrary centrifugal terms. Such a system is quasi-maximally
superintegrable since this is endowed with 2N-3 functionally independent
constants of the motion (plus the Hamiltonian). Secondly, we identify two
maximally superintegrable Hamiltonians by choosing a specific central potential
and finding at the same time the remaining integral. The former is the
generalization of the Smorodinsky-Winternitz system to the above six spaces,
while the latter is a generalization of the Kepler-Coulomb potential, for which
the Laplace-Runge-Lenz N-vector is also given. All the systems and constants of
the motion are explicitly expressed in a unified form in terms of ambient and
polar coordinates as they are parametrized by two contraction parameters
(curvature and signature of the metric).Comment: 14 pages. Based on the contribution presented at the "XII
International Conference on Symmetry Methods in Physics", Yerevan (Armenia),
July 2006. To appear in Physics of Atomic Nucle
Integrable potentials on spaces with curvature from quantum groups
A family of classical integrable systems defined on a deformation of the
two-dimensional sphere, hyperbolic and (anti-)de Sitter spaces is constructed
through Hamiltonians defined on the non-standard quantum deformation of a sl(2)
Poisson coalgebra. All these spaces have a non-constant curvature that depends
on the deformation parameter z. As particular cases, the analogues of the
harmonic oscillator and Kepler--Coulomb potentials on such spaces are proposed.
Another deformed Hamiltonian is also shown to provide superintegrable systems
on the usual sphere, hyperbolic and (anti-)de Sitter spaces with a constant
curvature that exactly coincides with z. According to each specific space, the
resulting potential is interpreted as the superposition of a central harmonic
oscillator with either two more oscillators or centrifugal barriers. The
non-deformed limit z=0 of all these Hamiltonians can then be regarded as the
zero-curvature limit (contraction) which leads to the corresponding
(super)integrable systems on the flat Euclidean and Minkowskian spaces.Comment: 19 pages, 1 figure. Two references adde
Real-space study of the growth of magnesium on ruthenium
The growth of magnesium on ruthenium has been studied by low-energy electron
microscopy (LEEM) and scanning tunneling microscopy (STM). In LEEM, a
layer-by-layer growth is observed except in the first monolayer, where the
completion of the first layer in inferred by a clear peak in electron
reflectivity. Desorption from the films is readily observable at 400 K.
Real-space STM and low-energy electron diffraction confirm that sub-monolayer
coverage presents a moir\'e pattern with a 1.2 nm periodicity, which evolves
with further Mg deposition by compressing the Mg layer to a 2.2 nm periodicity.
Layer-by-layer growth is followed in LEEM up to 10 ML. On films several ML
thick a substantial density of stacking faults are observed by dark-field
imaging on large terraces of the substrate, while screw dislocations appear in
the stepped areas. The latter are suggested to result from the mismatch in
heights of the Mg and Ru steps. Quantum size effect oscillations in the
reflected LEEM intensity are observed as a function of thickness, indicating an
abrupt Mg/Ru interface.Comment: 21 pages, 10 figure
Maximal superintegrability on N-dimensional curved spaces
A unified algebraic construction of the classical Smorodinsky-Winternitz
systems on the ND sphere, Euclidean and hyperbolic spaces through the Lie
groups SO(N+1), ISO(N), and SO(N,1) is presented. Firstly, general expressions
for the Hamiltonian and its integrals of motion are given in a linear ambient
space , and secondly they are expressed in terms of two geodesic
coordinate systems on the ND spaces themselves, with an explicit dependence on
the curvature as a parameter. On the sphere, the potential is interpreted as a
superposition of N+1 oscillators. Furthermore each Lie algebra generator
provides an integral of motion and a set of 2N-1 functionally independent ones
are explicitly given. In this way the maximal superintegrability of the ND
Euclidean Smorodinsky-Winternitz system is shown for any value of the
curvature.Comment: 8 pages, LaTe
Detection/estimation of the modulus of a vector. Application to point source detection in polarization data
Given a set of images, whose pixel values can be considered as the components
of a vector, it is interesting to estimate the modulus of such a vector in some
localised areas corresponding to a compact signal. For instance, the
detection/estimation of a polarized signal in compact sources immersed in a
background is relevant in some fields like astrophysics. We develop two
different techniques, one based on the Neyman-Pearson lemma, the Neyman-Pearson
filter (NPF), and another based on prefiltering-before-fusion, the filtered
fusion (FF), to deal with the problem of detection of the source and estimation
of the polarization given two or three images corresponding to the different
components of polarization (two for linear polarization, three including
circular polarization). For the case of linear polarization, we have performed
numerical simulations on two-dimensional patches to test these filters
following two different approaches (a blind and a non-blind detection),
considering extragalactic point sources immersed in cosmic microwave background
(CMB) and non-stationary noise with the conditions of the 70 GHz \emph{Planck}
channel. The FF outperforms the NPF, especially for low fluxes. We can detect
with the FF extragalactic sources in a high noise zone with fluxes >=
(0.42,0.36) Jy for (blind/non-blind) detection and in a low noise zone with
fluxes >= (0.22,0.18) Jy for (blind/non-blind) detection with low errors in the
estimated flux and position.Comment: 11 pages, 5 figure
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