1,603 research outputs found
Rigid motions: action-angles, relative cohomology and polynomials with roots on the unit circle
Revisiting canonical integration of the classical solid near a uniform
rotation, canonical action angle coordinates, hyperbolic and elliptic, are
constructed in terms of various power series with coefficients which are
polynomials in a variable depending on the inertia moments. Normal forms
are derived via the analysis of a relative cohomology problem and shown to be
obtainable without the use of ellitptic integrals (unlike the derivation of the
action-angles). Results and conjectures also emerge about the properties of the
above polynomials and the location of their roots. In particular a class of
polynomials with all roots on the unit circle arises.Comment: 26 pages, 1 figur
Quadratic Algebra associated with Rational Calogero-Moser Models
Classical Calogero-Moser models with rational potential are known to be
superintegrable. That is, on top of the r involutive conserved quantities
necessary for the integrability of a system with r degrees of freedom, they
possess an additional set of r-1 algebraically and functionally independent
globally defined conserved quantities. At the quantum level, Kuznetsov
uncovered the existence of a quadratic algebra structure as an underlying key
for superintegrability for the models based on A type root systems. Here we
demonstrate in a universal way the quadratic algebra structure for quantum
rational Calogero-Moser models based on any root systems.Comment: 19 pages, LaTeX2e, no figure
Algebraic Linearization of Dynamics of Calogero Type for any Coxeter Group
Calogero-Moser systems can be generalized for any root system (including the
non-crystallographic cases). The algebraic linearization of the generalized
Calogero-Moser systems and of their quadratic (resp. quartic) perturbations are
discussed.Comment: LaTeX2e, 13 pages, no figure
The first derivative of the period function of a plane vector field
The algorithm of the successive derivatives introduced in \cite{5} was implemented in \cite{7}, \cite{8}. This algorithm is based on the existence of a decomposition of 1-forms associated to the relative cohomology of the Hamiltonian function which is perturbed. We explain here how the first step of this algorithm gives also the first derivative of the period function. This includes, for instance, new presentations of formulas obtained by Carmen Chicone and Marc Jacobs in \cite{3}
Short-pulse photoassociation in rubidium below the D line
Photoassociation of two ultracold rubidium atoms and the subsequent formation
of stable molecules in the singlet ground and lowest triplet states is
investigated theoretically. The method employs laser pulses inducing
transitions via excited states correlated to the asymptote.
Weakly bound molecules in the singlet ground or lowest triplet state can be
created by a single pulse while the formation of more deeply bound molecules
requires a two-color pump-dump scenario. More deeply bound molecules in the
singlet ground or lowest triplet state can be produced only if efficient
mechanisms for both pump and dump steps exist. While long-range
-potentials allow for efficient photoassociation, stabilization is
facilitated by the resonant spin-orbit coupling of the states.
Molecules in the singlet ground state bound by a few wavenumbers can thus be
formed. This provides a promising first step toward ground state molecules
which are ultracold in both translational and vibrational degrees of freedom
Algebraically linearizable dynamical systems
The main result of this paper is the evidence of an explicit linearization
of dynamical systems of Ruijsenaars-Schneider (RS) type and of the perturbations
introduced by F. Calogero of these systems with all orbits periodic
of same period. Several other systems share the existence of this explicit
linearization, among them, the Calogero-Moser system (with and without
external potential) and the Calogero-Sutherland system. This explicit linearization
is compared with the notion of maximal superintegrability which
has been discussed in several articles (to quote few of them, Hietarinta [12],
Henon [11], Harnad-Winternitz [10], S. Wojchiechowsky [15])
Astronomical Data Management
We present a summary of the major contributions to the Special Session on
Data Management held at the IAU General Assembly in Prague in 2006. While
recent years have seen enormous improvements in access to astronomical data,
and the Virtual Observatory aims to provide astronomers with seamless access to
on-line resources, more attention needs to be paid to ensuring the quality and
completeness of those resources. For example, data produced by telescopes are
not always made available to the astronomical community, and new instruments
are sometimes designed and built with insufficient planning for data
management, while older but valuable legacy data often remain undigitised. Data
and results published in journals do not always appear in the data centres, and
astronomers in developing countries sometimes have inadequate access to on-line
resources. To address these issues, an 'Astronomers Data Manifesto' has been
formulated with the aim of initiating a discussion that will lead to the
development of a 'code of best practice' in astronomical data management.Comment: Proceedings of Special Session SPS6 (Astronomical Data Management) at
the IAU GA 2006. To appear in Highlights of Astronomy, Volume 14, ed. K.A.
van der Huch
Stabilization of Ultracold Molecules Using Optimal Control Theory
In recent experiments on ultracold matter, molecules have been produced from
ultracold atoms by photoassociation, Feshbach resonances, and three-body
recombination. The created molecules are translationally cold, but
vibrationally highly excited. This will eventually lead them to be lost from
the trap due to collisions. We propose shaped laser pulses to transfer these
highly excited molecules to their ground vibrational level. Optimal control
theory is employed to find the light field that will carry out this task with
minimum intensity. We present results for the sodium dimer. The final target
can be reached to within 99% if the initial guess field is physically
motivated. We find that the optimal fields contain the transition frequencies
required by a good Franck-Condon pumping scheme. The analysis is able to
identify the ranges of intensity and pulse duration which are able to achieve
this task before other competing process take place. Such a scheme could
produce stable ultracold molecular samples or even stable molecular
Bose-Einstein condensates
Detection of water at z = 0.685 towards B0218+357
We report the detection of the H_2O molecule in absorption at a redshift z =
0.68466 in front of the gravitationally lensed quasar B0218+357. We detect the
fundamental transition of ortho-water at 556.93 GHz (redshifted to 330.59 GHz).
The line is highly optically thick and relatively wide (15 km/s FWHM), with a
profile that is similar to that of the previously detected CO(2--1) and
HCO^+(2--1) optically thick absorption lines toward this quasar. From the
measured level of the continuum at 330.59 GHz, which corresponds to the level
expected from the power-law spectrum already
observed at lower frequencies, we deduce that the filling factor of the H_2O
absorption is large. It was already known from the high optical thickness of
the CO, ^{13}CO and C^{18}O lines that the molecular clouds entirely cover one
of the two lensed images of the quasar (all its continuum is absorbed); our
present results indicate that the H_2O clouds are covering a comparable
surface. The H_2O molecules are therefore not confined to small cores with a
tiny filling factor, but are extended over parsec scales. The H_2O line has a
very large optical depth, and only isotopic lines could give us the water
abundance. We have also searched for the 183 GHz line in absorption, obtaining
only an upper limit; this yields constraints on the excitation temperature.Comment: 4 pages, 3 figures, accepted in ApJ Letter
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