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 $r^2$ 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 D1_1 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 $5S+5P_{1/2}$ 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 $1/R^3$-potentials allow for efficient photoassociation, stabilization is facilitated by the resonant spin-orbit coupling of the $0_u^+$ 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 $S(\nu) \propto \nu^{-0.25}$ 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