Global Action-Angle Variables for Non-Commutative Integrable Systems

In this paper we analyze the obstructions to the existence of global action-angle variables for regular non-commutative integrable systems (NCI systems) on Poisson manifolds. In contrast with local action-angle variables, which exist as soon as the fibers of the momentum map of such an integrable system are compact, global action-angle variables rarely exist. This fact was first observed and analyzed by Duistermaat in the case of Liouville integrable systems on symplectic manifolds and later by Dazord-Delzant in the case of non-commutative integrable systems on symplectic manifolds. In our more general case where phase space is an arbitrary Poisson manifold, there are more obstructions, as we will show both abstractly and on concrete examples. Our approach makes use of a few new features which we introduce: the action bundle and the action lattice bundle of the NCI system (these bundles are canonically defined) and three foliations (the action, angle and transverse foliation), whose existence is also subject to obstructions, often of a cohomological nature

ICP-MS Measurement of 11B/10B Isotope Ratios in Grapevine Leaves and the Investigation of Possible Boron Isotope Fractionation in Grapevine Plants

The correlation between the 11B/10B ratio in grapevine leaves and that in the growth medium was establishedin a series of hydroponic experiments with grapevine cuttings for different cultivar/rootstocks combinations.The hydroponic growth medium was alternately spiked with boric acid containing B with natural isotopecomposition and B enriched in 10B, so as to vary the 11B/10B ratio. B isotope ratios in grapevine leaves weredetermined by quadrupole-based ICP-MS after digestion and complete matrix removal through microwavedigestion and isolation of matrix-free B species using ion exchange separation. It was found that the B isotoperatios in the leaves were not identical to those in the growth medium, but that a change in the ratio in the growthmedium induced a similar change in the leaves. For a particular cultivar/rootstock combination, a characteristicB isotope ratio was found that was different from the ratio in a group of plants with a different cultivar/rootstockcombination

Strong-coupling effects in the relaxation dynamics of ultracold neutral plasmas

We describe a hybrid molecular dynamics approach for the description of ultracold neutral plasmas, based on an adiabatic treatment of the electron gas and a full molecular dynamics simulation of the ions, which allows us to follow the long-time evolution of the plasma including the effect of the strongly coupled ion motion. The plasma shows a rather complex relaxation behavior, connected with temporal as well as spatial oscillations of the ion temperature. Furthermore, additional laser cooling of the ions during the plasma evolution drastically modifies the expansion dynamics, so that crystallization of the ion component can occur in this nonequilibrium system, leading to lattice-like structures or even long-range order resulting in concentric shells

Towards magnetic slowing of atoms and molecules

We outline a method to slow paramagnetic atoms or molecules using pulsed magnetic fields. We also discuss the possibility of producing trapped particles by adiabatic deceleration of a magnetic trap. We present numerical simulation results for the slowing and trapping of molecular oxygen