Hydration of Kr(aq) in dilute and concentrated solutions

Molecular dynamics simulations of water with both multi-Kr and single Kr atomic solutes are carried out to implement quasi-chemical theory evaluation of the hydration free energy of Kr(aq). This approach obtains free energy differences reflecting Kr-Kr interactions at higher concentrations. Those differences are negative changes in hydration free energies with increasing concentrations at constant pressure. The changes are due to a slight reduction of packing contributions in the higher concentration case. The observed Kr-Kr distributions, analyzed with the extrapolation procedure of Kr\"{u}ger, \emph{et al.}, yield a modestly attractive osmotic second virial coefficient, $B_2\approx -60~\mathrm{cm}^3$/mol. The thermodynamic analysis interconnecting these two approaches shows that they are closely consistent with each other, providing support for both.Comment: 6 pages, 7 figures. Revision follows the extrapolation procedure of Refs. 33 and 34 which works nicely. The thermodynamic results are now clearly consistent. The $k \rightarrow 0$ extrapolation of the Fourier transform was not was satisfactor

Rigidity of escaping dynamics for transcendental entire functions

We prove an analog of Boettcher's theorem for transcendental entire functions in the Eremenko-Lyubich class B. More precisely, let f and g be entire functions with bounded sets of singular values and suppose that f and g belong to the same parameter space (i.e., are *quasiconformally equivalent* in the sense of Eremenko and Lyubich). Then f and g are conjugate when restricted to the set of points which remain in some sufficiently small neighborhood of infinity under iteration. Furthermore, this conjugacy extends to a quasiconformal self-map of the plane. We also prove that this conjugacy is essentially unique. In particular, we show that an Eremenko-Lyubich class function f has no invariant line fields on its escaping set. Finally, we show that any two hyperbolic Eremenko-Lyubich class functions f and g which belong to the same parameter space are conjugate on their sets of escaping points.Comment: 28 pages; 2 figures. Final version (October 2008). Various modificiations were made, including the introduction of Proposition 3.6, which was not formally stated previously, and the inclusion of a new figure. No major changes otherwis

Internal-state thermometry by depletion spectroscopy in a cold guided beam of formaldehyde

We present measurements of the internal state distribution of electrostatically guided formaldehyde. Upon excitation with continuous tunable ultraviolet laser light the molecules dissociate, leading to a decrease in the molecular flux. The population of individual guided states is measured by addressing transitions originating from them. The measured populations of selected states show good agreement with theoretical calculations for different temperatures of the molecule source. The purity of the guided beam as deduced from the entropy of the guided sample using a source temperature of 150K corresponds to that of a thermal ensemble with a temperature of about 30 K

Lossless State Detection of Single Neutral Atoms

We introduce lossless state detection of trapped neutral atoms based on cavity-enhanced fluorescence. In an experiment with a single 87-Rb atom, a hyperfine-state-detection fidelity of 99.4% is achieved in 85 microseconds. The quantum bit is interrogated many hundreds of times without loss of the atom while a result is obtained in every readout attempt. The fidelity proves robust against atomic frequency shifts induced by the trapping potential. Our scheme does not require strong coupling between the atom and cavity and can be generalized to other systems with an optically accessible quantum bit.Comment: 4 pages, 4 figure

Hyperbolic entire functions and the Eremenko–Lyubich class: Class B or not class B?

Hyperbolicity plays an important role in the study of dynamical systems, and is a key concept in the iteration of rational functions of one complex variable. Hyperbolic systems have also been considered in the study of transcendental entire functions. There does not appear to be an agreed definition of the concept in this context, due to complications arising from the non-compactness of the phase space. In this article, we consider a natural definition of hyperbolicity that requires expanding properties on the preimage of a punctured neighbourhood of the isolated singularity. We show that this definition is equivalent to another commonly used one: a transcendental entire function is hyperbolic if and only if its postsingular set is a compact subset of the Fatou set. This leads us to propose that this notion should be used as the general definition of hyperbolicity in the context of entire functions, and, in particular, that speaking about hyperbolicity makes sense only within the Eremenko–Lyubich classB of transcendental entire functions with a bounded set of singular values. We also considerably strengthen a recent characterisation of the class B, by showing that functions outside of this class cannot be expanding with respect to a metric whose density decays at most polynomially. In particular, this implies that no transcendental entire function can be expanding with respect to the spherical metric. Finally we give a characterisation of an analogous class of functions analytic in a hyperbolic domain

Cold guided beams of water isotopologs

Electrostatic velocity filtering and guiding is an established technique to produce high fluxes of cold polar molecules. In this paper we clarify different aspects of this technique by comparing experiments to detailed calculations. In the experiment, we produce cold guided beams of the three water isotopologs H2O, D2O and HDO. Their different rotational constants and orientations of electric dipole moments lead to remarkably different Stark shift properties, despite the molecules being very similar in a chemical sense. Therefore, the signals of the guided water isotopologs differ on an absolute scale and also exhibit characteristic electrode voltage dependencies. We find excellent agreement between the relative guided fractions and voltage dependencies of the investigated isotopologs and predictions made by our theoretical model of electrostatic velocity filtering.Comment: 14 pages, 13 figures; small changes to the text, updated reference