Superintegrability of rational Ruijsenaars-Schneider systems and their action-angle duals

We explain that the action-angle duality between the rational Ruijsenaars-Schneider and hyperbolic Sutherland systems implies immediately the maximal superintegrability of these many-body systems. We also present a new direct proof of the Darboux form of the reduced symplectic structure that arises in the `Ruijsenaars gauge' of the symplectic reduction underlying this case of action-angle duality. The same arguments apply to the BC(n) generalization of the pertinent dual pair, which was recently studied by Pusztai developing a method utilized in our direct calculation of the reduced symplectic structure.Comment: Extended version of talk at the conference "Geometry, Integrability and Quantization XIV" (Varna, June 2012), 15 page

Generalized NLS Hierarchies from Rational WW Algebras

Finite rational \cw algebras are very natural structures appearing in coset constructions when a Kac-Moody subalgebra is factored out. In this letter we address the problem of relating these algebras to integrable hierarchies of equations, by showing how to associate to a rational \cw algebra its corresponding hierarchy. We work out two examples: the $sl(2)/U(1)$ coset, leading to the Non-Linear Schr\"{o}dinger hierarchy, and the $U(1)$ coset of the Polyakov-Bershadsky \cw algebra, leading to a $3$-field representation of the KP hierarchy already encountered in the literature. In such examples a rational algebra appears as algebra of constraints when reducing a KP hierarchy to a finite field representation. This fact arises the natural question whether rational algebras are always associated to such reductions and whether a classification of rational algebras can lead to a classification of the integrable hierarchies.Comment: 12 pages, latex, preprint ENSLAPP-L-448/9

Estudio de la influencia de los rasgos y el individualismo en la satisfacción vital entre naciones: un modelo multinivel

The current cross-cultural study explored the associations between relationship enhancing traits (interpersonal trust, importance of close relationships, sociability), characteristics corresponding to an individualistic attitude (competition, autonomy), and life satisfaction. Data for this study was from 24 of the 59 countries used in the World Values Survey Wave 6. Multilevel modelling was used as a means to analyse the influence of individual level (Level 1) and country level (Level 2) variables on life satisfaction. Results indicated that the individual level predictors interpersonal trust and importance of close relationships made meaningful positive contributions to life satisfaction. The competition variable aggregated at the country level significantly negatively predicted life satisfaction, while country-level aggregated autonomy shared a positive relationship with life satisfaction

Undirectional calcium and nucleotide fluxes in cardiac sarcoplasmic reticulum. II. Experimental results

Unidirectional calcium influx and efflux were evaluated in cardiac sarcoplasmic reticulum (SR) by 45Ca- 0Ca exchange at steady state calcium uptake in the absence of calcium precipitating anions. Calcium efflux was partitioned into a pump-mediated efflux and a parallel passive efflux by separately measuring passive efflux referable to the steady state. Unidirectional and net ATP-ADP fluxes were measured using [3H]-ATP -- ADP and [3H]- ADP -- ATP exchanges. Methods are presented that take into account changing specific activities and sizes of the nucleotide pools during the measurement of nucleotide fluxes. The contribution of competent and incompetent vesicles to the unidirectional and net nucleotide fluxes was evaluated from the specific activity of these fluxes in incompetent vesicles and from the fraction of vesicles that were incompetent. The results indicate that, in cardiac SR, unidirectional calcium fluxes are larger than the unidirectional nucleotide fluxes contributed by competent vesicles. Because the net ATPase rate of competent vesicles is similar to the parallel passive efflux, it appears that cardiac SR Ca-ATPase tightly couples ATP hydrolysis to calcium transport even at static head, with a coupling ratio near 1.0

Remarks on Finite W Algebras

The property of some finite W algebras to be the commutant of a particular subalgebra of a simple Lie algebra G is used to construct realizations of G. When G=so(4,2), unitary representations of the conformal and Poincare algebras are recognized in this approach, which can be compared to the usual induced representation technique. When G=sp(2,R) or sp(4,R), the anyonic parameter can be seen as the eigenvalue of a W generator in such W representations of G. The generalization of such properties to the affine case is also discussed in the conclusion, where an alternative of the Wakimoto construction for sl(2) level k is briefly presented. This mini review is based on invited talks presented by P. Sorba at the ``Vth International Colloquium on Quantum Groups and Integrable Systems'', Prague (Czech Republic), June 1996; ``Extended and Quantum Algebras and their Applications to Physics'', Tianjin (China), August 1996; ``Selected Topics of Theoretical and Modern Mathematical Physics'', Tbilisi (Georgia), September 1996; to be published in the Proceedings.Comment: LaTeX, 16 pages, references adde

Magnetic fullerenes inside single-wall carbon nanotubes

C59N magnetic fullerenes were formed inside single-wall carbon nanotubes by vacuum annealing functionalized C59N molecules encapsulated inside the tubes. A hindered, anisotropic rotation of C59N was deduced from the temperature dependence of the electron spin resonance spectra near room temperature. Shortening of spin-lattice relaxation time, T_1, of C59N indicates a reversible charge transfer toward the host nanotubes above $\sim 350$ K. Bound C59N-C60 heterodimers are formed at lower temperatures when C60 is co-encapsulated with the functionalized C59N. In the 10-300 K range, T_1 of the heterodimer shows a relaxation dominated by the conduction electrons on the nanotubes

Finite W Algebras and Intermediate Statistics

New realizations of finite W algebras are constructed by relaxing the usual constraint conditions. Then, finite W algebras are recognized in the Heisenberg quantization recently proposed by Leinaas and Myrheim, for a system of two identical particles in d dimensions. As the anyonic parameter is directly associated to the W-algebra involved in the d=1 case, it is natural to consider that the W-algebra framework is well-adapted for a possible generalization of the anyon statistics.Comment: 16 pp., Latex, Preprint ENSLAPP-489/9

Cu NMR evidence for enhanced antiferromagnetic correlations around Zn impurities in YBa2Cu3O6.7

Doping the high-Tc superconductor YBa2Cu3O6.7 with 1.5 % of non-magnetic Zn impurities in CuO2 planes is shown to produce a considerable broadening of 63Cu NMR spectra, as well as an increase of low-energy magnetic fluctuations detected in 63Cu spin-lattice relaxation measurements. A model-independent analysis demonstrates that these effects are due to the development of staggered magnetic moments on many Cu sites around each Zn and that the Zn-induced moment in the bulk susceptibility might be explained by this staggered magnetization. Several implications of these enhanced antiferromagnetic correlations are discussed.Comment: 4 pages including 2 figure

Optical Detection of a Single Nuclear Spin

We propose a method to optically detect the spin state of a 31-P nucleus embedded in a 28-Si matrix. The nuclear-electron hyperfine splitting of the 31-P neutral-donor ground state can be resolved via a direct frequency discrimination measurement of the 31-P bound exciton photoluminescence using single photon detectors. The measurement time is expected to be shorter than the lifetime of the nuclear spin at 4 K and 10 T.Comment: 4 pages, 3 figure