Spectrum Generating Algebras for the free motion in S3S^3

We construct the spectrum generating algebra (SGA) for a free particle in the three dimensional sphere $S^3$ for both, classical and quantum descriptions. In the classical approach, the SGA supplies time-dependent constants of motion that allow to solve algebraically the motion. In the quantum case, the SGA include the ladder operators that give the eigenstates of the free Hamiltonian. We study this quantum case from two equivalent points of view.Comment: 29 pages, 1 figur

Coulomb-oscillator duality in spaces of constant curvature

In this paper we construct generalizations to spheres of the well known Levi-Civita, Kustaanheimo-Steifel and Hurwitz regularizing transformations in Euclidean spaces of dimensions 2, 3 and 5. The corresponding classical and quantum mechanical analogues of the Kepler-Coulomb problem on these spheres are discussed.Comment: 33 pages, LaTeX fil

Close binary stars in the solar-age Galactic open cluster M67

We present multi-colour time-series CCD photometry of the solar-age galactic open cluster M67 (NGC 2682). About 3600 frames spread over 28 nights were obtained with the 1.5 m Russian-Turkish and 1.2 m Mercator telescopes. High-precision observations of the close binary stars AH Cnc, EV Cnc, ES Cnc, the $\delta$ Scuti type systems EX Cnc and EW Cnc, and some long-period variables belonging to M67 are presented. Three full multi-colour light curves of the overcontact binary AH Cnc were obtained during three observing seasons. Likewise we gathered three light curves of EV Cnc, an EB-type binary, and two light curves of ES Cnc, a blue straggler binary. Parts of the light change of long-term variables S1024, S1040, S1045, S1063, S1242, and S1264 are obtained. Period variation analysis of AH Cnc, EV Cnc, and ES Cnc were done using all times of mid-eclipse available in the literature and those obtained in this study. In addition, we analyzed multi-colour light curves of the close binaries and also determined new frequencies for the $\delta$ Scuti systems. The physical parameters of the close binary stars were determined with simultaneous solutions of multi-colour light and radial velocity curves. Finally we determined the distance of M67 as 857(33) pc via binary star parameters, which is consistent with an independent method from earlier studies.Comment: 12 pages, 9 Figures, 13 Table

The Mass of the Compact Object in the X-Ray Binary Her X-1/HZ Her

We have obtained the first estimates of the masses of the components of the Her X-1/HZ Her X-ray binary system taking into account non-LTE effects in the formation of the H_gamma absorption line: mx=1.8Msun and mv=2.5Msun. These mass estimates were made in a Roche model based on the observed radial-velocity curve of the optical star, HZ Her. The masses for the X-ray pulsar and optical star obtained for an LTE model lie are mx=0.85\pm0.15Msun and mv=1.87\pm0.13Msun. These mass estimates for the components of Her X-1/HZ Her derived from the radial-velocity curve should be considered tentative. Further mass estimates from high-precision observations of the orbital variability of the absorption profiles in a non-LTE model for the atmosphere of the optical component should be made.Comment: 20 pages, 4 tables, 8 figure

Two-body quantum mechanical problem on spheres

The quantum mechanical two-body problem with a central interaction on the sphere ${\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.Comment: 41 pages, no figures, typos corrected; appendix D was adde

Two-Dimensional Spectroscopy of Extended Molecular Systems: Applications to Energy Transport and Relaxation in an α-Helix

A simulation study of the coupled dynamics of amide I and amide II vibrations in an α-helix dissolved in water shows that two-dimensional (2D) infrared spectroscopy may be used to disentangle the energy transport along the helix through each of these modes from the energy relaxation between them. Time scales for both types of processes are obtained. Using polarization-dependent 2D spectroscopy is an important ingredient in the method we propose. The method may also be applied to other two-band systems, both in the infrared (collective vibrations) and the visible (excitons) parts of the spectrum.

What are the hot R Coronae Borealis stars?

We investigate the evolutionary status of four stars: V348 Sgr, DY Cen, and MV Sgr in the Galaxy and HV 2671 in the LMC. These stars have in common random deep declines in visual brightness, which are characteristic of R Coronae Borealis (RCB) stars. RCB stars are typically cool hydrogen-deficient supergiants. The four stars studied in this paper are hotter (Teff = 15–20 kK) than the majority of RCB stars (Teff = 5000–7000 K). Although these are commonly grouped together as the hot RCB stars they do not necessarily share a common evolutionary history. We present new observational data and an extensive collection of archival and previously published data that is reassessed to ensure internal consistency. We find temporal variations of various properties on different timescales that will eventually help us to uncover the evolutionary history of these objects. DY Cen and MV Sgr have typical RCB helium abundances, which exclude any currently known post–asymptotic giant branch (post-AGB) evolutionary models. Moreover, their carbon and nitrogen abundances present us with further problems for their interpretation. V348 Sgr and HV 2671 are in general agreement with a born-again post-AGB evolution, and their abundances are similar to Wolf-Rayet central stars of planetary nebulae (PNs). The three Galactic stars in the sample have circumstellar nebulae, which produce forbidden line radiation (for HV 2671 we have no information). V348 Sgr and DY Cen have low-density, low-expansion velocity nebulae (resolved in the case of V348 Sgr), while MV Sgr has a higher density, higher expansion velocity nebula. All three stars, on the other hand, have split emission lines, which indicate the presence of an equatorial bulge but not of a Keplerian disk. In addition, the historical light curves for the three Galactic hot RCB stars show evidence for a significant fading in their maximum-light brightnesses of ~1 mag over the last 70 yr. From this we deduce that their effective temperatures increased by a few thousand degrees. If V348 Sgr is a born-again star, as we presume, this means that the star is returning from the born-again AGB phase to the phase of a central star of PN. Spectroscopically, no dramatic change is observed over the last 50 years for V348 Sgr and MV Sgr. However, there is some evidence that the winds of V348 Sgr and DY Cen have increased in strength in the last decade. HV 2671, located in the LMC, has not been analyzed in detail but at 5 Å… resolution is almost identical to V348 Sgr. Through the bolometric correction derived for V348 Sgr and the known distance, we can estimate the absolute ν magnitude of HV 2671 (Mν = -3.0 mag) and its bolometric luminosity (~6000 L⊙)

Standalone vertex finding in the ATLAS muon spectrometer

A dedicated reconstruction algorithm to find decay vertices in the ATLAS muon spectrometer is presented. The algorithm searches the region just upstream of or inside the muon spectrometer volume for multi-particle vertices that originate from the decay of particles with long decay paths. The performance of the algorithm is evaluated using both a sample of simulated Higgs boson events, in which the Higgs boson decays to long-lived neutral particles that in turn decay to bbar b final states, and pp collision data at √s = 7 TeV collected with the ATLAS detector at the LHC during 2011