On a Generalized Oscillator: Invariance Algebra and Interbasis Expansions

This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D=2 and the coefficients connecting the Cartesian and cylindrical bases as well as the cylindrical and spherical bases for D=3. These interbasis expansion coefficients are found to be analytic continuations to real values of their arguments of the Clebsch-Gordan coefficients for the group SU(2). For D=2, the superintegrable character for the generalized oscillator system is investigated from the points of view of a quadratic invariance algebra.Comment: 13 pages, Latex file. Submitted for publication to Yadernaya Fizik

Superintegrability on the two dimensional hyperboloid II

This work is devoted to the investigation of the quantum mechanical systems on the two dimensional hyperboloid which admit separation of variables in at least two coordinate systems. Here we consider two potentials introduced in a paper of C.P.Boyer, E.G.Kalnins and P.Winternitz, which haven't yet been studied. We give an example of an interbasis expansion and work out the structure of the quadratic algebra generated by the integrals of motion.Comment: 18 pages, LaTex; 1 figure (eps

Searching for solar siblings among the HARPS data

The search for the solar siblings has been particularly fruitful in the last few years. Until now, there are four plausible candidates pointed out in the literature: HIP21158, HIP87382, HIP47399, and HIP92831. In this study we conduct a search for solar siblings among the HARPS high-resolution FGK dwarfs sample, which includes precise chemical abundances and kinematics for 1111 stars. Using a new approach based on chemical abundance trends with the condensation temperature, kinematics, and ages we found one (additional) potential solar sibling candidate: HIP97507.Comment: 4 pages, 2 figures, 1 table. Accepted in A&

From stellar to planetary composition: Galactic chemical evolution of Mg/Si mineralogical ratio

The main goal of this work is to study element ratios that are important for the formation of planets of different masses. We study potential correlations between the existence of planetary companions and the relative elemental abundances of their host stars. We use a large sample of FGK-type dwarf stars for which precise Mg, Si, and Fe abundances have been derived using HARPS high-resolution and high-quality data. A first analysis of the data suggests that low-mass planet host stars show higher [Mg/Si] ratios, while giant planet hosts present [Mg/Si] that is lower than field stars. However, we found that the [Mg/Si] ratio significantly depends on metallicity through Galactic chemical evolution. After removing the Galactic evolution trend only the difference in the [Mg/Si] elemental ratio between low-mass planet hosts and non-hosts was present in a significant way. These results suggests that low-mass planets are more prevalent around stars with high [Mg/Si]. Our results demonstrate the importance of Galactic chemical evolution and indicate that it may play an important role in the planetary internal structure and composition.Comment: Accepted by A&A (Letter to the Editor