Chemical evolution models with a new stellar nucleosynthesis

Numerical models for the chemical evolution of the Galaxy have been computed with the new stellar yields published by Maeder (1992). These metallicity dependent yields represent an important improvement in the chemical evolution of galaxies but there are still uncertainties in the stellar evolution which prevent completely satisfactory results. {}From the comparison of the model predictions with the corresponding observational constraints we find that Maeder's nucleosynthesis reproduces the oxygen and carbon abundances and provides consistent $\Delta$Y/$\Delta$(O/H) ratios if a significant amount of gas is accreted by the galactic disc during its whole lifetime. The lower mass limit for the black hole formation (M$_{bh}$) must be larger than 22.5 M$_{\odot}$ to avoid oxygen underproduction.Comment: 6 pages, MNRAS LaTex style, figures available on request from [email protected]

Time-Dependent Density-Functional Theory for Superfluids

A density-functional theory is established for inhomogeneous superfluids at finite temperature, subject to time-dependent external fields in isothermal conditions. After outlining parallelisms between a neutral superfluid and a charged superconductor, Hohenberg-Kohn-Sham-type theorems are proved for gauge-invariant densities and a set of Bogolubov-Popov equations including exchange and correlation is set up. Earlier results applying in the linear response regime are recovered.Comment: 12 pages. Europhysics Letters, in pres

Collective excitations of a periodic Bose condensate in the Wannier representation

We study the dispersion relation of the excitations of a dilute Bose-Einstein condensate confined in a periodic optical potential and its Bloch oscillations in an accelerated frame. The problem is reduced to one-dimensionality through a renormalization of the s-wave scattering length and the solution of the Bogolubov - de Gennes equations is formulated in terms of the appropriate Wannier functions. Some exact properties of a periodic one-dimensional condensate are easily demonstrated: (i) the lowest band at positive energy refers to phase modulations of the condensate and has a linear dispersion relation near the Brillouin zone centre; (ii) the higher bands arise from the superposition of localized excitations with definite phase relationships; and (iii) the wavenumber-dependent current under a constant force in the semiclassical transport regime vanishes at the zone boundaries. Early results by J. C. Slater [Phys. Rev. 87, 807 (1952)] on a soluble problem in electron energy bands are used to specify the conditions under which the Wannier functions may be approximated by on-site tight-binding orbitals of harmonic- oscillator form. In this approximation the connections between the low-lying excitations in a lattice and those in a harmonic well are easily visualized. Analytic results are obtained in the tight-binding scheme and are illustrated with simple numerical calculations for the dispersion relation and semiclassical transport in the lowest energy band, at values of the system parameters which are relevant to experiment.Comment: 20 pages, 2 figures, 22 reference