Implementation of screened hybrid functionals based on the Yukawa potential within the LAPW basis set

The implementation of screened hybrid functionals into the WIEN2k code, which is based on the LAPW basis set, is reported. The Hartree-Fock exchange energy and potential are screened by means of the Yukawa potential as proposed by Bylander and Kleinman [Phys. Rev. B 41, 7868 (1990)] for the calculation of the electronic structure of solids with the screened-exchange local density approximation. Details of the formalism, which is based on the method of Massidda, Posternak, and Baldereschi [Phys. Rev. B 48, 5058 (1993)] for the unscreened Hartree-Fock exchange are given. The results for the transition-energy and structural properties of several test cases are presented. Results of calculations of the Cu electric-field gradient in Cu2O are also presented, and it is shown that the hybrid functionals are much more accurate than the standard local-density or generalized gradient approximations

Velocity Dispersions of CNOC Clusters and the Evolution of the Cluster Abundance

We present the results of the analysis of the internal velocity dispersions, \sigma_v, for the CNOC sample of distant galaxy clusters, based on an interlopers removal algorithm, which is different from that originally applied by Carlberg et al. (1996, C96). We find that the resulting \sigma_v values are consistent within <10% with the original C96 estimates. This result points in favor of a substantial robustness of currently applied methods for optical studies of the internal cluster dynamics. The resulting distribution of velocity dispersions is used to trace the redshift evolution of the cluster abundance with the aim of constraining the matter density parameter, \Omega_m. We find that constraints on \Omega_m are very sensitive to the adopted value of \sigma_8, as obtainable from the local cluster abundance: as \sigma_8 varies from 0.5 to 0.6 (for Omega_m=1), the best fitting Omega_m varies in the range 0.3-1.0.Comment: 11 pages, 8 figures, 1 table, LateX, uses apj.sty, ApJ, corrected some typo

Pole structure of the Hamiltonian ζ\zeta-function for a singular potential

We study the pole structure of the $\zeta$-function associated to the Hamiltonian $H$ of a quantum mechanical particle living in the half-line $\mathbf{R}^+$, subject to the singular potential $g x^{-2}+x^2$. We show that $H$ admits nontrivial self-adjoint extensions (SAE) in a given range of values of the parameter $g$. The $\zeta$-functions of these operators present poles which depend on $g$ and, in general, do not coincide with half an integer (they can even be irrational). The corresponding residues depend on the SAE considered.Comment: 12 pages, 1 figure, RevTeX. References added. Version to appear in Jour. Phys. A: Math. Ge

BCS-BEC crossover at finite temperature in the broken-symmetry phase

The BCS-BEC crossover is studied in a systematic way in the broken-symmetry phase between zero temperature and the critical temperature. This study bridges two regimes where quantum and thermal fluctuations are, respectively, important. The theory is implemented on physical grounds, by adopting a fermionic self-energy in the broken-symmetry phase that represents fermions coupled to superconducting fluctuations in weak coupling and to bosons described by the Bogoliubov theory in strong coupling. This extension of the theory beyond mean field proves important at finite temperature, to connect with the results in the normal phase. The order parameter, the chemical potential, and the single-particle spectral function are calculated numerically for a wide range of coupling and temperature. This enables us to assess the quantitative importance of superconducting fluctuations in the broken-symmetry phase over the whole BCS-BEC crossover. Our results are relevant to the possible realizations of this crossover with high-temperature cuprate superconductors and with ultracold fermionic atoms in a trap.Comment: 21 pages, 15 figure

Correlation effects in MgO and CaO: Cohesive energies and lattice constants

A recently proposed computational scheme based on local increments has been applied to the calculation of correlation contributions to the cohesive energy of the CaO crystal. Using ab-initio quantum chemical methods for evaluating individual increments, we obtain 80% of the difference between the experimental and Hartree-Fock cohesive energies. Lattice constants corrected for correlation effects deviate by less than 1% from experimental values, in the case of MgO and CaO.Comment: LaTeX, 4 figure

Observational Mass-to-Light Ratio of Galaxy Systems: from Poor Groups to Rich Clusters

We study the mass-to-light ratio of galaxy systems from poor groups to rich clusters, and present for the first time a large database for useful comparisons with theoretical predictions. We extend a previous work, where B_j band luminosities and optical virial masses were analyzed for a sample of 89 clusters. Here we also consider a sample of 52 more clusters, 36 poor clusters, 7 rich groups, and two catalogs, of about 500 groups each, recently identified in the Nearby Optical Galaxy sample by using two different algorithms. We obtain the blue luminosity and virial mass for all systems considered. We devote a large effort to establishing the homogeneity of the resulting values, as well as to considering comparable physical regions, i.e. those included within the virial radius. By analyzing a fiducial, combined sample of 294 systems we find that the mass increases faster than the luminosity: the linear fit gives M\propto L_B^{1.34 \pm 0.03}, with a tendency for a steeper increase in the low--mass range. In agreement with the previous work, our present results are superior owing to the much higher statistical significance and the wider dynamical range covered (about 10^{12}-10^{15} M_solar). We present a comparison between our results and the theoretical predictions on the relation between M/L_B and halo mass, obtained by combining cosmological numerical simulations and semianalytic modeling of galaxy formation.Comment: 25 pages, 12 eps figures, accepted for publication in Ap

Muonium as a hydrogen analogue in silicon and germanium; quantum effects and hyperfine parameters

We report a first-principles theoretical study of hyperfine interactions, zero-point effects and defect energetics of muonium and hydrogen impurities in silicon and germanium. The spin-polarized density functional method is used, with the crystalline orbitals expanded in all-electron Gaussian basis sets. The behaviour of hydrogen and muonium impurities at both the tetrahedral and bond-centred sites is investigated within a supercell approximation. To describe the zero-point motion of the impurities, a double adiabatic approximation is employed in which the electron, muon/proton and host lattice degrees of freedom are decoupled. Within this approximation the relaxation of the atoms of the host lattice may differ for the muon and proton, although in practice the difference is found to be slight. With the inclusion of zero-point motion the tetrahedral site is energetically preferred over the bond-centred site in both silicon and germanium. The hyperfine and superhyperfine parameters, calculated as averages over the motion of the muon, agree reasonably well with the available data from muon spin resonance experiments.Comment: 20 pages, including 9 figures. To appear in Phys. Rev.

The Dynamics of Poor Systems of Galaxies

We assemble and observe a sample of poor galaxy systems that is suitable for testing N-body simulations of hierarchical clustering (Navarro, Frenk, & White 1997; NFW) and other dynamical halo models (e.g., Hernquist 1990). We (1) determine the parameters of the density profile rho(r) and the velocity dispersion profile sigma(R), (2) separate emission-line galaxies from absorption-line galaxies, examining the model parameters and as a function of spectroscopic type, and (3) for the best-behaved subsample, constrain the velocity anisotropy parameter, beta, which determines the shapes of the galaxy orbits. The NFW universal profile and the Hernquist (1990) model both provide good descriptions of the spatial data. In most cases an isothermal sphere is ruled out. Systems with declining sigma(R) are well-matched by theoretical profiles in which the star-forming galaxies have predominantly radial orbits (beta > 0); many of these galaxies are probably falling in for the first time. There is significant evidence for spatial segregation of the spectroscopic classes regardless of sigma(R).Comment: 36 pages, 20 figures, and 5 tables. To appear in the Astrophysical Journa

Ground-state properties of rutile: electron-correlation effects

Electron-correlation effects on cohesive energy, lattice constant and bulk compressibility of rutile are calculated using an ab-initio scheme. A competition between the two groups of partially covalent Ti-O bonds is the reason that the correlation energy does not change linearly with deviations from the equilibrium geometry, but is dominated by quadratic terms instead. As a consequence, the Hartree-Fock lattice constants are close to the experimental ones, while the compressibility is strongly renormalized by electronic correlations.Comment: 1 figure to appear in Phys. Rev.