Weakly-Interacting Bosons in a Trap within Approximate Second Quantization Approach

The theory of Bogoliubov is generalized for the case of a weakly-interacting Bose-gas in harmonic trap. A set of nonlinear matrix equations is obtained to make the diagonalization of Hamiltonian possible. Its perturbative solution is used for the calculation of the energy and the condensate fraction of the model system to show the applicability of the method.Comment: 6 pages, two figures .Presented at the International Symposium on Quantum Fluids and Solids QFS2006 (Kyoto, Japan

Spin-wave spectrum in La2CuO4 -- double occupancy and competing interaction effects

The recently observed spin-wave energy dispersion along the AF zone boundary in La2CuO4 is discussed in terms of double occupancy and competing interaction effects in the $t-t'$ Hubbard model on a square lattice.Comment: 4 pages, 2 figure

Finite temperature scaling theory for the collapse of Bose-Einstein condensate

We show how to apply the scaling theory in an inhomogeneous system like harmonically trapped Bose condensate at finite temperatures. We calculate the temperature dependence of the critical number of particles by a scaling theory within the Hartree-Fock approximation and find that there is a dramatic increase in the critical number of particles as the condensation point is approached.Comment: Published online [6 pages, 3 figures

Effective Actions and Phase Fluctuations in d-wave Superconductors

We study effective actions for order parameter fluctuations at low temperature in layered d-wave superconductors such as the cuprates. The order parameter lives on the bonds of a square lattice and has two amplitude and two phase modes associated with it. The low frequency spectral weights for amplitude and relative phase fluctuations is determined and found to be subdominant to quasiparticle contributions. The Goldstone phase mode and its coupling to density fluctuations in charged systems is treated in a gauge-invariant manner. The Gaussian phase action is used to study both the $c$-axis Josephson plasmon and the more conventional in-plane plasmon in the cuprates. We go beyond the Gaussian theory by deriving a coarse-grained quantum XY model, which incorporates important cutoff effects overlooked in previous studies. A variational analysis of this effective model shows that in the cuprates, quantum effects of phase fluctuations are important in reducing the zero temperature superfluid stiffness, but thermal effects are small for $T << T_c$.Comment: Some numerical estimates corrected and figures changed. to appear in PRB, Sept.1 (2000

E1 amplitudes, lifetimes, and polarizabilities of the low-lying levels of atomic ytterbium

The results of ab initio calculation of E1 amplitudes, lifetimes,and polarizabilities for several low-lying levels of ytterbium are reported. The effective Hamiltonian for the valence electrons has been constructed in the frame of CI+MBPT method and solutions of many electron equation are found.Comment: 11 pages, submitted to Phys.Rev.

Natural Orbitals and BEC in traps, a diffusion Monte Carlo analysis

We investigate the properties of hard core Bosons in harmonic traps over a wide range of densities. Bose-Einstein condensation is formulated using the one-body Density Matrix (OBDM) which is equally valid at low and high densities. The OBDM is calculated using diffusion Monte Carlo methods and it is diagonalized to obtain the "natural" single particle orbitals and their occupation, including the condensate fraction. At low Boson density, $na^3 < 10^{-5}$, where $n = N/V$ and $a$ is the hard core diameter, the condensate is localized at the center of the trap. As $na^3$ increases, the condensate moves to the edges of the trap. At high density it is localized at the edges of the trap. At $na^3 \leq 10^{-4}$ the Gross-Pitaevskii theory of the condensate describes the whole system within 1%. At $na^3 \approx 10^{-3}$ corrections are 3% to the GP energy but 30% to the Bogoliubov prediction of the condensate depletion. At $na^3 \gtrsim 10^{-2}$, mean field theory fails. At $na^3 \gtrsim 0.1$, the Bosons behave more like a liquid $^4$He droplet than a trapped Boson gas.Comment: 13 pages, 14 figures, submitted Phys. Rev.

Complimentary Narrative Commentaries of Statutory Accounts in the Annual Reports of UK Listed Companies

This paper, for the first time, classifies narrative information into complementary and supplementary. For the purpose of the paper, complementary narrative information is defined as that information which refers to specific numbers presented in the statutory accounts (profit and loss and balance sheet). Non-specific narrative information is classified as supplementary. Having made the distinction and provided reasons for such a distinction the study investigates the extent of complementary narrative commentaries on numbers from the statutory accounts. The study also investigates which company-specific characteristics are associated with the extent of complementary narrative commentaries. An index consisting of 46 items which must be reported in the statutory accounts was used to measure the extent of complementary narrative commentaries in the annual reports of 170 listed UK companies. the findings suggest that, on average, the companies comment on 3909% of the numbers appearing in their statutory accounts. using the Ordinary Least Squares (OLS) regression model, the results indicate that company size, gearing, profitability, liquidity ratio, the presence of exceptional items, and substantial institutional investment are significantly associated with the extent of complementary narrative commentaries. However, auditory type, directors' share ownership, and the proportion of non-executive directors are not significantly associated with the extent of complementary narrative commentaries. The research has important implications for accounting regulators, users of annual reports and future research into the usefulness narrative information provided in annual reports