Axial Anomaly for Eguchi-Hanson Metrics with Nonzero Total Mass

We compute the Dirac indexes for. the two spin structures kappa(0) and kappa(1) for Eguchi-Hanson metrics with nonzero total mass. It shows that the Dirac indexes do not vanish in general, and axial anomaly exists. When the metric has zero total mass, the Dirac index vanishes for the spin structure no, and no axial anomaly exists in this case.

Iterative quantum computations of HO2 bound states and resonances for J=4 and 5

Bound and resonance states of HO2 have been calculated by both the complex Lanczos homogeneous filter diagonalisation (LHFD) method(1,2) and the real Chebyshev filter diagonalisation method(3,4) for non-zero total angular momentum J = 4 and 5. For bound states, the agreement between the two methods is quite satisfactory; for resonances while the energies are in good agreement, the widths are only in general agreement. The relative performances of the two iterative FD methods have also been discussed in terms of efficiency as well as convergence behaviour for such a computationally challenging problem. A helicity quantum number Ohm assignment (within the helicity conserving approximation) is performed and the results indicate that Coriolis coupling becomes more important as J increases and the helicity conserving approximation is not a good one for the HO2 resonance states.

Recent developments in the quantum dynamical characterization of unimolecular resonances

We give a selective review of quantum mechanical methods for calculating and characterizing resonances in small molecular systems, with an emphasis on recent progress in Chebyshev and Lanczos iterative methods. Two archetypal molecular systems are discussed: isolated resonances in HCO, which exhibit regular mode and state specificity, and overlapping resonances in strongly bound HO2, which exhibit irregular and chaotic behavior. Recent progresses for non-zero total angular momentum J calculations of resonances including parallel computing models are also included and future directions in this field are discussed.

Impact of pre-existing sulfate on retention of imported chloride and nitrate in variable charge soil profiles

In variable charge soils, anion retention and accumulation through adsorption at exchange sites is a competitive process. The objectives of this study in the wet tropics of far north Queensland were to investigate (i) whether the pre-existing high sulphate in variable charge soils had any impact on the retention of chloride and nitrate, derived mostly from the applied fertilizer; and (ii) whether chloride competed with nitrate during the adsorption processes. Soil cores up to 12.5 m depth were taken from seven sites, representing four soil types, in the Johnstone River Catchment. Six of these sites had been under sugarcane (Saccharum officinarum-S) cultivation for at least 50 years and one was an undisturbed rainforest. The cores were segmented at 1.0 m depth increments, and subsamples were analysed for nitrate-N, cation (CEC)- and anion-exchange capacities (AEC), pH, exchangeable cations (Ca, Mg, K, Na), soil organic C (SOC), electrical conductivity (EC), sulphate-S, and chloride. Sulphate-S load in 1-12 m depth under cropping ranged from 9.4 to 73.9 t ha(-1) (mean= 40 t ha(-1)) compared with 74.4 t ha(-1) in the rainforest. Chloride load under cropping ranged from 1.5 to 9.6 t ha(-1) (mean= 4.9 t ha(-1)) compared to 0.9 t ha(-1) in the rainforest, and the nitrate-N load from 113 to 2760 kg ha(-1) (mean = 910 kg ha(-1)) under cropping compared to 12 kg ha(-1) in the rainforest. Regardless of the soil type, the total chloride or nitrate-N input in fertilisers was 7.5 t ha(-1), during the last 50 years. Sulphate-S distribution in soil profiles decreased with depth at >2 m, whereas bulges of chloride or nitrate-N were observed at depths >2 m. This suggests that chloride or nitrate adsorption and retention increased with decreasing sulphate dominance. Abrupt decreases in equivalent fraction of sulphate (EFSO4), at depths >2 m, were accompanied by rapid increases in equivalent fraction of chloride (EFCl), followed by nitrate (EFNO3). The stepwise regression for EFCl and EFNO3 indicated that nitrate retention was reduced by the pre-existing sulphate and imported chloride, whereas only sulphate reduced chloride adsorption. The results indicate that chloride and nitrate adsorption and retention occurred, in the order chloride>nitrate, in soils containing large amounts of sulphate under approximately similar total inputs of N- and Cl-fertilisers. (C) 2004 Elsevier B.V. All rights reserved.

Theory of strongly correlated electron systems. I. Intersite coulomb interaction and the approximation of renormalized fermions in total energy calculations

The diagrammatic strong-coupling perturbation theory (SCPT) for correlated electron systems is developed for intersite Coulomb interaction and for a nonorthogonal basis set. The construction is based on iterations of exact closed equations for many - electron Green functions (GFs) for Hubbard operators in terms of functional derivatives with respect to external sources. The graphs, which do not contain the contributions from the fluctuations of the local population numbers of the ion states, play a special role: a one-to-one correspondence is found between the subset of such graphs for the many - electron GFs and the complete set of Feynman graphs of weak-coupling perturbation theory (WCPT) for single-electron GFs. This fact is used for formulation of the approximation of renormalized Fermions (ARF) in which the many-electron quasi-particles behave analogously to normal Fermions. Then, by analyzing: (a) Sham's equation, which connects the self-energy and the exchange- correlation potential in density functional theory (DFT); and (b) the Galitskii and Migdal expressions for the total energy, written within WCPT and within ARF SCPT, a way we suggest a method to improve the description of the systems with correlated electrons within the local density approximation (LDA) to DFT. The formulation, in terms of renormalized Fermions LIDA (RF LDA), is obtained by introducing the spectral weights of the many electron GFs into the definitions of the charge density, the overlap matrices, effective mixing and hopping matrix elements, into existing electronic structure codes, whereas the weights themselves have to be found from an additional set of equations. Compared with LDA+U and self-interaction correction (SIC) methods, RF LDA has the advantage of taking into account the transfer of spectral weights, and, when formulated in terms of GFs, also allows for consideration of excitations and nonzero temperature. Going beyond the ARF SCPT, as well as RF LIDA, and taking into account the fluctuations of ion population numbers would require writing completely new codes for ab initio calculations. The application of RF LDA for ab initio band structure calculations for rare earth metals is presented in part 11 of this study (this issue). (c) 2005 Wiley Periodicals, Inc.

Orbital currents and charge density waves in a generalized Hubbard ladder

We study a generalized Hubbard model on the two-leg ladder at zero temperature, focusing on a parameter region with staggered flux (SF)/d-density wave (DDW) order. To guide our numerical calculations, we first investigate the location of a SF/DDW phase in the phase diagram of the half-filled weakly interacting ladder using a perturbative renormalization group (RG) and bosonization approach. For hole doping 6 away from half-filling, finite-system density-matrix renormalizationgroup (DMRG) calculations are used to study ladders with up to 200 rungs for intermediate-strength interactions. In the doped SF/DDW phase, the staggered rung current and the rung electron density both show periodic spatial oscillations, with characteristic wavelengths 2/delta and 1/delta, respectively, corresponding to ordering wavevectors 2k(F) and 4k(F) for the currents and densities, where 2k(F) = pi(1 - delta). The density minima are located at the anti-phase domain walls of the staggered current. For sufficiently large dopings, SF/DDW order is suppressed. The rung density modulation also exists in neighboring phases where currents decay exponentially. We show that most of the DMRG results can be qualitatively understood from weak-coupling RG/bosonization arguments. However, while these arguments seem to suggest a crossover from non-decaying correlations to power-law decay at a length scale of order 1/delta, the DMRG results are consistent with a true long-range order scenario for the currents and densities. (c) 2005 Elsevier Inc. All rights reserved.