Order-N Density-Matrix Electronic-Structure Method for General Potentials

A new order-N method for calculating the electronic structure of general (non-tight-binding) potentials is presented. The method uses a combination of the ``purification''-based approaches used by Li, Nunes and Vanderbilt, and Daw, and a representation of the density matrix based on ``travelling basis orbitals''. The method is applied to several one-dimensional examples, including the free electron gas, the ``Morse'' bound-state potential, a discontinuous potential that mimics an interface, and an oscillatory potential that mimics a semiconductor. The method is found to contain Friedel oscillations, quantization of charge in bound states, and band gap formation. Quantitatively accurate agreement with exact results is found in most cases. Possible advantages with regard to treating electron-electron interactions and arbitrary boundary conditions are discussed.Comment: 13 pages, REVTEX, 7 postscript figures (not quite perfect

Morphology and Dynamics of the Low Solar Chromosphere

The Interferometric Bidimensional Spectrometer (IBIS) installed at the Dunn Solar Telescope of the NSO/SP is used to investigate the morphology and dynamics of the lower chromosphere and the virtually non-magnetic fluctosphere below. The study addresses in particular the structure of magnetic elements that extend into these layers. We choose different quiet Sun regions in and outside coronal holes. In inter-network regions with no significant magnetic flux contributions above the detection limit of IBIS, we find intensity structures with the characteristics of a shock wave pattern. The magnetic flux elements in the network are long lived and seem to resemble the spatially extended counterparts to the underlying photospheric magnetic elements. We suggest a modification to common methods to derive the line-of-sight magnetic field strength and explain some of the difficulties in deriving the magnetic field vector from observations of the fluctosphere.Comment: accepted by ApJ, 16 pages, 8 figure

Modeling of Covalent Bonding in Solids by Inversion of Cohesive Energy Curves

We provide a systematic test of empirical theories of covalent bonding in solids using an exact procedure to invert ab initio cohesive energy curves. By considering multiple structures of the same material, it is possible for the first time to test competing angular functions, expose inconsistencies in the basic assumption of a cluster expansion, and extract general features of covalent bonding. We test our methods on silicon, and provide the direct evidence that the Tersoff-type bond order formalism correctly describes coordination dependence. For bond-bending forces, we obtain skewed angular functions that favor small angles, unlike existing models. As a proof-of-principle demonstration, we derive a Si interatomic potential which exhibits comparable accuracy to existing models.Comment: 4 pages revtex (twocolumn, psfig), 3 figures. Title and some wording (but no content) changed since original submission on 24 April 199

Effects of three-nucleon forces and two-body currents on Gamow-Teller strengths

We optimize chiral interactions at next-to-next-to leading order to observables in two- and three-nucleon systems, and compute Gamow-Teller transitions in carbon-14, oxygen-22 and oxygen-24 using consistent two-body currents. We compute spectra of the daughter nuclei nitrogen-14, fluorine-22 and fluorine-24 via an isospin-breaking coupled-cluster technique, with several predictions. The two-body currents reduce the Ikeda sum rule, corresponding to a quenching factor q^2 ~ 0.84-0.92 of the axial-vector coupling. The half life of carbon-14 depends on the energy of the first excited 1+ state, the three-nucleon force, and the two-body current

Calculation of Elastic Green's Functions for Lattices with Cavities

In this Brief Report, we present an algorithm for calculating the elastic Lattice Greens Function of a regular lattice, in which defects are created by removing lattice points. The method is computationally efficient, since the required matrix operations are on matrices that scale with the size of the defect subspace, and not with the size of the full lattice. This method allows the treatment of force fields with multi-atom interactions.Comment: 3 pages. RevTeX, using epsfig.sty. One figur

Class and rank of differential modules

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a substitute for the length of a free complex--and on the rank of a differential module in terms of invariants of its homology. These results specialize to basic theorems in commutative algebra and algebraic topology. One instance is a common generalization of the equicharacteristic case of the New Intersection Theorem of Hochster, Peskine, P. Roberts, and Szpiro, concerning complexes over noetherian commutative rings, and of a theorem of G. Carlsson on differential graded modules over graded polynomial rings.Comment: 27 pages. Minor changes; mainly stylistic. To appear in Inventiones Mathematica

Band structures of P-, D-, and G-surfaces

We present a theoretical study on the band structures of the electron constrained to move along triply-periodic minimal surfaces. Three well known surfaces connected via Bonnet transformations, namely P-, D-, and G-surfaces, are considered. The six-dimensional algebra of the Bonnet transformations [C. Oguey and J.-F. Sadoc, J. Phys. I France 3, 839 (1993)] is used to prove that the eigenstates for these surfaces are interrelated at a set of special points in the Brillouin zones. The global connectivity of the band structures is, however, different due to the topological differences of the surfaces. A numerical investigation of the band structures as well as a detailed analysis on their symmetry properties is presented. It is shown that the presence of nodal lines are closely related to the symmetry properties. The present study will provide a basis for understanding further the connection between the topology and the band structures.Comment: 21 pages, 8 figures, 3 tables, submitted to Phys. Rev.

The Quiet-Sun Photosphere and Chromosphere

The overall structure and the fine structure of the solar photosphere outside active regions are largely understood, except possibly important roles of a turbulent near-surface dynamo at its bottom, internal gravity waves at its top, and small-scale vorticity. Classical 1D static radiation-escape modelling has been replaced by 3D time-dependent MHD simulations that come closer to reality. The solar chromosphere, in contrast, remains ill-understood although its pivotal role in coronal mass and energy loading makes it a principal research area. Its fine structure defines its overall structure, so that hard-to-observe and hard-to-model small-scale dynamical processes are the key to understanding. However, both chromospheric observation and chromospheric simulation presently mature towards the required sophistication. The open-field features seem of greater interest than the easier-to-see closed-field features.Comment: Accepted for special issue "Astrophysical Processes on the Sun" of Phil. Trans. Royal Soc. A, ed. C. Parnell. Note: clicking on the year in a citation opens the corresponding ADS abstract page in the browse

Linear response strength functions with iterative Arnoldi diagonalization

We report on an implementation of a new method to calculate RPA strength functions with iterative non-hermitian Arnoldi diagonalization method, which does not explicitly calculate and store the RPA matrix. We discuss the treatment of spurious modes, numerical stability, and how the method scales as the used model space is enlarged. We perform the particle-hole RPA benchmark calculations for double magic nucleus 132Sn and compare the resulting electromagnetic strength functions against those obtained within the standard RPA.Comment: 9 RevTeX pages, 11 figures, submitted to Physical Review