The correlation potential in density functional theory at the GW-level: spherical atoms

As part of a project to obtain better optical response functions for nano materials and other systems with strong excitonic effects we here calculate the exchange-correlation (XC) potential of density-functional theory (DFT) at a level of approximation which corresponds to the dynamically- screened-exchange or GW approximation. In this process we have designed a new numerical method based on cubic splines which appears to be superior to other techniques previously applied to the "inverse engineering problem" of DFT, i.e., the problem of finding an XC potential from a known particle density. The potentials we obtain do not suffer from unphysical ripple and have, to within a reasonable accuracy, the correct asymptotic tails outside localized systems. The XC potential is an important ingredient in finding the particle-conserving excitation energies in atoms and molecules and our potentials perform better in this regard as compared to the LDA potential, potentials from GGA:s, and a DFT potential based on MP2 theory.Comment: 13 pages, 9 figure

Electronic properties of disordered corner-sharing tetrahedral lattices

We have examined the behaviour of noninteracting electrons moving on a corner-sharing tetrahedral lattice into which we introduce a uniform (box) distribution, of width W, of random on-site energies. We have used both the relative localization length and the spectral rigidity to analyze the nature of the eigenstates, and have determined both the mobility edge trajectories as a function of W, and the critical disorder, Wc, beyond which all states are localized. We find (i) that the mobility edge trajectories (energies Ec vs. disorder W) are qualitatively different from those found for a simple cubic lattice, and (ii) that the spectral rigidity is scale invariant at Wc and thus provides a reliable method of estimating this quantity -- we find Wc/t=14.5. We discuss our results in the context of the metal-to-insulator transition undergone by LiAlyTi{2-y}O4 in a quantum site percolation model that also includes the above-mentioned Anderson disorder, and show that the effects produced by Anderson disorder are far less important than those produced by quantum site percolation, at least in the determination of the doping concentration at which the metal-to-insulator transition is predicted to occur

Measurement of gamma p --> K+ Lambda and gamma p --> K+ Sigma0 at photon energies up to 2.6 GeV

The reactions gamma p --> K+ Lambda and gamma p --> K+ Sigma0 were measured in the energy range from threshold up to a photon energy of 2.6 GeV. The data were taken with the SAPHIR detector at the electron stretcher facility, ELSA. Results on cross sections and hyperon polarizations are presented as a function of kaon production angle and photon energy. The total cross section for Lambda production rises steeply with energy close to threshold, whereas the Sigma0 cross section rises slowly to a maximum at about E_gamma = 1.45 GeV. Cross sections together with their angular decompositions into Legendre polynomials suggest contributions from resonance production for both reactions. In general, the induced polarization of Lambda has negative values in the kaon forward direction and positive values in the backward direction. The magnitude varies with energy. The polarization of Sigma0 follows a similar angular and energy dependence as that of Lambda, but with opposite sign.Comment: 21 pages, 25 figures, submitted to Eur. Phys. J.

Composition Conditions for Classes of Analytic Functions

We prove that for classes of analytic functions tree composition condition and composition condition coincide.Comment: 13 page

Investigating Atomic Details of the CaF2_2(111) Surface with a qPlus Sensor

The (111) surface of CaF$_2$ has been intensively studied with large-amplitude frequency-modulation atomic force microscopy and atomic contrast formation is now well understood. It has been shown that the apparent contrast patterns obtained with a polar tip strongly depend on the tip terminating ion and three sub-lattices of anions and cations can be imaged. Here, we study the details of atomic contrast formation on CaF$_2$(111) with small-amplitude force microscopy utilizing the qPlus sensor that has been shown to provide utmost resolution at high scanning stability. Step edges resulting from cleaving crystals in-situ in the ultra-high vacuum appear as very sharp structures and on flat terraces, the atomic corrugation is seen in high clarity even for large area scans. The atomic structure is also not lost when scanning across triple layer step edges. High resolution scans of small surface areas yield contrast features of anion- and cation sub-lattices with unprecedented resolution. These contrast patterns are related to previously reported theoretical results.Comment: 18 pages, 9 Figures, presented at 7th Int Conf Noncontact AFM Seattle, USA Sep 12-15 2004, accepted for publication in Nanotechnology, http://www.iop.or

Measurement of the reaction \gamma p \TO K^ + \Lambda(1520) at photon energies up to 2.65 GeV

The reaction \gamma p \TO K^+\Lambda(1520) was measured in the energy range from threshold to 2.65 GeV with the SAPHIR detector at the electron stretcher facility ELSA in Bonn. The $\Lambda(1520)$ production cross section was analyzed in the decay modes $pK^-$, $n \bar{K}^0$, $\Sigma^{\pm}\pi^{\mp}$, and $\Lambda\pi^+\pi^-$ as a function of the photon energy and the squared four-momentum transfer $t$. While the cross sections for the inclusive reactions rise steadily with energy, the cross section of the process \gamma p \TO K^+\Lambda(1520) peaks at a photon energy of about 2.0 GeV, falls off exponentially with $t$, and shows a slope flattening with increasing photon energy. The angular distributions in the $t$-channel helicity system indicate neither a $K$ nor a $K^\star$ exchange dominance. The interpretation of the $\Lambda(1520)$ as a $\Sigma(1385)\pi$ molecule is not supported.Comment: 11 pages, 16 figures, 4 table

Optimized Effective Potential Model for the Double Perovskites Sr2-xYxVMoO6 and Sr2-xYxVTcO6

In attempt to explore half-metallic properties of the double perovskites Sr2-xYxVMoO6 and Sr2-xYxVTcO6, we construct an effective low-energy model, which describes the behavior of the t2g-states of these compounds. All parameters of such model are derived rigorously on the basis of first-principles electronic structure calculations. In order to solve this model we employ the optimized effective potential method and treat the correlation interactions in the random phase approximation. Although correlation interactions considerably reduce the intraatomic exchange splitting in comparison with the Hartree-Fock method, this splitting still substantially exceeds the typical values obtained in the local-spin-density approximation (LSDA), which alters many predictions based on the LSDA. Our main results are summarized as follows: (i) all ferromagnetic states are expected to be half-metallic. However, their energies are generally higher than those of the ferrimagnetic ordering between V- and Mo/Tc-sites (except Sr2VMoO6); (ii) all ferrimagnetic states are metallic (except fully insulating Y2VTcO6) and no half-metallic antiferromagnetism has been found; (iii) moreover, many of the ferrimagnetic structures appear to be unstable with respect to the spin-spiral alignment. Thus, the true magnetic ground state of the most of these systems is expected to be more complex. In addition, we discuss several methodological issues related to the nonuniqueness of the effective potential for the magnetic half-metallic and insulating states.Comment: 15 pages, 9 figure

Pseudoconvex domains spread over complex homogeneous manifolds

Using the concept of inner integral curves defined by Hirschowitz we generalize a recent result by Kim, Levenberg and Yamaguchi concerning the obstruction of a pseudoconvex domain spread over a complex homogeneous manifold to be Stein. This is then applied to study the holomorphic reduction of pseudoconvex complex homogeneous manifolds X=G/H. Under the assumption that G is solvable or reductive we prove that X is the total space of a G-equivariant holomorphic fiber bundle over a Stein manifold such that all holomorphic functions on the fiber are constant.Comment: 21 page

Fibrations of genus two on complex surfaces

We consider fibrations of genus 2 over complex surfaces. The purpose of this paper is primarily to provide a geometric description of the possible structures of the fibration on a neighborhood of a singular fiber. In particular it is shown that the "geometric data" of the singular fiber determines the fibration on its neighborhood up to a transversely holomorphic $C^{\infty}$-diffeomorphism. The method employed is quite flexible and it applies to good extent to fibrations of arbitrary genus.Comment: This is the final version, June 201