Regularization as Quantization in Reducible Representations of CCR

A covariant quantization scheme employing reducible representations of canonical commutation relations with positive-definite metric and Hermitian four-potentials (an alternative to the Gupta-Bleuler method) is tested on the example of quantum electromagnetic fields produced by a classical current. The Heisenberg dynamics can be consistently formulated since the fields are given by operators and not operator-valued distributions. The scheme involves a Hamiltonian whose free part is modified but the minimal-coupling interaction is the standard one. Solving Heisenberg equations of motion under the assumption that the fields are free for times t ₀ = ±∞ we arrive at retarded and advanced solutions. Once we have these solutions we can deduce the form of evolution of retarded and advanced fields between two arbitrary finite times. The appropriate unitary evolution operators are found and their generators are computed. Now the generators involve the same free part as before, but the interaction term turns out to be modified. For a pointlike charge localized on a world-line z ^a (t) we find the interaction term of the form where the integration is along those parts of the charge world-line where the charge velocity is nonzero. There is no self-energy contribution. Next we compute photon statistics. Poisson statistics naturally results and infrared divergence can be avoided even for pointlike sources. Classical fields produced by classical sources can be obtained if one computes coherent-state averages of Heisenberg-picture operators. It is shown that the new form of representation automatically smears out pointlike currents. We discuss in detail Poincaré covariance of the theory and the role of Bogoliubov transformations for the issue of gauge invariance. The representation we employ is parametrized by a number that is related to Rényi’s α. It is shown that the “Shannon limit” α→ 1 plays here a role of a correspondence principle with the standard regularized formalism. PACS: 03.70.+k, 41.20.Jb, 42.50.-p.     

Raman microscopy of haidingerite Ca(AsO3OH)·H2O and brassite Mg(AsO3OH)·4H2O

Raman spectroscopy has been used to study the arsenate minerals haidingerite Ca(AsO₃OH)·H₂O and brassite Mg(AsO₃OH)·4H₂O. Intense Raman bands in the haidingerite spectrum observed at 745 and 855 cm⁻¹ are assigned to the (AsO₃OH)²⁻ν₃ antisymmetric stretching and ν₁ symmetric stretching vibrational modes. For brassite, two similarly assigned intense bands are found at 809 and 862 cm⁻¹. The observation of multiple Raman bands in the (AsO₃OH)²⁻ stretching and bending regions suggests that the arsenate tetrahedrons in the crystal structures of both minerals studied are strongly distorted. Broad Raman bands observed at 2842 cm⁻¹ for haidingerite and 3035 cm⁻¹ for brassite indicate strong hydrogen bonding of water molecules in the structure of these minerals. OH···O hydrogen‐bond lengths were calculated from the Raman spectra based on empirical relations. Copyright © 2009 John Wiley & Sons, Ltd.     

Diffusional transport in manganous sulphide

Using a novel diffusion-evaporation method, the self-diffusion coefficient of manganese in manganous sulphide has been determined as a function of temperature (1073–1373 K) in equilibrium with the metallic phase. It has been shown that the activation energy of this process at constant sulphur activity amounts to 269 kJ/mol and the self-diffusion coefficient is the following function of temperature and sulphur vapour pressure: . Diffusion of Mn²⁺ cations in Mn_1+yS proceeds via the interstitialcy mechanism and the activation enthalpy of successive jumps of these defects, δH_m is equal to 118 kJ/mol. It has been demonstrated that the mobility of interstitial cations in the Mn_1+yS lattice does not depend on their concentration and the diffusion coefficient of these defects has the following function of temperature: D_i=0.759 exp(-118 kJ/mol/RT).     

A note on the Percus-Yevick and hypernetted chain theories of adsorption: The second and third virial coefficients for a hard-sphere gas in contact with a wall with a soft surface layer

The first three virial coefficients of a new type in the density expansion of the adsorption isotherm for hard spheres in contact with a wall with a soft surface layer are calculated. The results are compared with those for hard spheres in contact with a hard wall.     

An extension theorem for separately holomorphic functions with pluripolar singularities

Let be a pseudoconvex domain and let be a locally pluriregular set, . Put

Let be an open neighborhood of and let be a relatively closed subset of . For let be the set of all for which the fiber is not pluripolar. Assume that are pluripolar. Put

Then there exists a relatively closed pluripolar subset of the ``envelope of holomorphy' of such that:

,

for every function separately holomorphic on there exists exactly one function holomorphic on with on , and

is singular with respect to the family of all functions .

     

On the existence of solutions to the Navier–Stokes equations of a two‐dimensional compressible flow

We consider the Navier–Stokes equations for compressible, barotropic flow in two space dimensions. We introduce useful tools from the theory of Orlicz spaces. Then we prove the existence of globally defined finite energy weak solutions for the pressure satisfying p(?) = a?log^d(?) for large ?. Here d>1 and a > 0. Copyright © 2003 John Wiley & Sons, Ltd.     

Local convergence of the (exact and inexact) iterative aggregation method for linear systems and Markov operators

Summary. The iterative aggregation method for the solution of linear systems is extended in several directions: to operators on Banach spaces; to the method with inexact correction, i.e., to methods where the (inner) linear system is in turn solved iteratively; and to the problem of finding stationary distributions of Markov operators. Local convergence is shown in all cases. Convergence results apply to the particular case of stochastic matrices. Moreover, an argument is given which suggests why the iterative aggregation method works so well for nearly uncoupled Markov chains, as well as for Markov chains with other zero-nonzero structures. Received May 25, 1991/Revised version received February 23, 1994     

XAFS spectra from X-ray fluorescence Kβ line using conventional energy-discriminating detector

X-ray fluorescence spectra of copper (Cu) metal, copper monoxide (CuO), and potassium chromate (K₂CrO₄) were recorded as a function of incident X-ray energy near the Cu K-edge and chromium (Cr) K-edge, respectively, using a conventional silicon drift detector. The spectra contained components due to elastic, inelastic, and multiple scattering, in addition to the Kα and Kβ lines. Cu and Cr K-edge X-ray absorption fine structure (XAFS) spectra of Cu, CuO, and K₂CrO₄ were obtained by an intensity analysis of the Kα and Kβ lines. The intensity of the Kβ line for the different incident photon energies was obtained by numerically removing the additional scattering components using the MUSCAT program. These spectra exhibited a jump near the K absorption edges, which reproduced the spectral features obtained in transmission mode for both Cu, CuO, and K₂CrO₄. A chemical shift was also clearly identified in the X-ray absorption near edges structure using the X-ray fluorescence Kβ line. In addition, the Cr K-edge extended XAFS spectrum of K₂CrO₄ was clearly observed using the Cr Kβ fluorescent line. The XAFS measurements on the Kα and Kβ lines are possible, and they carry equally valuable information.     

CO adsorption on Cu(1 1 1) and Cu(0 0 1) surfaces: Improving site preference in DFT calculations

CO adsorption on Cu(1 1 1) and Cu(0 0 1) surfaces has been studied within ab initio density functional theory (DFT). The structural, vibrational and thermodynamic properties of the adsorbate–substrate complex have been calculated. Calculations within the generalized gradient approximation (GGA) predict adsorption in the threefold hollow on Cu(1 1 1) and in the bridge-site on Cu(0 0 1), instead of on-top as found experimentally. It is demonstrated that the correct site preference is achieved if the underestimation of the HOMO–LUMO gap of CO characteristic for DFT is corrected by applying a molecular DFT + U approach. The DFT + U approach also produces good agreement with the experimentally measured adsorption energies, while introducing only small changes in the calculated geometrical and vibrational properties further improving agreement with experiment which is fair already at the GGA level.     

Energy-loss near-edge fine structures of iron nanoparticles

Body centered cubic (bcc) Fe nanoparticles were fabricated by in situ decomposition of iron fluoride films in a transmission electron microscope. Electron energy-loss near edge structure (ELNES) was used to characterize this exposure process. In particular, the L(3)/L(2) white-line intensity ratio (WLR) was used to monitor the iron valence state during exposure, and as an indicator of other properties of the iron nanoparticles. Iron nanoparticles with sizes between 2 and 20nm exhibit a constant WLR, whose value is same as that for a continuous bcc iron film, suggesting little or no dependence of the local magnetic moment or structure on the particle size. A broad but prominent peak which occurs 40eV after the L(3)-ionization threshold in the iron fluoride, is absent for a metallic iron film but reappears when the iron is converted to an oxide. Long-range ferromagnetic coupling was observed in samples densely populated with iron nanoparticles. Because there is little interaction between particles and the supporting carbon substrate, these samples provide an ideal model system for studying the influence of particle size and interparticle distance on magnetic properties.