Wavelets and graph C∗C^*-algebras

Here we give an overview on the connection between wavelet theory and representation theory for graph $C^{\ast}$-algebras, including the higher-rank graph $C^*$-algebras of A. Kumjian and D. Pask. Many authors have studied different aspects of this connection over the last 20 years, and we begin this paper with a survey of the known results. We then discuss several new ways to generalize these results and obtain wavelets associated to representations of higher-rank graphs. In \cite{FGKP}, we introduced the "cubical wavelets" associated to a higher-rank graph. Here, we generalize this construction to build wavelets of arbitrary shapes. We also present a different but related construction of wavelets associated to a higher-rank graph, which we anticipate will have applications to traffic analysis on networks. Finally, we generalize the spectral graph wavelets of \cite{hammond} to higher-rank graphs, giving a third family of wavelets associated to higher-rank graphs

Lifetime quenching in Yb-doped fibres

We have discovered that in ytterbium-doped silica fibres the excited state lifetime of a fraction of the Yb ions can be quenched to a very small value, leading to a strong unbleachable loss. This unexpected behaviour seems to be caused by some, yet unidentified, impurity or structural defect. It is of considerable relevance for various Yb doped lasers and-amplifiers including Er:Yb codoped fibres as used in telecommunication amplifiers although it should also be emphasized that fibres can be produced that are free from the quenching effect

Electronic and magnetic properties of zinc blende half-metal superlattices

Zinc blende half-metallic compounds such as CrAs, with large magnetic moments and high Curie temperatures, are promising materials for spintronic applications. We explore layered materials, consisting of alternating layers of zinc blende half-metals, by first principles calculations, and find that superlattices of (CrAs)1(MnAs)1 and (CrAs)2(MnAs)2 are half-metallic with magnetic moments of 7.0mB and 14.0mB per unit cell, respectively. We discuss the nature of the bonding and half-metallicity in these materials and, based on the understanding acquired, develop a simple expression for the magnetic moment in such materials. We explore the range of lattice constants over which half-metallicity is manifested, and suggest corresponding substrates for growth in thin film form

Six low-strain zinc-blende half metals: An ab initio investigation

A class of spintronic materials, the zinc-blende (ZB) half metals, has recently been synthesized in thin-film form. We apply all-electron and pseudopotential ab initio methods to investigate the electronic and structural properties of ZB Mn and Cr pnictides and carbides, and find six compounds to be half metallic at or near their respective equilibrium lattice constants, making them excellent candidates for growth at low strain. Based on these findings, we further propose substrates on which the growth may be accomplished with minimum strain. Our findings are supported by the recent successful synthesis of ZB CrAs on GaAs and ZB CrSb on GaSb, where our predicted equilibrium lattice constants are within 0.5% of the lattice constants of the substrates on which the growth was accomplished. We confirm previous theoretical results for ZB MnAs, but find ZB MnSb to be half metallic at its equilibrium lattice constant, whereas previous work has found it to be only nearly so. We report here two low-strain half metallic ZB compounds, CrP and MnC, and suggest appropriate substrates for each. Unlike the other five compounds, we predict ZB MnC to become/remain half metallic with compression rather than expansion, and to exhibit metallicity in the minority-rather than majority-spin channel. These fundamentally different properties of MnC can be connected to substantially greater p-d hybridization and d-d overlap, and correspondingly larger bonding-antibonding splitting and smaller exchange splitting. We examine the relative stability of each of the six ZB compounds against NiAs and MnP structures, and find stabilities for the compounds not yet grown comparable to those already grown

Non-Equilibrium Electron Transport in Two-Dimensional Nano-Structures Modeled by Green's Functions and the Finite-Element Method

We use the effective-mass approximation and the density-functional theory with the local-density approximation for modeling two-dimensional nano-structures connected phase-coherently to two infinite leads. Using the non-equilibrium Green's function method the electron density and the current are calculated under a bias voltage. The problem of solving for the Green's functions numerically is formulated using the finite-element method (FEM). The Green's functions have non-reflecting open boundary conditions to take care of the infinite size of the system. We show how these boundary conditions are formulated in the FEM. The scheme is tested by calculating transmission probabilities for simple model potentials. The potential of the scheme is demonstrated by determining non-linear current-voltage behaviors of resonant tunneling structures.Comment: 13 pages,15 figure

Spin-polarized ballistic transport in a thin superlattice of zinc blende half-metallic compounds

We examine theoretically ballistic conduction in thin layers of zinc blende half metals, considering as an example a superlattice consisting of monolayers of GaAs and MnAs, a bilayer of CrAs, and a bilayer of GaAs. By artificially separating bilayers, we show that surface states thwart half metallicity. However, capping the metal-As bilayers restores half metallicity, and ballistic conduction of electrons within ∼0.3 eV of the Fermi level will give nearly 100% spin-polarized transmission in the direction of the superlattice. Recent developments suggest atomic layer epitaxy can be used to produce such thin layers for spintronic applications. ©2005 The American Physical Society

Parallel finite element density functional computations exploiting grid refinement and subspace recycling

In this communication computational methods that facilitate finite element analysis of density functional computations are developed. They are: (i) h¿adaptive grid refinement techniques that reduce the total number of degrees of freedom in the real space grid while improving on the approximate resolution of the wanted solution; and (ii) subspace recycling of the approximate solution in self-consistent cycles with the aim of improving the performance of the generalized eigenproblem solver. These techniques are shown to give a convincing speed-up in the computation process by alleviating the overhead normally associated with computing systems with many degrees-of-freedom.The anonymous referees whose comments improved the presentation of this work are gratefully acknowledged. The work was supported by the Polish Ministry of Science and Higher Education N N519402837 and by the Spanish Ministry of Science and Innovation TIN2009-07519 and TIN2012-32846. The resources provided by the Barcelona Supercomputing Center are also acknowledged.Young, TD.; Romero Alcalde, E.; Román Moltó, JE. (2013). Parallel finite element density functional computations exploiting grid refinement and subspace recycling. Computer Physics Communications. 184(1):66-72. doi:10.1016/j.cpc.2012.08.011S6672184

Operation of ytterbium-doped silica fibre lasers at specific wavelengths using fibre gratings

Yb-doped fibre lasers have been previously reported as versatile, efficient laser sources in the 1 µspectral region. The very broad Stark splitting of Yb energy levels in silica results in wide pump (830 - 1064 nm) and emission (975 - 1160 nm) bands. The emission band includes a number of wavelengths of interest for specific uses; examples include 1020 nm, the optimum pump wavelength for the Pr:ZBLAN amplifier and upconversion laser, and 1128 nm. which has been utilised to pump a Tm:ZBLAN upconversion laser

Real-space local polynomial basis for solid-state electronic-structure calculations: A finite-element approach

We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the method is completely general and its convergence can be controlled systematically. Because the basis functions are strictly local in real space, the method allows for variable resolution in real space; produces sparse, structured matrices, enabling the effective use of iterative solution methods; and is well suited to parallel implementation. The method thus combines the significant advantages of both real-space-grid and basis-oriented approaches and so promises to be particularly well suited for large, accurate ab initio calculations. We develop the theory of our approach in detail, discuss advantages and disadvantages, and report initial results, including the first fully three-dimensional electronic band structures calculated by the method.Comment: replacement: single spaced, included figures, added journal referenc