Many body contributions to the electronic structure of nickel

The full temperature-dependence of the electronic quasiparticle properties of ferromagnetic Ni is investigated by use of a theoretical model, which takes into account all intraatomic interactions in thed-band complex. After introduction of effective spin operators the model-Hamiltonian consists of a one-particle term, an intraband-interaction of Hubbardtype, and an interband-exchange as in thes-f (ord-f model. The one-particle energies are taken from a realistic bandstructure calculation in order to incorporate approximately all those interactions, which are not directly covered by our model. The model contains two parameters, the intraband couplingU and the interband exchangeJ. ChoosingU=6 eV,J=0.4 eV and applying a Green-function technique we get results in almost quantitative agreement with the experiment:T _c=635 K,m(T=0)=0.56 [ _B , Curie-Weiss behaviour of the static susceptibility, satellite peak with temperature-dependent spinpolarization some 6 eV below the chemical potential , exchange splittings atT=0 of order 0.2–0.35 eV. The full temperature-dependencies of the electronic selfenergy, the one-particle spectral density, the quasiparticle density of states, and the quasiparticle bandstructure for two high symmetry directions are derived and discussed.     

Influence of electron correlations on Auger electron —and appearance potential — spectra of solids

Within the framework of the Hubbard-model the influence of electron correlations on AES and APS for a non-degenerate energy band is investigated. Both spectroscopies are determined by the same two-particle Green function which is solved by a diagrammatic vertex-correction method in the Matsubara-formalism. For empty (n=0) and for completely filled (n=2) bands the method turns out to be exact. The spectra are strongly influenced by the Coulomb interactionU/W and by the degreen of band-filling. Already very weakU/W are sufficient for a substantial deviation of APS and AES from the self-fold of the one particle density of states. For intermediate or even strongU/W(>1) the spectra consist of two parts, a relatively broad band-like region and a sharp satellite. As soon as the satellite splits off, it takes practically the whole spectral weight. In all cases the satellite has almost exactly the shape of the free density of states. The two-hole (electron) bound state, which causes the satellite, propagates virtually without scattering through the lattice. For fixedU/W the band occupationn must be below (above) a critical value to push away a satellite in APS (AES). The temperature-dependence of the spectra is non-negligible for partially filled bands (exceptionsn=0,2), being, however, qualitatively not very striking as long as a non-magnetic systems is considered.     

Dependence of “Reststrahlen” bands in far-infrared reflectivity on configuration of GaAs/AlAs multiple quantum well heterostructures

Far infrared reflectivity measurements are performed on a series of GaAs/AlAs multiple quantum well (MQW) heterostructures with systematically varied thicknesses of the constituent layers. In addition to the artificial anisotropy we observe two distinct bulk-like Reststrahlen regions. The widths of the GaAs-like and the AlAs-like Reststrahlen bands strongly depend on the relative thicknesses of the constituent layers of the MQW heterostructures, in excellent agreement with the predictions of the effective-medium theory.Prof. Aldo Cingolani passed away just before the publication of this article. We would like to dedicate this paper to his memory     

Non-characteristic mixed problems for non-linear symmetric hyperbolic systems

In this paper the existence and uniqueness of solutions of the following initial boundary value problem for non-linear symmetric hyperbolic equations of the first order are shown, where M = I ⁺ ? S , has the same from as the Kreiss' condition, but S must be sufficiently small ( I ⁺ is the unit matrix in the space generated by eigenvectors of the matrix ? A · n? , corresponding to positive eigenvalues) and n? is a unit outward vector normal to the boundary. The main result of the paper is obtaining an a priori estimate for non-linear equations. This estimate is obtained for sufficiently small time and norms of given data functions. The existence of solutions is proved by the method of successive approximations, which can be used because at each step such properties as symmetry of matrices and the numbers of positive and negative eigenvalues of the matrix ? A · n? are assured. This can be done because we restrict our attention to such systems of equations for which these properties are satisfied for solutions from some neighbourhood of initial data u ₀. Therefore, using the fact that solutions in the class of continuous functions are sought, these properties can be satisfied for sufficiently small time. Moreover, some examples of initial boundary value problems for equations of hydrodynamics and magnetohydrodynamics are considered.     

A global existence theorem for the general coagulation–fragmentation equation with unbounded kernels

In this article an existence theorem is proved for the coagulation–fragmentation equation with unbounded kernel rates. Solutions are shown to be in the space X⁺ = {c∈L¹: ∫ (1 + x)∣c(x)∣dx < ∞} whenever the kernels satisfy certain growth properties and the non-negative initial data belong to X⁺. The proof is based on weak L¹ compactness methods applied to suitably chosen approximating equations.     

Local nondeterminism and local times for stable processes

Summary Our main theorem gives sufficient conditions for symmetric stable processes and fields to have a jointly continuous local time. The approach is through the L ^p representation for such processes. We develop a measure of dependence for vectors in a normed linear space and use that to analyze the probabilistic independence of the increments of a stable process. Local nondeterminism is defined for stable processes and shown to be equivalent to locally approximately independent increments. Sufficient conditions for several classes of stable processes to be local nondeterministic are given. These ideas are extended to multidimensional stable random fields and we prove existence of jointly continuous local times. The results extend most Gaussian results to their stable analogs.     

Implicitly representing arrangements of lines or segments

Anarrangement ofn lines (or line segments) in the plane is the partition of the plane defined by these objects. Such an arrangement consists ofO(n ²) regions, calledfaces. In this paper we study the problem of calculating and storing arrangementsimplicitly, using subquadratic space and preprocessing, so that, given any query pointp, we can calculate efficiently the face containingp. First, we consider the case of lines and show that with (n) space¹ and (n ^3/2) preprocessing time, we can answer face queries in (n)+O(K) time, whereK is the output size. (The query time is achieved with high probability.) In the process, we solve three interesting subproblems: (1) given a set ofn points, find a straight-edge spanning tree of these points such that any line intersects only a few edges of the tree, (2) given a simple polygonal path , form a data structure from which we can find the convex hull of any subpath of quickly, and (3) given a set of points, organize them so that the convex hull of their subset lying above a query line can be found quickly. Second, using random sampling, we give a tradeoff between increasing space and decreasing query time. Third, we extend our structure to report faces in an arrangement of line segments in (n ^1/3)+O(K) time, given(n ^4/3) space and (n ^5/3) preprocessing time. Lastly, we note that our techniques allow us to computem faces in an arrangement ofn lines in time (m ^2/3 n ^2/3+n), which is nearly optimal.The first author is pleased to acknowledge the support of Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862 and National Science Foundation Grant CCR-8714565. Work on this paper by the fifth author has been supported by Office of Naval Research Grant N00014-87-K-0129, by National Science Foundation Grant NSF-DCR-83-20085, by grants from the Digital Equipment Corporation, and the IBM Corporation, and by a research grant from the NCRD—the Israeli National Council for Research and Development. The sixth author was supported in part by a National Science Foundation Graduate Fellowship. This work was begun while the non-DEC authors were visiting at the DEC Systems Research Center.     

Partial regularity for minimisers of certain functionals having nonquadratic growth

We prove partial regularity results for local minimisers of