Coherent motion of a hole in a two-dimensional quantum antiferromagnet

The dispersion relation for the coherent propagation of a hole moving in a two-dimensional quantum antiferromagnet is discussed. The system is described by two model Hamiltonians, thet-J model and thet-t-J model, which have been used frequently to discuss strong electron-correlation effects present in high-T _c superconductors. The calculations are based on the introduction of a new wave function which is constructed by use of equations derived by Shraiman and Siggia. The different mechanisms for the coherent propagation, which are due to the spin fluctuation and the hopping terms of the Hamiltonian, are treated on the same footing. As a result of the inclusion of an effective hopping mechanism along spiral paths-first discussed by Trugman-the minimum of the band is somewhat changed compared to results recently obtained in the literature. For large values of the ratiot/J an inversion of the whole dispersion relation occurs. The overall shapes of the dispersion within both models are found to agree quite well, though for small values oft/J the bandwidth within thet-J model becomes significantly smaller than that of thet-t-J model.     

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.     

Finite-Element Approximation of a Plasma Equilibrium Problem

The plasma problem studied is: given R⁺ find (, d, u) R ?R ? H¹() such that Let ₁ < ₂ be the first two eigenvalues of the associatedlinear eigenvalue problem: find $$\left(\lambda ,\phi \right)\in\mathrm{R;}\times {\hbox{ H }}_{0}^{1}\left(\Omega \right)$$such that For ₀(0,₂) it is well known that there exists a unique solution(₀, d₀, u₀) to the above problem. We show that the standard continuous piecewise linear Galerkinfinite-element approximatinon $$\left({\lambda }_{0},{\hbox{d }}_{0}^{k},{u}_{0}^{h}\right)$$, for ₀(0,₂), converges atthe optimal rate in the H¹, L², and L norms as h, the mesh length,tends to 0. In addition, we show that dist (, ^h)Ch² ln 1/h,where $${\Gamma }^{\left(h\right)}=\left\{x\in \Omega :{u}_{0}^{\left(h\right)}\left(x\right)=0\right\}$$.Finally we consider a more practical approximation involvingnumerical integration.     

Insights into dolphin sonar discrimination capabilities from human listening experiments

A variety of dolphin sonar discrimination experiments have been conducted, yet little is known about the cues utilized by dolphins in making fine target discriminations. In order to gain insights on cues available to echolocating dolphins, sonar discrimination experiments were conducted with human subjects using the same targets employed in dolphin experiments. When digital recordings of echoes from targets ensonified with a dolphinlike signal were played back at a slower rate to human subjects, they could also make fine target discriminations under controlled laboratory conditions about as well as dolphins under less controlled conditions. Subjects reported that time-separation-pitch and duration cues were important. They also reported that low-amplitude echo components 32 dB below the maximum echo component were usable. The signal-to-noise ratio had to be greater than 10 dB above the detection threshold for simple discrimination and 30 dB for difficult discrimination. Except for two cases in which spectral cues in the form of "click pitch" were important, subjects indicated that time-domain rather than frequency-domain processing seemed to be more relevant in analyzing the echoes.     

Optimal birth control of population dynamics

The authors studied optimal birth control policies for an age-structured population of McKendrick type which is a distributed parameter system involving 1st order partial differential equations with nonlocal bilinear boundary control. The functional analytic approach of Dubovitskii and Milyutin is adopted in the investigation. Maximum principles for problems with a free end condition and fixed final horizon are developed, and the time optimal control problems, the problem with target sets, and infinite planning horizon case are investigated.     

Covering the Plane with Congruent Copies of a Convex Body

It is shown that every plane compact convex set K with an interiorpoint admits a covering of the plane with density smaller thanor equal to 8(23 – 3)/3 = 1.2376043.... For comparison,the thinnest covering of the plane with congruent circles isof density 2 / 27 = 1.209199576.... (see R. Kershner [3]), whichshows that the covering density bound obtained here is closeto the best possible. It is conjectured that the best possibleis 2 / 27. The coverings produced here are of the double-latticekind consisting of translates of K and translates of —K.