Fano-type interpretation of red shifts and red tails in hole array transmission spectra

We present a unifying point of view which allows to understand spectral features reported in recent experiments with two-dimensional arrays of subwavelength holes in metal films. We develop a Fano analysis of the related scattering problem by distinguishing two interfering contributions to the transmission process, namely a non-resonant contribution (direct scattering) and a resonant contribution (surface plasmon excitation). The introduction of a coupling strength between these two contributions naturally induces resonance shifts and asymmetry of profiles which satisfy simple scaling relations. We also report an experiment to confirm this analysis.Comment: 5 page

Invariant classification and the generalised invariant formalism: conformally flat pure radiation metrics, with zero cosmological constant

Metrics obtained by integrating within the generalised invariant formalism are structured around their intrinsic coordinates, and this considerably simplifies their invariant classification and symmetry analysis. We illustrate this by presenting a simple and transparent complete invariant classification of the conformally flat pure radiation metrics (except plane waves) in such intrinsic coordinates; in particular we confirm that the three apparently non-redundant functions of one variable are genuinely non-redundant, and easily identify the subclasses which admit a Killing and/or a homothetic Killing vector. Most of our results agree with the earlier classification carried out by Skea in the different Koutras-McIntosh coordinates, which required much more involved calculations; but there are some subtle differences. Therefore, we also rework the classification in the Koutras-McIntosh coordinates, and by paying attention to some of the subtleties involving arbitrary functions, we are able to obtain complete agreement with the results obtained in intrinsic coordinates. In particular, we have corrected and completed statements and results by Edgar and Vickers, and by Skea, about the orders of Cartan invariants at which particular information becomes available.Comment: Extended version of GRG publication, with some typos etc correcte

Dynamical Structure Factor for the Alternating Heisenberg Chain: A Linked Cluster Calculation

We develop a linked cluster method to calculate the spectral weights of many-particle excitations at zero temperature. The dynamical structure factor is expressed as a sum of exclusive structure factors, each representing contributions from a given set of excited states. A linked cluster technique to obtain high order series expansions for these quantities is discussed. We apply these methods to the alternating Heisenberg chain around the dimerized limit ($\lambda=0$), where complete wavevector and frequency dependent spectral weights for one and two-particle excitations (continuum and bound-states) are obtained. For small to moderate values of the inter-dimer coupling parameter $\lambda$, these lead to extremely accurate calculations of the dynamical structure factors. We also examine the variation of the relative spectral weights of one and two-particle states with bond alternation all the way up to the limit of the uniform chain ($\lambda=1$). In agreement with Schmidt and Uhrig, we find that the spectral weight is dominated by 2-triplet states even at $\lambda=1$, which implies that a description in terms of triplet-pair excitations remains a good quantitative description of the system even for the uniform chain.Comment: 26 pages, 17 figure

Obtaining a class of Type O pure radiation metrics with a cosmological constant, using invariant operators

Using the generalised invariant formalism we derive a class of conformally flat spacetimes whose Ricci tensor has a pure radiation and a Ricci scalar component. The method used is a development of the methods used earlier for pure radiation spacetimes of Petrov types O and N respectively. In this paper we demonstrate how to handle, in the generalised invariant formalism, spacetimes with isotropy freedom and rich Killing vector structure. Once the spacetimes have been constructed, it is straightforward to deduce their Karlhede classification: the Karlhede algorithm terminates at the fourth derivative order, and the spacetimes all have one degree of null isotropy and three, four or five Killing vectors.Comment: 29 page

Microsatellite and mating type primers for the maize and sorghum pathogen, Exserohilum turcicum

Northern corn leaf blight (NCLB) is a destructive foliar disease of maize that results from infection with the fungal pathogen, Exserohilum turcicum. Annual yield losses incurred from NCLB in South Africa may exceed 50 % when environmental conditions optimal for disease development prevail. In order to study the genetic diversity of E. turcicum, 13 microsatellite markers and mating type PCR primers were developed. Thirty-two primer pairs were designed from the E. turcicum genome sequence to flank microsatellite regions. A multiplex PCR assay amplifying both mating type idiomorphs was designed from the MAT1-1 and MAT1-2 gene sequences, and a protocol for multiplex PCR amplification of MAT loci was optimized. Initial screening identified 13 microsatellite regions that were polymorphic in 9 isolates of E. turcicum. To test the efficacy of the markers, 26 isolates of E. turcicum from 6 South African provinces, including 2 isolates from sorghum, were genotyped. A total of 90 alleles across 13 loci were obtained and the gene diversity ranged from 0.074 to 0.929. Cross-species amplification withE. rostratum was obtained for one SSR marker (SSR27). The MAT markers were specific to E. turcicum and could be used to differentiate isolates of E. turcicum and E. rostratum. The markers developed in this study will be useful to elucidate the population genetic structure, genetic diversity and mode of reproduction of E. turcicum on maize and sorghum.Research supported in part by the National Research Foundation of South Africa (grant specific unique reference number (UID) 85076), and by the Maize Trust and the University of Pretoria’s Research and Development Programme.http://link.springer.com/journal/133132015-09-30hb201

A Study of the S=1/2 Alternating Chain using Multiprecision Methods

In this paper we present results for the ground state and low-lying excitations of the $S=1/2$ alternating Heisenberg antiferromagnetic chain. Our more conventional techniques include perturbation theory about the dimer limit and numerical diagonalization of systems of up to 28 spins. A novel application of multiple precision numerical diagonalization allows us to determine analytical perturbation series to high order; the results found using this approach include ninth-order perturbation series for the ground state energy and one magnon gap, which were previously known only to third order. We also give the fifth-order dispersion relation and third-order exclusive neutron scattering structure factor for one-magnon modes and numerical and analytical binding energies of S=0 and S=1 two-magnon bound states.Comment: 16 pages, 9 figures. for submission to Phys.Rev.B. PICT files of figs available at http://csep2.phy.ornl.gov/theory_group/people/barnes/barnes.htm

NN Core Interactions and Differential Cross Sections from One Gluon Exchange

We derive nonstrange baryon-baryon scattering amplitudes in the nonrelativistic quark model using the ``quark Born diagram" formalism. This approach describes the scattering as a single interaction, here the one-gluon-exchange (OGE) spin-spin term followed by constituent interchange, with external nonrelativistic baryon wavefunctions attached to the scattering diagrams to incorporate higher-twist wavefunction effects. The short-range repulsive core in the NN interaction has previously been attributed to this spin-spin interaction in the literature; we find that these perturbative constituent-interchange diagrams do indeed predict repulsive interactions in all I,S channels of the nucleon-nucleon system, and we compare our results for the equivalent short-range potentials to the core potentials found by other authors using nonperturbative methods. We also apply our perturbative techniques to the N$\Delta$ and $\Delta\Delta$ systems: Some $\Delta\Delta$ channels are found to have attractive core potentials and may accommodate ``molecular" bound states near threshold. Finally we use our Born formalism to calculate the NN differential cross section, which we compare with experimental results for unpolarised proton-proton elastic scattering. We find that several familiar features of the experimental differential cross section are reproduced by our Born-order result.Comment: 27 pages, figures available from the authors, revtex, CEBAF-TH-93-04, MIT-CTP-2187, ORNL-CCIP-93-0

Thermodynamic Properties of the Dimerised and Frustrated S=1/2 Chain

By high temperature series expansion, exact diagonalisation and temperature density-matrix renormalisation the magnetic susceptibility $\chi(T)$ and the specific heat $C(T)$ of dimerised and frustrated $S=1/2$ chains are computed. All three methods yield reliable results, in particular for not too small temperatures or not too small gaps. The series expansion results are provided in the form of polynomials allowing very fast and convenient fits in data analysis using algebraic programmes. We discuss the difficulty to extract more than two coupling constants from the temperature dependence of $\chi(T)$.Comment: 14 pages, 13 figures, 4 table

Single-hole properties in the tt-JJ and strong-coupling models

We report numerical results for the single-hole properties in the $t$-$J$ model and the strong-coupling approximation to the Hubbard model in two dimensions. Using the hopping basis with over $10^6$ states we discuss (for an infinite system) the bandwidth, the leading Fourier coefficients in the dispersion, the band masses, and the spin-spin correlations near the hole. We compare our results with those obtained by other methods. The band minimum is found to be at ($\pi/2,\pi/2$) for the $t$-$J$ model for $0.1 \leq t/J \leq 10$, and for the strong-coupling model for $1 \leq t/J \leq 10$. The bandwidth in both models is approximately $2J$ at large $t/J$, in rough agreement with loop-expansion results but in disagreement with other results. The strong-coupling bandwidth for t/J\agt6 can be obtained from the $t$-$J$ model by treating the three-site terms in first-order perturbation theory. The dispersion along the magnetic zone face is flat, giving a large parallel/perpendicular band mass ratio.Comment: 1 RevTeX file with epsf directives to include 8 .eps figures 8 figure files encoded using uufile

Reflection and Ducting of Gravity Waves Inside the Sun

Internal gravity waves excited by overshoot at the bottom of the convection zone can be influenced by rotation and by the strong toroidal magnetic field that is likely to be present in the solar tachocline. Using a simple Cartesian model, we show how waves with a vertical component of propagation can be reflected when traveling through a layer containing a horizontal magnetic field with a strength that varies with depth. This interaction can prevent a portion of the downward-traveling wave energy flux from reaching the deep solar interior. If a highly reflecting magnetized layer is located some distance below the convection zone base, a duct or wave guide can be set up, wherein vertical propagation is restricted by successive reflections at the upper and lower boundaries. The presence of both upward- and downward-traveling disturbances inside the duct leads to the existence of a set of horizontally propagating modes that have significantly enhanced amplitudes. We point out that the helical structure of these waves makes them capable of generating an alpha-effect, and briefly consider the possibility that propagation in a shear of sufficient strength could lead to instability, the result of wave growth due to over-reflection.Comment: 23 pages, 5 figures. Accepted for publication in Solar Physic