Finite gap Jacobi matrices: An announcement

We consider Jacobi matrices whose essential spectrum is a finite union of closed intervals. We focus on Szeg?’s theorem, Jost solutions, and Szeg? asymptotics for this situation. This announcement describes talks the authors gave at OPSFA 2007.     

“Horseshoe chaos” in the space-independent double sine-Gordon system

For the driven, damped space-independent double sine-Gordon equation threshold curves for horseshoe chaos of the Smale type are derived by the Melnikov technique. Different qualitative behaviour of the solutions is found in different regions of parameter space.     

Benchmarking two-photon absorption with CC3 quadratic response theory, and comparison with density-functional response theory

We present a detailed study of the effects of electron correlation on two-photon absorption calculated by coupled cluster quadratic response theory. The hierarchy of coupled cluster models CCS, CC2, CCSD, and CC3 has been used to investigate the effects of electron correlation on the two-photon absorption cross sections of formaldehyde (CH2O), diacetylene (C4H2), and water (H2O). In particular, the effects of triple excitations on two-photon transition cross sections are determined for the first time. In addition, we present a detailed comparison of the coupled cluster results with those obtained from Hartree-Fock and density-functional response theories. We have investigated the local-density approximation, the pure Becke-Lee-Yang-Parr (BLYP) functional, the hybrid Becke-3-parameter-Lee-Yang-Parr (B3LYP), and the Coulomb-attenuated B3LYP (CAM-B3LYP) functionals. Our results show that the CAM-B3LYP functional, when used in conjuction with a one-particle basis-set containing diffuse functions, has much promise; however, care must still be exercised for diffuse Rydberg-type states.     

Finite Gap Jacobi Matrices, I. The Isospectral Torus

Let frake ì mathbbRfrak{e}subsetmathbb{R} be a finite union of disjoint closed intervals. In the study of orthogonal polynomials on the real line with measures whose essential support is  frakefrak{e} , a fundamental role is played by the isospectral torus. In this paper, we use a covering map formalism to define and study this isospectral torus. Our goal is to make a coherent presentation of properties and bounds for this special class as a tool for ourselves and others to study perturbations. One important result is the expression of Jost functions for the torus in terms of theta functions.     

Stacked Josephson junctions

Long Josephson junctions have for some time been considered as a source of THz radiation. We consider here a stack of Josephson junctions as a model for the anisotropic high temperature superconductors in particular those of the BSCCO family. Solitons (fluxons) moving coherently in such junctions is a possible source for radiation. Analytical computations of the bunched state as well as bunching inducing methods are discussed. A new model for the interpretation of THz radiation experiments is suggested.     

Effects of light localization in photoluminescence and Raman scattering in silicon nanostructures

The effect of light localization in photoluminescence (PL) and Raman scattering (RS) in silicon nanowires with diameter of 100 nm was investigated. The optical excitation was done by CW radiation of a YAG:Nd laser at 1.064 μm. The PL an RS intensities were found to increase strongly for the samples with Si nanowires in comparison with corresponding values of c-Si substrate. The effect is explained by an increase of the lifetime of photons in silicon nanowire structures.     

Biosynthesis and structure of aeruginoside 126A and 126B, cyanobacterial peptide glycosides bearing a 2-carboxy-6-hydroxyoctahydroindole moiety

Aeruginosins represent a group of peptide metabolites isolated from various cyanobacterial genera and from marine sponges that potently inhibit different types of serine proteases. Members of this family are characterized by the presence of a 2-carboxy-6-hydroxyoctahydroindole (Choi) moiety. We have identified and fully sequenced a NRPS gene cluster in the genome of the cyanobacterium Planktothrix agardhii CYA126/8. Insertional mutagenesis of a NRPS component led to the discovery and structural elucidation of two glycopeptides that were designated aeruginoside 126A and aeruginoside 126B. One variant of the aglycone contains a 1-amino-2-(N-amidino-Delta(3)-pyrrolinyl)ethyl moiety at the C terminus, the other bears an agmatine residue. In silico analyses of the aeruginoside biosynthetic genes aerA-aerI as well as additional mutagenesis and feeding studies allowed the prediction of enzymatic steps leading to the formation of aeruginosides and the unusual Choi moiety.     

One- and two-photon photosensitized singlet oxygen production: characterization of aromatic ketones as sensitizer standards

Singlet molecular oxygen, O2(a1Deltag), can be efficiently produced in a photosensitized process using either one- or two-photon irradiation. The aromatic ketone 1-phenalenone (PN) is an established one-photon singlet oxygen sensitizer with many desirable attributes for use as a standard. In the present work, photophysical properties of two other aromatic ketones, pyrene-1,6-dione (PD) and benzo[cd]pyren-5-one (BP), are reported and compared to those of PN. Both PD and BP sensitize the production of singlet oxygen with near unit quantum efficiency in a nonpolar (toluene) and a polar (acetonitrile) solvent. With their more extensive pi networks, the one-photon absorption spectra for PD and BP extend out to longer wavelengths than that for PN, thus providing increased flexibility for sensitizer excitation over the range approximately 300-520 nm. Moreover, PD and BP have much larger two-photon absorption cross sections than PN over the range 655-840 nm which, in turn, results in amounts of singlet oxygen that are readily detected in optical experiments. One- and two-photon absorption spectra of PD and BP obtained using high-level calculations model the salient features of the experimental data well. In particular, the ramifications of molecular symmetry are clearly reflected in both the experimental and calculated spectra. The use of PD and BP as standards for both the one- and two-photon photosensitized production of singlet oxygen is expected to facilitate the development of new sensitizers for application in singlet-oxygen-based imaging experiments.