Decomposition of spectral density in individual eigenvalue contributions

The eigenvalue densities of two random matrix ensembles, the Wigner Gaussian matrices and the Wishart covariant matrices, are decomposed in the contributions of each individual eigenvalue distribution. It is shown that the fluctuations of all eigenvalues, for medium matrix sizes, are described with a good precision by nearly normal distributions.

Self-adjoint extensions and spectral analysis in the Calogero problem

In this paper, we present a mathematically rigorous quantum-mechanical treatment of a one-dimensional motion of a particle in the Calogero potential alpha x(-2). Although the problem is quite old and well studied, we believe that our consideration based on a uniform approach to constructing a correct quantum-mechanical description for systems with singular potentials and/or boundaries, proposed in our previous works, adds some new points to its solution. To demonstrate that a consideration of the Calogero problem requires mathematical accuracy, we discuss some `paradoxes` inherent in the `naive` quantum-mechanical treatment. Using a self-adjoint extension method, we construct and study all possible self-adjoint operators (self-adjoint Hamiltonians) associated with a formal differential expression for the Calogero Hamiltonian. In particular, we discuss a spontaneous scale-symmetry breaking associated with self-adjoint extensions. A complete spectral analysis of all self-adjoint Hamiltonians is presented.

Self-adjoint extensions and spectral analysis in the generalized Kratzer problem

We present a mathematically rigorous quantum-mechanical treatment of a one-dimensional non-relativistic motion of a particle in the potential field V(x) = g(1)x(-1) + g(2)x(-2), x is an element of R(+) = [0, infinity). For g(2) > 0 and g(1) < 0, the potential is known as the Kratzer potential V(K)(x) and is usually used to describe molecular energy and structure, interactions between different molecules and interactions between non-bonded atoms. We construct all self-adjoint Schrodinger operators with the potential V(x) and represent rigorous solutions of the corresponding spectral problems. Solving the first part of the problem, we use a method of specifying self-adjoint extensions by (asymptotic) self-adjoint boundary conditions. Solving spectral problems, we follow Krein`s method of guiding functionals. This work is a continuation of our previous works devoted to the Coulomb, Calogero and Aharonov-Bohm potentials.

Two-photon absorption of perylene derivatives: Interpreting the spectral structure

This work investigates the two-photon absorption spectrum of perylene tetracarboxylic derivatives using the white-light continuum Z-scan technique. Perylene derivatives present relatively high two-photon absorption cross-section, which makes them attractive for applications in photonics. Because of the spectral resolution of the white-light continuum Z-scan, we were able to observe a well defined structure in the two-photon absorption spectrum, composed by two distinct peaks. These peaks, as well as the resonant enhancement of the nonlinearity, were modeled using the sum-over-states approach considering a four-level energy diagram with two final two-photon states. The existence of such states was confirmed using the response function formalism within the DFT framework. (C) 2009 Elsevier B.V. All rights reserved.

Control of Two-Photon Absorption in Organic Compounds by Pulse Shaping: Spectral Dependence

In this work, we investigate the control of the two-photon absorption process of a series of organic compounds via spectral phase modulation of the excitation pulse. We analyzed the effect of the pulse central wavelength on the control of the two-photon absorption process for each compound. Depending on the molecules` two-photon absorption position relative to the excitation pulse wavelength, different levels of coherent control were observed. By simulating the two-photon transition probability in molecular systems, taking into account the band structure and its positions, we could explain the experimental results trends. We observed that the intrapulse coherent interference plays an important role in the nonlinear process control besides just the pulse intensity modulation.

Phase diagram and spectral properties of a new exactly integrable spin-1 quantum chain

The spectral properties and phase diagram of the exactly integrable spin-1 quantum chain introduced by Alcaraz and Bariev are presented. The model has a U(1) symmetry and its integrability is associated with an unknown R-matrix whose dependence on the spectral parameters is not of a different form. The associated Bethe ansatz equations that fix the eigenspectra are distinct from those associated with other known integrable spin models. The model has a free parameter t(p). We show that at the special point t(p) = 1, the model acquires an extra U(1) symmetry and reduces to the deformed SU(3) Perk-Schultz model at a special value of its anisotropy q = exp(i2 pi/3) and in the presence of an external magnetic field. Our analysis is carried out either by solving the associated Bethe ansatz equations or by direct diagonalization of the quantum Hamiltonian for small lattice sizes. The phase diagram is calculated by exploring the consequences of conformal invariance on the finite-size corrections of the Hamiltonian eigenspectrum. The model exhibits a critical phase ruled by the c = 1 conformal field theory separated from a massive phase by first-order phase transitions.

Structural and spectroscopic characterization of poly(styrene sulfonate) films doped with neodymium ions

This work reports the structural and spectroscopy characterization of poly(styrene sulfonate) (PSS) films doped with neodymium (Nd) ions. Nd-PSS films were processed using the acid of poly(styrene sulfonate) - H-PSS and neodymium nitrate - Nd(NO(3))(3); the maximum incorporation of Nd ions in the polymeric matrix was equal 19.3%. The absorption in the UV-Vis-NIR spectral region presents typical electronic transitions of Nd 3, ions, with well resolved peaks. The infrared spectra present the transition bands of PSS with characteristic line shape broadening, and the presence of vibrational modes of N-O groups in the range of 1400-720 cm(-1), prove the permanence of Nd(NO(3))(x), with x = 1, 2 and/or 3. in the H-PSS matrix. UV-Vis site selective photoluminescence data indicate that the incorporation of Nd 31 introduces a blue shift in PSS emission (325-800 nm), decreasing the interaction between adjacent PSS lateral groups (aromatic rings). Nd(3+) reabsorption and energy transfer effects between the PSS matrix and Nd(3+) were also observed. The IR emission of Nd-PSS films at 1076 rim ((4)F(3/2) -> (4)I(11/2)) present constant efficiency, independent on Nd(3+) concentration. The Judd-Ofelt theory was employed to analyze radiative properties. The excitation spectra prove the energy transfer between the polymeric matrix and Nd(3+). Complex impedance data was used to probe relaxation processes during the charge transport within the polymeric matrix. (C) 2008 Elsevier B.V. All rights reserved.

Evidence for magnetic phase separation in La(0.86)Sr(0.14)Mn(1-x)Cu(x)O(3+delta) manganites from NMR and magnetic measurements

Polycrystalline La(0.86)Sr(0.14)Mn(1-x)Cu(x)O(3+delta) (x = 0, 0.05, 0.10, 0.15, 0.20) manganites were investigated by means of magnetic measurements and zero-field (139)La and (55)Mn nuclear magnetic resonance (NMR) spectroscopy. Magnetization versus temperature measurements revealed a paramagnetic to ferromagnetic transition in most samples, with lower Curie temperatures and broader transitions for samples with higher Cu contents. The details of the magnetization measurements suggested a phase-separated scenario, with ferromagnetic clusters embedded in an antiferromagnetic matrix, especially for the samples with large Cu contents (x = 0.15 and 0.20). Zero-field (139)La NMR measurements confirmed this finding, since the spectral features remained almost unchanged for all Cu-doped samples, whereas the bulk magnetization was drastically reduced with increasing Cu content. (55)Mn NMR spectra were again typical of ferromagnetic regions, with a broadening of the resonance line caused by the disorder introduced by the Cu doping. The results indicate a coexistence of different magnetic phases in the manganites studied, with the addition of Cu contributing to the weakening of the double-exchange interaction in most parts of the material.

Spectral flow and iteration of closed semi-Riemannian geodesics

We introduce the notion of spectral flow along a periodic semi-Riemannian geodesic, as a suitable substitute of the Morse index in the Riemannian case. We study the growth of the spectral flow along a closed geodesic under iteration, determining its asymptotic behavior.

On a formula for the spectral flow and its applications

We consider a continuous path of bounded symmetric Fredholm bilinear forms with arbitrary endpoints on a real Hilbert space, and we prove a formula that gives the spectral flow of the path in terms of the spectral flow of the restriction to a finite codimensional closed subspace. We also discuss the case of restrictions to a continuous path of finite codimensional closed subspaces. As an application of the formula, we introduce the notion of spectral flow for a periodic semi-Riemannian geodesic, and we compute its value in terms of the Maslov index. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Vision in click beetles (Coleoptera: Elateridae): pigments and spectral correspondence between visual sensitivity and species bioluminescence emission

Among lampyrids, intraspecific sexual communication is facilitated by spectral correspondence between visual sensitivity and bioluminescence emission from the single lantern in the tail. Could a similar strategy be utilized by the elaterids (click beetles), which have one ventral abdominal and two dorsal prothoracic lanterns? Spectral sensitivity [S(lambda)] and bioluminescence were investigated in four Brazilian click beetle species Fulgeochlizus bruchii, Pyrearinus termitilluminans, Pyrophorus punctatissimus and P. divergens, representing three genera. In addition, in situ microspectrophotometric absorption spectra were obtained for visual and screening pigments in P. punctatissimus and P. divergens species. In all species, the electroretinographic S(lambda) functions showed broad peaks in the green with a shoulder in the near-ultraviolet, suggesting the presence of short- and long-wavelength receptors in the compound eyes. The long-wavelength receptor in Pyrophorus species is mediated by a P540 rhodopsin in conjunction with a species-specific screening pigment. A correspondence was found between green to yellow bioluminescence emissions and its broad S(lambda) maximum in each of the four species. It is hypothesized that in elaterids, bioluminescence of the abdominal lantern is an optical signal for intraspecifc sexual communication, while the signals from the prothoracic lanterns serve to warn predators and may also provide illumination in flight.

Synthesis, spectral studies and X-ray crystal structure of N,N `-(+/-)-trans-1,2-cyclohexylenebis(3-ethoxysalicylideneamine) H-2(t-3-EtOsalchxn)

The synthesis, spectra and X-ray crystal structure of N,N`-(+/-)-trans-1,2-cyclohexylenebis(3-ethoxysalicylideneamine) H-2(t-3-EtOsalchxn), a salen-type ligand, are reported. The Schiff base was characterized by elemental analysis, m.p., IR, electronic spectra, H-1 and C-13 NMR spectra. The spectra are discussed and compared with those of N,N`-(+/-)-trans-1,2-cyclohexylenebis(salicylideneamine), H-2(t-salchxn). The electronic and IR spectra were also resolved by deconvolution. The influence of the ethoxy group on the IR, electronic spectrum, H-1 and C-13 NMR spectra is discussed. Strong intramolecular forces are present as supported by the IR and H-1 NMR spectra and the X-ray crystal structure. An intermolecular hydrogen bond is observed and appears twice in a pair of molecules in the unit cell. (c) 2007 Elsevier B.V. All rights reserved.

Spectral properties of temporally aggregated long memory processes

This paper derives the spectral density function of aggregated long memory processes in light of the aliasing effect. The results are different from previous analyses in the literature and a small simulation exercise provides evidence in our favour. The main result point to that flow aggregates from long memory processes shall be less biased than stock ones, although both retain the degree of long memory. This result is illustrated with the daily US Dollar/ French Franc exchange rate series.

Retrievals of a size parameter for phytoplankton and spectral light absorption by colored detrital matter from water-leaving radiances at SeaWiFS channels in a continental shelf region off Brazil

Many efforts are currently oriented toward extracting more information from ocean color than the chlorophyll a concentration. Among biological parameters potentially accessible from space, estimates of phytoplankton cell size and light absorption by colored detrital matter (CDM) would lead to an indirect assessment of major components of the organic carbon pool in the ocean, which would benefit oceanic carbon budget models. We present here 2 procedures to retrieve simultaneously from ocean color measurements in a limited number of bands, magnitudes, and spectral shapes for both light absorption by CDM and phytoplankton, along with a size parameter for phytoplankton. The performance of the 2 procedures was evaluated using different data sets that correspond to increasing uncertainties: ( 1) measured absorption coefficients of phytoplankton, particulate detritus, and colored dissolved organic matter ( CDOM) and measured chlorophyll a concentrations and ( 2) SeaWiFS upwelling radiance measurements and chlorophyll a concentrations estimated from global algorithms. In situ data were acquired during 3 cruises, differing by their relative proportions in CDM and phytoplankton, over a continental shelf off Brazil. No local information was introduced in either procedure, to make them more generally applicable. Over the study area, the absorption coefficient of CDM at 443 nm was retrieved from SeaWiFS radiances with a relative root mean square error (RMSE) of 33%, and phytoplankton light absorption coefficients in SeaWiFS bands ( from 412 to 510 nm) were retrieved with RMSEs between 28% and 33%. These results are comparable to or better than those obtained by 3 published models. In addition, a size parameter of phytoplankton and the spectral slope of CDM absorption were retrieved with RMSEs of 17% and 22%, respectively. If these methods are applied at a regional scale, the performances could be substantially improved by locally tuning some empirical relationships.

Effects of irradiance and spectral composition on the establishment of macroalgae in streams in southern Brazil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)