A study about the solutions of Schrödinger equation with an asymptotically linear potential

We determine the solutions of the Schrödinger equation for an asymptotically linear potential. Analytical solutions are obtained by superalgebra in quantum mechanics and we establish when these solutions are possible. Numerical solutions for the spectra are obtained by the shifted 1/N expansion method.

Dissipative three-wave structures in stimulated backscattering. I. A subluminous solitary attractor

We present a solitary solution of the three-wave nonlinear partial differential equation (PDE) model - governing resonant space-time stimulated Brillouin or Raman backscattering - in the presence of a cw pump and dissipative material and Stokes waves. The study is motivated by pulse formation in optical fiber experiments. As a result of the instability any initial bounded Stokes signal is amplified and evolves to a subluminous backscattered Stokes pulse whose shape and velocity are uniquely determined by the damping coefficients and the cw-pump level. This asymptotically stable solitary three-wave structure is an attractor for any initial conditions in a compact support, in contrast to the known superluminous dissipative soliton solution which calls for an unbounded support. The linear asymptotic theory based on the Kolmogorov-Petrovskii-Piskunov assertion allows us to determine analytically the wave-front slope and the subluminous velocity, which are in remarkable agreement with the numerical computation of the nonlinear PDE model when the dynamics attains the asymptotic steady regime. © 1997 The American Physical Society.

Optical properties of chromium-doped fluoroindate glasses

This work reports on the optical properties of Cr3+ ions in the pseudoternary system InF3-GdF3-GaF3. Linear properties, investigated through absorption and emission spectra, provide information on the crystal field, the frequency, and number of phonons emitted during the absorption to the 4T2 band and the emission to the 4A2 ground state, and the Fano antiresonance line shape in the vicinity of the 4A2→2E transition. A study of the nonlinear refractive index as a function of the wavelength, carried out with the Z-scan technique, provides spectroscopic data about electronic transitions starting from the excited state.

Giant non-linear absorption in Er3+-doped fluoroindate glass

Non-linear absorption is observed in Er3+-doped fluoroindate glass (in mol% 37InF2:20ZnF2:20SrF2:16BaF2:2GdF2: 2NaF:1GaF3:2ErF3) when the sample is irradiated with a CW laser emitting at 650 nm. An intensity dependence of the optical transmittance is detected. Saturation and sequential absorption of two photons are responsible for the decrease of 50% in the transmittance. The results are explained by simple models which are solved based on rate-equations for the populations of energy levels.

Quantum scattering in one dimension

A self-contained discussion of non-relativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three dimensions. The present discussion illustrates in a simple way the concepts of partial-wave decomposition, phase shift, optical theorem and effective-range expansion.

Direct signals for large extra dimensions in the production of fermion pairs at linear colliders

We analyze the potential of the next generation of e+e- linear colliders to search for large extra dimensions via the production of fermion pairs in association with Kaluza-Klein gravitons (G), i.e., e+e- →ff̃G. This process leads to a final state exhibiting a significant amount of missing energy in addition to acoplanar lepton or jet pairs. We study in detail this reaction using the full tree level contributions due to the graviton emission and the standard model backgrounds. After choosing the cuts to enhance the signal, we show that a linear collider with a center-of-mass energy of 500 GeV will be able to probe quantum gravity scales from 0.96 (0.86) up to 4.1 (3.3) TeV at a 2 (5)σ level, depending on the number of extra dimensions. ©2001 The American Physical Society.

Effect of a heat-treatment on the linear dimensional change of a hard chairside reline resin

Statement of problem. Little data are available regarding the effect of heat-treatments on the dimensional stability of hard chairside reline resins. Purpose. The objective of this in vitro study was to evaluate whether a heat-treatment improves the dimensional stability of the reline resin Duraliner II and to compare the linear dimensional changes of this material with the heat-polymerized acrylic resin Lucitone 550. Material and methods. The materials were mixed according to the manufacturer's instructions and packed into a stainless steel split mold (50.0 mm diameter and 0.5 mm thickness) with reference points (A, B, C, and D). Duraliner II specimens were polymerized for 12 minutes in water at 37°C and bench cooled to room temperature before being removed from the mold. Twelve specimens were made and divided into 2 groups: group 1 specimens (n=6) were left untreated, and group 2 specimens (n=6) were submitted to a heat-treatment in a water bath at 55°C for 10 minutes and then bench cooled to room temperature. The 6 Lucitone specimens (control group) were polymerized in a water bath for 9 hours at 71°C. The specimens were removed after the mold reached the room temperature. A Nikon optical comparator was used to measure the distances between the reference points (AB and CD) on the stainless steel mold (baseline readings) and on the specimens to the nearest 0.001 mm. Measurements were made after processing and after the specimens had been stored in distilled water at 37°C for 8 different periods of time. Data were subjected to analysis of variance with repeated measures, followed by Tukey's multiple comparison test (P<.05). Results. All specimens exhibited shrinkage after processing (control, -0.41%; group 1, -0.26%; and group 2, -0.51%). Group 1 specimens showed greater shrinkage (-1.23%) than the control (-0.23%) and group 2 (-0.81%) specimens after 60 days of storage in water (P<.05). Conclusion. Within the limitations of this study, a significant improvement of the long-term dimensional stability of the Duraliner II reline resin was observed when the specimens were heat-treated. However, the shrinkage remained considerably higher than the denture base resin Lucitone 550. Copyright © 2002 by The Editorial Council of The Journal of Prosthetic Dentistry.

Dynamic analysis of a new piezoelectric flextensional actuator using the J1-J4 optical interferometric method

Piezoelectric actuators are widely used in positioning systems which demand high resolution such as scanning microscopy, fast mirror scanners, vibration cancellation, cell manipulation, etc. In this work a piezoelectric flextensional actuator (PFA), designed with the topology optimization method, is experimentally characterized by the measurement of its nanometric displacements using a Michelson interferometer. Because this detection process is non-linear, adequate techniques must be applied to obtain a linear relationship between an output electrical signal and the induced optical phase shift. Ideally, the bias phase shift in the interferometer should remain constant, but in practice it suffers from fading. The J1-J4 spectral analysis method provides a linear and direct measurement of dynamic phase shift in a no-feedback and no-phase bias optical homodyne interferometer. PFA application such as micromanipulation in biotechnology demands fast and precise movements. So, in order to operate with arbitrary control signals the PFA must have frequency bandwidth of several kHz. However as the natural frequencies of the PFA are low, unwanted dynamics of the structure are often a problem, especially for scanning motion, but also if trajectories have to be followed with high velocities, because of the tracking error phenomenon. So the PFA must be designed in such a manner that the first mechanical resonance occurs far beyond this band. Thus it is important to know all the PFA resonance frequencies. In this work the linearity and frequency response of the PFA are evaluated up to 50 kHz using optical interferometry and the J1-J4 method.

Detecção de bordas em imagens digitais através de um processo de difusão anisotrópica não linear

The edges detection model by a non-linear anisotropic diffusion, consists in a mathematical model of smoothing based in Partial Differential Equation (PDE), alternative to the conventional low-pass filters. The smoothing model consists in a selective process, where homogeneous areas of the image are smoothed intensely in agreement with the temporal evolution applied to the model. The level of smoothing is related with the amount of undesired information contained in the image, i.e., the model is directly related with the optimal level of smoothing, eliminating the undesired information and keeping selectively the interest features for Cartography area. The model is primordial for cartographic applications, its function is to realize the image preprocessing without losing edges and other important details on the image, mainly airports tracks and paved roads. Experiments carried out with digital images showed that the methodology allows to obtain the features, e.g. airports tracks, with efficiency.

Localization of a Bose-Einstein condensate in a bichromatic optical lattice

By direct numerical simulation of the time-dependent Gross-Pitaevskii equation, we study different aspects of the localization of a noninteracting ideal Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasiperiodic optical-lattice potential. Such a quasiperiodic potential, used in a recent experiment on the localization of a BEC, can be formed by the superposition of two standing-wave polarized laser beams with different wavelengths. We investigate the effect of the variation of optical amplitudes and wavelengths on the localization of a noninteracting BEC. We also simulate the nonlinear dynamics when a harmonically trapped BEC is suddenly released into a quasiperiodic potential, as done experimentally in a laser speckle potential. We finally study the destruction of the localization in an interacting BEC due to the repulsion generated by a positive scattering length between the bosonic atoms. © 2009 The American Physical Society.

Coupling rate measurement of a novel multi-actuated piezoelectric device using optical interferometry

The class of piezoelectric actuators considered in this paper consists of a multi-flexible structure actuated by two or more piezoceramic devices that must generate different output displacements and forces at different specified points of the domain and in different directions. The devices were modeled by finite element using the software ANSYS and the topology optimization method. The following XY actuators were build to achieve maximum displacement in the X and Y directions with a minimum crosstalk between them. The actuator prototypes are composed of an aluminum structure, manufactured by using a wire Electrical Discharge Machining, which are bonded to rectangular PZT5A piezoceramic blocks by using epoxy resin. Multi-actuator piezoelectric device displacements can be measured by using optical interferometry, since it allows dynamic measurements in the kHz range, which is of the order of the first resonance frequency of these piezomechanisms. A Michelson-type interferometer, with a He-Ne laser source, is used to measure the displacement amplitudes in nanometric range. A new optical phase demodulation technique is applied, based on the properties of the triangular waveform drive voltage applied to the XY piezoelectric nanopositioner. This is a low-phase-modulation-depth-like technique that allows the rapid interferometer auto-calibration. The measurements were performed at 100 Hz frequency, and revealed that the device is linear voltage range utilized in this work. The ratio between the generated and coupled output displacements and the drive voltages is equal to 10.97 nm/V and 1.76 nm/V, respectively, which corresponds to a 16% coupling rate. © 2010 IEEE.

The role of Bi2O3 on the thermal, structural, and optical properties of tungsten-phosphate glasses

Glasses in the ternary system (70 - x)NaPO3-30WO 3-xBi2O3, with x = 0-30 mol %, were prepared by the conventional melt-quenching technique. X-ray diffraction (XRD) measurements were performed to confirm the noncrystalline nature of the samples. The influence of the Bi2O3 on the thermal, structural, and optical properties was investigated. Differential scanning calorimetry analysis showed that the glass transition temperature, Tg, increases from 405 to 440 C for 0 ≤ x ≤ 15 mol % and decreases to 417 C for x = 30 mol %. The thermal stability against devitrification decreases from 156 to 67 C with the increase of the Bi2O3 content. The structural modifications were studied by Raman scattering, showing a bismuth insertion into the phosphate chains by Bi-O-P linkage. Furthermore, up to 15 mol % of Bi 2O3 formation of BiO6 clusters is observed, associated with Bi-O-Bi linkage, resulting in a progressive break of the linear phosphate chains that leads to orthophosphate Q0 units. The linear refractive index, n0, was measured using the prism-coupler technique at 532, 633, and 1550 nm, whereas the nonlinear (NL) refractive index, n 2 was measured at 1064 nm using the Z-scan technique. Values of 1.58 ≤ n0 ≤ 1.88, n2 ≥ 10-15 cm 2/W and NL absorption coefficient, α2 ≤ 0.01 cm/GW, were determined. The linear and NL refractive indices increase with the increase of the Bi2O3 concentration. The large values of n0 and n2, as well as the very small α2, indicate that these materials have large potential for all-optical switching applications in the near-infrared. © 2012 American Chemical Society.

Sending classical information through relativistic quantum channels

We investigate how special relativity influences the transmission of classical information through quantum channels by evaluating the Holevo bound when the sender and the receiver are in (relativistic) relative motion. By using the spin degrees of freedom of spin-1/2 fermions to encode the classical information, we show that, for some configurations, the accessible information in the receiver can be increased when the spin detector moves fast enough. This is possible by allowing the momentum wave packet of one of the particles to be sufficiently wide while the momentum wave packets of other particles are kept relatively narrow. In this way, one can take advantage of the fact that boosts entangle the spin and momentum degrees of freedom of spin-1/2 fermions to increase the accessible information in the former. We close the paper with a discussion of how this relativistic quantum channel cannot in general be described by completely positive quantum maps. © 2013 American Physical Society.

A combined theoretical and experimental study of electronic structure and optical properties of β-ZnMoO4 microcrystals

In this paper, a combined theoretical and experimental study on the electronic structure and photoluminescence (PL) properties of beta zinc molybdate (β-ZnMoO4) microcrystals synthesized by the hydrothermal method has been employed. These crystals were structurally characterized by X-ray diffraction (XRD), Rietveld refinement, Fourier transform Raman (FT-Raman) and Fourier transform infrared (FT-IR) spectroscopies. Their optical properties were investigated by ultraviolet-visible (UV-Vis) absorption spectroscopy and PL measurements. First-principles quantum mechanical calculations based on the density functional theory at the B3LYP level have been carried out. XRD patterns, Rietveld refinement, FT-Raman and FT-IR spectra showed that these crystals have a wolframite-type monoclinic structure. The Raman and IR frequencies experimental results are in reasonable agreement with theoretically calculated results. UV-Vis absorption measurements shows an optical band gap value of 3.17 eV, while the calculated band structure has a value of 3.22 eV. The density of states indicate that the main orbitals involved in the electronic structure of β-ZnMoO4 crystals are (O 2p-valence band and Mo 4d-conduction band). Finally, PL properties of β-ZnMoO4 crystals are explained by means of distortions effects in octahedral [ZnO6] and [MoO6] clusters and inhomogeneous electronic distribution into the lattice with the electron density map. © 2013 Elsevier Ltd. All rights reserved.

Local electronic structure, optical bandgap and photoluminescence (PL) properties of Ba(Zr0.75Ti0.25)O3 powders

Ba(Zr0.75Ti0.25)O3 (BZT-75/25) powders were synthesized by the polymeric precursor method. Samples were structurally characterized by X-ray diffraction (XRD), Rietveld refinement, X-ray absorption near-edge structure (XANES) and extended X-ray absorption fine structure (EXAFS) techniques. Their electronic structures were evaluated by first-principle quantum mechanical calculations based on density functional theory at the B3LYP level. Their optical properties were investigated by ultraviolet-visible (UV-Vis) spectroscopy and photoluminescence (PL) measurements at room temperature. XRD patterns and Rietveld refinement data indicate that the samples have a cubic structure. XANES spectra confirm the presence of pyramidal [TiO5] clusters and octahedral [TiO6] clusters in the disordered BZT-75/25 powders. EXAFS spectra indicate distortion of Ti-O and Ti-O-Ti bonds the first and second coordination shells, respectively. UV-Vis absorption spectra confirm the presence of different optical bandgap values and the band structure indicates an indirect bandgap for this material. The density of states demonstrates that intermediate energy levels occur between the valence band (VB) and the conduction band (CB). These electronic levels are due to the predominance of 4d orbitals of Zr atoms in relation to 3d orbitals of Ti atoms in the CB, while the VB is dominated by 2p orbitals related to O atoms. There was good correlation between the experimental and theoretical optical bandgap values. When excited at 482 nm at room temperature, BZT-75/25 powder treated at 500 C for 2 h exhibited broad and intense PL emission with a maximum at 578 nm in the yellow region. © 2013 Elsevier Ltd. All rights reserved.