Estudo de sistemas não-lineares em mecânica quântica

The main goal of this work is to investigate the effects of a nonlinear cubic term inserted in the Schrödinger equation for one-dimensional potentials studied in Quantum Mechanics textbooks. Being the main tool the numerical analysis in a large number of works, the analysis of this effect by this term in the potential itself, in order to work with an analytical solution, can be considered something new. For the harmonic oscillator potential, the analysis was made from a numerical method, comparing the result with the known results in the literature. In the case of the infinite well potential and the step potential, hoping to work with an analytical solution, by construction we started with the known wavefunction for the linear case noting the effects in the other physical quantities. The coupling of the physical quantities involved in this work has yielded, besides many complications in the calculations, a series of conditions on the existence and validity of the solutions in regard to the system possible configurations

Teoria quântica da computação

This undergraduate thesis aims formally define aspects of Quantum Turing Machine using as a basis quantum finite automata. We introduce the basic concepts of quantum mechanics and quantum computing through principles such as superposition, entanglement of quantum states, quantum bits and algorithms. We demonstrate the Bell's teleportation theorem, enunciated in the form of Deutsch-Jozsa definition for quantum algorithms. The way as the overall text were written omits formal aspects of quantum mechanics, encouraging computer scientists to understand the framework of quantum computation. We conclude our thesis by listing the Quantum Turing Machine's main limitations regarding the well-known Classical Turing Machines

Oscilador harmônico unidimensional via transformada unilateral de Fourier e mapeamento do potencial de morse unidimensional nos potenciais pseudo-harmônico e de kratzer tridimensionais

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

Estudo de sistemas não-lineares em mecânica quântica

The main goal of this work is to investigate the effects of a nonlinear cubic term inserted in the Schrödinger equation for one-dimensional potentials studied in Quantum Mechanics textbooks. Being the main tool the numerical analysis in a large number of works, the analysis of this effect by this term in the potential itself, in order to work with an analytical solution, can be considered something new. For the harmonic oscillator potential, the analysis was made from a numerical method, comparing the result with the known results in the literature. In the case of the infinite well potential and the step potential, hoping to work with an analytical solution, by construction we started with the known wavefunction for the linear case noting the effects in the other physical quantities. The coupling of the physical quantities involved in this work has yielded, besides many complications in the calculations, a series of conditions on the existence and validity of the solutions in regard to the system possible configurations

BRAZILIAN OFFSHORE WAVE CLIMATE BASED ON NWW3 REANALYSIS

This paper provides a description of the wave climate off the Brazilian coast based on an eleven-year time series (Jan/1997-Dec/2007) obtained from the NWW3 operational model hindcast reanalysis. Information about wave climate in Brazilian waters is very scarce and mainly based on occasional short-term observations, the present analysis being the first covering such temporal and spatial scales. To define the wave climate, six sectors were defined and analyzed along the Brazilian shelf-break: South (W1), Southeast (W2), Central (W3), East (W4), Northeast (W5) and North (W6). W1, W2 and W3 wave regimes are determined by the South Atlantic High (SAH) and the passage of synoptic cold fronts; W4, W5 and W6 are controlled by the Intertropical Convergence Zone (ITCZ) and its meridional oscillation. The most energetic waves are from the S, generated by the strong winds associated to the passage of cold fronts, which mainly affect the southern region. Wave power presents a decrease in energy levels from south to north, with its annual variation showing that the winter months are the most energetic in W1 to W4, while in W5 and W6 the most energetic conditions occur during the austral summer. The information presented here provides boundary conditions for studies related to coastal processes, fundamental for a better understanding of the Brazilian coastal zone.

One-dimensional point interaction with Griffiths' boundary conditions

Griffiths proposed a pair of boundary conditions that define a point interaction in one dimensional quantum mechanics. The conditions involve the nth derivative of the wave function where n is a non-negative integer. We re-examine the interaction so defined and explicitly confirm that it is self-adjoint for any even value of n and for n = 1. The interaction is not self-adjoint for odd n > 1. We then propose a similar but different pair of boundary conditions with the nth derivative of the wave function such that the ensuing point interaction is self-adjoint for any value of n.

Structural refinement, optical and microwave dielectric properties of BaZrO3

In this work, barium zirconate (BaZrO3) ceramics synthesized by solid state reaction method and sintered at 1670 degrees C for 4 h were characterized by X-ray diffraction (XRD), Rietveld refinement, and Fourier transform infrared (FT-IR) spectroscopy. XRD patterns, Rietveld refinement data and FT-IR spectra which confirmed that BaZrO3 ceramics have a perovskite-type cubic structure. Optical properties were investigated by ultraviolet-visible (UV-vis) absorption and photoluminescence (PL) measurements. UV-vis absorption spectra suggested an indirect allowed transition with the existence of intermediary energy levels within the band gap. Intense visible green PL emission was observed in BaZrO3 ceramics upon excitation with a 350 nm wavelength. This behavior is due to a majority of deep defects within the band gap caused by symmetry breaking in octahedral [ZrO6] clusters in the lattice. The microwave dielectric constant and quality factor were measured using the method proposed by Hakki-Coleman. The dielectric resonator antenna (DRA) was investigated experimentally and numerically using a monopole antenna through an infinite ground plane and Ansoft's high frequency structure simulator software, respectively. The required resonance frequency and bandwidth of DRA were investigated by adjusting the dimension of the same material. (C) 2011 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

APTES-Modified RE2O3:Eu3+ Luminescent Beads: Structure and Properties

Europium-doped lanthanide oxide RE2O3:Eu3+ (RE = Y or Gd) luminescent beads, with a spherical shape and a diameter of 150 +/- 15 nm, have been modified by reaction with 3-aminopropyltriethoxysilane (APTES), in order to introduce reactive amine groups at their surfaces. The direct silanation has resulted in the formation of a nanometric layer at the surface of the beads, with an optimum grafting rate of 0.055 +/- 0.005 mol APTES/mol RE2O3. Fourier transform infrared (FTIR) and X-ray photoelectron (XPS) spectroscopies confirmed the condensation of an organosilane layer, made of cross-linked -O-Si-O-Si- and of groups -O-Si-R (with R = (CH2)(3)NH2 or O-Et). Titration of the accessible amine groups has been performed by simultaneously measuring the luminescence of grafted fluorescein isothiocyanate and that of core particles: there are about 2.3 X 10(4) (2.8 X 10(4)) -NH2 per Y2O3:Eu3+ (Gd2O3:Eu3+) bead. The isoelectronic point was shifted by one pH unit after APTES modification. The surface modification by APTES at least preserved (for Gd2O3:Eu3+) or improved (for Y2O3:Eu3+) the red emission of the beads.

The search for a potentially new molecular species, SiAs: A theoretical contribution

Electronic states of a new molecular species, SiAs, correlating with the three lowest dissociation channels are characterized at a high-level of theory using the CASSCF/MRCI approach along with quintuple-xi quality basis sets. This characterization includes potential energy curves, vibrational energy levels, spectroscopic parameters, dipole and transition dipole moment functions, transition probabilities, and radiative lifetimes. For the ground state (X-2 Pi), an assessment of spin-orbit effects and the interaction with the close-lying A(2)Sigma(+) state is also reported. Similarities and differences with other isovalent species such as SiP and CAs are also discussed.

Calculations of the spectral shifts and line profiles of alkaline earth atoms in liquid helium environment

Liquid configurations generated by Metropolis Monte Carlo simulations are used in time-dependent density functional theory calculations of the spectral line shifts and line profiles of the lowest lying excitation of the alkaline earth atoms, Be, Mg, Ca, Sr and Ba embedded in liquid helium. The results are in very good agreement with the available experimental data. Special attention is given to the calculated spectroscopic shift and the associated line broadening. The analysis specifies the inhomogeneous broadening of the three separate contributions due to the splitting of the s -> p transition of the alkaline earth atom in the liquid environment. (C) 2012 Elsevier B. V. All rights reserved.

Rare-earth impurities in gallium nitride: The role of the Hubbard potential

We performed a first principles investigation on the electronic properties of 4f-rare earth substitutional impurities in zincblende gallium nitride (GaN:REGa, with RE=Eu, Gd, Tb, Dy, Ho, Er and Tm). The calculations were performed within the all electron methodology and the density functional theory. We investigated how the introduction of the on-site Hubbard U potential (GGA + U) corrects the electronic properties of those impurities. We showed that a self-consistent procedure to compute the Hubbard potential provides a reliable description on the position of the 4f-related energy levels with respect of the GaN valence band top. The results were compared to available data coming from a recent phenomenological model. (C) 2012 Elsevier B.V. All rights reserved.

Stochastic quantization of the spherical model and supersymmetry.

In this work, we reported some results about the stochastic quantization of the spherical model. We started by reviewing some basic aspects of this method with emphasis in the connection between the Langevin equation and the supersymmetric quantum mechanics, aiming at the application of the corresponding connection to the spherical model. An intuitive idea is that when applied to the spherical model this gives rise to a supersymmetric version that is identified with one studied in Phys. Rev. E 85, 061109, (2012). Before investigating in detail this aspect, we studied the stochastic quantization of the mean spherical model that is simpler to implement than the one with the strict constraint. We also highlight some points concerning more traditional methods discussed in the literature like canonical and path integral quantization. To produce a supersymmetric version, grounded in the Nicolai map, we investigated the stochastic quantization of the strict spherical model. We showed in fact that the result of this process is an off-shell supersymmetric extension of the quantum spherical model (with the precise supersymmetric constraint structure). That analysis establishes a connection between the classical model and its supersymmetric quantum counterpart. The supersymmetric version in this way constructed is a more natural one and gives further support and motivations to investigate similar connections in other models of the literature.

Autoionizing states and their relevance in electron-ion recombination

Atomic physics plays an important role in determining the evolution stages in a wide range of laboratory and cosmic plasmas. Therefore, the main contribution to our ability to model, infer and control plasma sources is the knowledge of underlying atomic processes. Of particular importance are reliable low temperature dielectronic recombination (DR) rate coefficients. This thesis provides systematically calculated DR rate coefficients of lithium-like beryllium and sodium ions via ∆n = 0 doubly excited resonant states. The calculations are based on complex-scaled relativistic many-body perturbation theory in an all-order formulation within the single- and double-excitation coupled-cluster scheme, including radiative corrections. Comparison of DR resonance parameters (energy levels, autoionization widths, radiative transition probabilities and strengths) between our theoretical predictions and the heavy-ion storage rings experiments (CRYRING-Stockholm and TSRHeidelberg) shows good agreement. The intruder state problem is a principal obstacle for general application of the coupled-cluster formalism on doubly excited states. Thus, we have developed a technique designed to avoid the intruder state problem. It is based on a convenient partitioning of the Hilbert space and reformulation of the conventional set of pairequations. The general aspects of this development are discussed, and the effectiveness of its numerical implementation (within the non-relativistic framework) is selectively illustrated on autoionizing doubly excited states of helium.

The incomplete ionization of substitutional dopants in Silicon Carbide

This thesis analyzes theoretically and computationally the phenomenon of partial ionization of the substitutional dopants in Silicon Carbide at thermal equilibrium. It is based on the solution of the charge neutrality equation and takes into account the following phenomena: several energy levels in the bandgap; Fermi-Dirac statistics for free carriers; screening effects on the dopant ionization energies; the formation of impurity bands. A self-consistent model and a corresponding simulation software have been realized. A preliminary comparison of our calculations with existing experimental results is carried out.

Photovoltaics from discotic liquid crystalline HBCs & poly(2,7-carbazole)s

In this study, the use of the discotic liquid crystalline HBCs and conjugated polymers based on 2,7-carbazole were investigated in detail as donor materials in organic bulk-heterojunction solar cells. It has been shown that they perform efficiently in photovoltaic devices in combination with suitable acceptors. The efficiency was found to depend strongly dependent on the morphology of the film. By investigation of a series of donor materials with similar molecular structures based on both discotic molecules and conjugated polymers, a structure-performance relation was established, which is not only instructive for these materials but also serves as a guideline for improved molecular design. For the series of HBCs used in this study, it is found that the device efficiency decreases with increasing length of the alkyl substituents in the HBC. Thus, the derivative with the smallest alkyl mantle, being more crystalline compared to the HBCs with longer alkyl chains, gave the highest EQE of 12%. A large interfacial separation was found in the blend of HBC-C6,2 and PDI, since the crystallization of the acceptor occurred in a solid matrix of HBC. This led to small dispersed organized domains and benefited the charge transport. In contrast, blends of HBC-C10,6/PDI or HBC-C14,10/PDI revealed a rather homogeneous film limiting the percolation pathways due to a mixed phase. For the first time, poly(2,7-carbazole) was incorporated as a donor material in solar cells using PDI as an electron acceptor. The good fit in orbital energy levels and absorption spectra led to high efficiency. This result indicates that conjugated polymers with high band-gap can also be applied as materials to build efficient solar cells if appropriate electron acceptors are chosen. In order to enhance the light absorption ability, new ladder-type polymers based on pentaphenylene and hexaphenylene with one and three nitrogen bridges per repeat unit have been synthesized and characterized. The polymer 2 with three nitrogen bridges showed more red-shifted absorbance and emission and better packing in the solid-state than the analogous polymer 3 with only one nitrogen bridge per monomer unit. An overall efficiency as high as 1.3% under solar light was obtained for the device based on 1 and PDI, compared with 0.7% for the PCz based device. Therefore, the device performance correlates to a large extent with the solar light absorption ability and the lateral distance between conjugated polymer chains. Since the lateral distance is determined by the length and number of attached alkyl side chains, it is possible to assume that these substituents insulate the charge carrier pathways and decrease the device performance. As an additional consequence, the active semiconductor is diluted in the insulating matrix leading to a lower light absorption. This work suggests ways to improve device performance by molecular design, viz. maintaining the HOMO level while bathochromically shifting the absorption by adopting a more rigid ladder-type structure. Also, a high ratio of nitrogen bridges with small alkyl substituents was a desirable feature both in terms of adjusting the absorption and maintaining a low lateral inter-chain separation, which was necessary for obtaining high current and efficiency values.