ANOMALIES OF VARIATIONAL PHASE-SHIFTS

It is demonstrated, contrary to various claims, that the phase shifts calculated via variational principles involving the Green function may exhibit anomalous behavior. These anomalies may appear in variational principles for the K matrix (Schwinger variational principle) of potential V, for (K-V) (Kohn-type and Newton variational principles), and other variational principles of higher order (Takatsuka-McKoy variational principle).

PHONON-SPECTRA OF RANDOMLY DISORDERED SYSTEM

We study the phonon density of states of a three dimensional disordered mixed crystal NaCl(x)Br1-x. The phonon structure is obtained by using a cluster method based on a continued fraction expansion of the Green function. The proposed dynamic model includes only short range interactions (first and second neighbors) but supports some qualitative features of the constituents binary alloys.

Design de nanodispositivos eletroluminescentes baseados no ALQ3

Neste trabalho reportamos a investigação teórica da solvatação dos isômeros do tris- (8-idroxiquinolinolato) de alumínio III – Alq3, as propriedades eletroluminescentes na solvatação de Alq3 em líquidos orgânicos como metanol, etanol, dimetilformamida (DMF) e acetonitrila, a fim de se entender a dependência na variação de ambientes do sistema, aperfeiçoando o funcionamento de filmes transportadores em dispositivos eletroluminescentes do tipo OLED (Organic Light-Emitting Diodes) e por fim investigamos o mecanismo do transporte eletrônico no Alq3 aplicando uma baixa corrente elétrica na molécula e evidenciando as curvas corrente-voltagem característica do dispositivo. A simulação consiste na aplicação do método sequencial Monte Carlo / Mecânica quântica (S-MC/MQ), que parte de um tratamento inicial estocástico para separação das estruturas mais prováveis de menor energia e posteriormente com um tratamento quântico para plotar os espectros eletrônicos das camadas de solvatação separadas através do método ZINDOS/S. Nas propriedades elétricas do transporte utilizamos o método da função de Green de não equilíbrio acoplado a teoria do funcional densidade (DFT) inferindo que as ramificações mais externas correspondentes aos anéis no Alq3 seriam terminais para o translado eletrônico. Nossos resultados mostraram que a média dos espectros de absorção para solvatação do Alq3 em soluções sofre um desvio mínimo com a mudança de ambiente, estando em ótimo acordo com os resultados experimentais da literatura; e as curvas I-V confirmaram o comportamento diodo do dispositivo, corroborando com os sentidos mais pertinentes quanto aos terminais no Alq3 para se ter um transporte eletrônico satisfatório.

Caracterização de polímeros unidimensionais (Poliacetileno, Poliazina e Poliazoeteno) através de cálculos espectroscópicos e transporte eletrônico

Neste trabalho é apresentado um estudo teórico da base neutro e bipolaron e estados excitados de moléculas a partir de polímeros isoeletrônicos compostos pelo Poliacetileno, Poliazina e Poliazoeteno. Os resultados obtidos, utilizando metodologia DFT e ab initio, revelam que uma boa descrição dos defeitos pode ser importante na investigação da transição isolante-metal de polímeros quase-unidimensional indicando um comportamento metálico em torno do nível de Fermi, como mecanismo de condutividade dos polímeros. Este resultado é consistente com dados experimentais e não faz menção a metodologia Su-Schrieffer-Heeger (SSH). E mais, os resultados são consistentes com características importantes como nanodispositivo e podem ser resumidos como: (i) poderia ser usado como retificador molecular uni-direcional com uma geometria conformacional com vantagem de pequeno acoplamento, (ii) a função de Green de não-equilíbrio presente na simulação poderia corrigir de tal maneira os Poliacetileno, Poliazina e Poliazoeteno sem corrente de porta, (iii) com base nas propriedades das ligações tipo, pode ser utilizada para projetar dispositivos com aplicações em eletrônica molecular.

Transporte eletrônico e quiralidade molecular: um estudo de dispositivos orgânicos em sistemas de dois terminais

No presente trabalho, investigamos o transporte eletrônico molecular em dois compostos orgânicos, o Ponceau SS (PSS) e o Oligo-(para)fenileno-vinileno (PPV) através de cálculos ab initio e função de Green de não equilíbrio (FGNE). Estes métodos demonstraram equivalência para a descrição destes dispositivos moleculares. Fizemos cálculos quânticos para o Hamiltoniano derivado de Hartree-Fock (HF) e obtivemos as propriedades de corrente-voltagem (I-V) para as duas estruturas moleculares. Com o método FGNE conseguimos modelar o transporte através de um sistema de multiníveis eletrônicos obtendo a corrente descrevendo as regiões de ressonância e a assimetria do sistema. Como resposta o PSS demonstrou assimetria para polarizações direta e reversa e a ressonância é alcançada mostrando que o dispositivo opere como um transistor molecular bi-direcional. Para o PPV investigamos também as propriedades geométricas através da conexão entre transporte eletrônico e o grau de quiralidade molecular que foi calculado usando o índice quiral que depende apenas das posições atômicas. Obtivemos que moléculas quirais e propriedades estruturais podem induzir uma assimetria no transporte eletrônico, resultando num processo de retificação. Também obtivemos que a resposta elétrica (I-V) e momento de dipolo elétrico são proporcionais ao grau de quiralidade molecular. Estes resultados sugerem que o transporte eletrônico neste sistema pode ser explorado na avaliação do seu grau de quiralidade.

Migração Kirchhoff pré-empilhamento em profundidade modificada usando o operador de feixes gaussianos

A teoria dos feixes gaussianos foi introduzida na literatura sísmica no início dos anos 80 por pesquisadores russos e tchecos, e foi originalmente utilizada no cálculo do campo de ondas eletromagnéticas, baseado na teoria escalar da difração. Na teoria dos feixes gaussianos, o campo de ondas sísmicas é obtido por uma integral, cujo o integrando é constituído de duas partes, a saber: (1) as amplitudes dos campos das ondas na vizinhança do ponto de observação e (2) a função fase de cada um desses campos de ondas, que neste caso é representada por um tempo de trânsito paraxial complexo. Como ferramenta de imageamento, mais precisamente como operador de migração, os primeiros trabalhos usando feixes gaussianos datam do final da década de 80 e início dos anos 90. A regularidade dos campos de ondas descritos pelos feixes gaussianos, além de sua alta precisão em regiões singulares do modelo de velocidades, tornaram o uso de feixes gaussianos como uma alternativa híbrida viável para a migração. Nesse trabalho, unimos a flexibilidade da migração tipo Kirchhoff em profundidade em verdadeira amplitude com a regularidade da descrição do campo de ondas, representado pela sobreposição de feixes gaussianos. Como forma de controlar de forma estável quantidades usadas na construção de feixes gaussianos, utilizamos informações advindas do volume de Fresnel, mais precisamente a zona de Fresnel ao redor do ponto de reflexão e a zona de Fresnel projetada, localizada ao redor do ponto de registro do sismograma e cuja a informação se encontra nas curvas de reflexão de dados sísmico. Nosso processo de migração pode ser chamado como uma migração Kirchhoff em verdadeira amplitude usando um operador de feixes gaussianos.

A quantum theory for the excitation spectrum of a rectangular Andreev billiard

We consider a N - S box system consisting of a rectangular conductor coupled to a superconductor. The Green functions are constructed by solving the Bogoliubov-de Gennes equations at each side of the interface, with the pairing potential described by a step-like function. Taking into account the mismatch in the Fermi wave number and the effective masses of the normal metal - superconductor and the tunnel barrier at the interface, we use the quantum section method in order to find the exact energy Green function yielding accurate computed eigenvalues and the density of states. Furthermore, this procedure allow us to analyze in detail the nontrivial semiclassical limit and examine the range of applicability of the Bohr-Sommerfeld quantization method.

Algebraic solution of an anisotropic nonquadratic potential

We show that an anisotropic nonquadratic potential, for which a path integral treatment has been recently discussed in the literature, possesses the SO(2, 1) ⊗SO(2, 1) ⊗SO(2, 1) dynamical symmetry, and construct its Green function algebraically. A particular case which generates new eigenvalues and eigenfunctions is also discussed. © 1990.

Algebraic solution of an anisotropic ring-shaped oscillator

Using an algebraic technique related to the SO (2, 1) group we construct the Green function for the potential ar2 + b(r sin θ)-2 + c(r cos θ)-2 + dr2 sin2θ + er2 cos2θ. The energy spectrum and the normalized wave functions are also obtained. © 1990.

Refined Estimation of Earthquake Source Parameters: Methods, Applications and Scaling Relationships

The objective of this work of thesis is the refined estimations of source parameters. To such a purpose we used two different approaches, one in the frequency domain and the other in the time domain. In frequency domain, we analyzed the P- and S-wave displacement spectra to estimate spectral parameters, that is corner frequencies and low frequency spectral amplitudes. We used a parametric modeling approach which is combined with a multi-step, non-linear inversion strategy and includes the correction for attenuation and site effects. The iterative multi-step procedure was applied to about 700 microearthquakes in the moment range 1011-1014 N•m and recorded at the dense, wide-dynamic range, seismic networks operating in Southern Apennines (Italy). The analysis of the source parameters is often complicated when we are not able to model the propagation accurately. In this case the empirical Green function approach is a very useful tool to study the seismic source properties. In fact the Empirical Green Functions (EGFs) consent to represent the contribution of propagation and site effects to signal without using approximate velocity models. An EGF is a recorded three-component set of time-histories of a small earthquake whose source mechanism and propagation path are similar to those of the master event. Thus, in time domain, the deconvolution method of Vallée (2004) was applied to calculate the source time functions (RSTFs) and to accurately estimate source size and rupture velocity. This technique was applied to 1) large event, that is Mw=6.3 2009 L’Aquila mainshock (Central Italy), 2) moderate events, that is cluster of earthquakes of 2009 L’Aquila sequence with moment magnitude ranging between 3 and 5.6, 3) small event, i.e. Mw=2.9 Laviano mainshock (Southern Italy).

Potential Analysis for Hypoelliptic Second Order PDEs with Nonnegative Characteristic Form

In this Thesis we consider a class of second order partial differential operators with non-negative characteristic form and with smooth coefficients. Main assumptions on the relevant operators are hypoellipticity and existence of a well-behaved global fundamental solution. We first make a deep analysis of the L-Green function for arbitrary open sets and of its applications to the Representation Theorems of Riesz-type for L-subharmonic and L-superharmonic functions. Then, we prove an Inverse Mean value Theorem characterizing the superlevel sets of the fundamental solution by means of L-harmonic functions. Furthermore, we establish a Lebesgue-type result showing the role of the mean-integal operator in solving the homogeneus Dirichlet problem related to L in the Perron-Wiener sense. Finally, we compare Perron-Wiener and weak variational solutions of the homogeneous Dirichlet problem, under specific hypothesis on the boundary datum.

Quantum transport in a single molecular junction

The craze for faster and smaller electronic devices has never gone down and this has always kept researchers on their toes. Following Moore’s law, which states that the number of transistors in a single chip will double in every 18 months, today “30 million transistors can fit into the head of a 1.5 mm diameter pin”. But this miniaturization cannot continue indefinitely due to the ‘quantum leakage’ limit in the thickness of the insulating layer between the gate electrode and the current carrying channel. To bypass this limitation, scientists came up with the idea of using vastly available organic molecules as components in an electronic device. One of the primary challenges in this field was the ability to perform conductance measurements across single molecular junctions. Once that was achieved the focus shifted to a deeper understanding of the underlying physics behind the electron transport across these molecular scale devices. Our initial theoretical approach is based on the conventional Non-Equilibrium Green Function(NEGF) formulation, but the self-energy of the leads is modified to include a weighting factor that ensures negligible current in the absence of a molecular pathway as observed in a Mechanically Controlled Break Junction (MCBJ) experiment. The formulation is then made parameter free by a more careful estimation of the self-energy of the leads. The calculated conductance turns out to be atleast an order more than the experimental values which is probably due to a strong chemical bond at the metal-molecule junction unlike in the experiments. The focus is then shifted to a comparative study of charge transport in molecular wires of different lengths within the same formalism. The molecular wires, composed of a series of organic molecules, are sanwiched between two gold electrodes to make a two terminal device. The length of the wire is increased by sequentially increasing the number of molecules in the wire from 1 to 3. In the low bias regime all the molecular devices are found to exhibit Ohmic behavior. However, the magnitude of conductance decreases exponentially with increase in length of the wire. In the next study, the relative contribution of the ‘in-phase’ and the ‘out-of-phase’ components of the total electronic current under the influence of an external bias is estimated for the wires of three different lengths. In the low bias regime, the ‘out-of-phase’ contribution to the total current is minimal and the ‘in-phase’ elastic tunneling of the electrons is responsible for the net electronic current. This is true irrespective of the length of the molecular spacer. In this regime, the current-voltage characteristics follow Ohm’s law and the conductance of the wires is found to decrease exponentially with increase in length which is in agreement with experimental results. However, after a certain ‘off-set’ voltage, the current increases non-linearly with bias and the ‘out-of-phase’ tunneling of electrons reduces the net current substantially. Subsequently, the interaction of conduction electrons with the vibrational modes as a function of external bias in the three different oligomers is studied since they are one of the main sources of phase-breaking scattering. The number of vibrational modes that couple strongly with the frontier molecular orbitals are found to increase with length of the spacer and the external field. This is consistent with the existence of lowest ‘off-set’ voltage for the longest wire under study.

Self-consistent theory of atomic Fermi gases with a Feshbach resonance at the superfluid transition

A self-consistent theory is derived to describe the BCS-Bose-Einstein-condensate crossover for a strongly interacting Fermi gas with a Feshbach resonance. In the theory the fluctuation of the dressed molecules, consisting of both preformed Cooper pairs and bare Feshbach molecules, has been included within a self-consistent T-matrix approximation, beyond the Nozieres and Schmitt-Rink strategy considered by Ohashi and Griffin. The resulting self-consistent equations are solved numerically to investigate the normal-state properties of the crossover at various resonance widths. It is found that the superfluid transition temperature T-c increases monotonically at all widths as the effective interaction between atoms becomes more attractive. Furthermore, a residue factor Z(m) of the molecule's Green function and a complex effective mass have been determined to characterize the fraction and lifetime of Feshbach molecules at T-c. Our many-body calculations of Z(m) agree qualitatively well with recent measurments of the gas of Li-6 atoms near the broad resonance at 834 G. The crossover from narrow to broad resonances has also been studied.

Functional integral bosonization for an impurity in a Luttinger liquid

We use a functional integral formalism developed earlier for the pure Luttinger liquid (LL) to find an exact representation for the electron Green function of the LL in the presence of a single backscattering impurity in the low-temperature limit. This allows us to reproduce results (well known from the bosonization techniques) for the suppression of the electron local density of states (LDOS) at the position of the impurity and for the Friedel oscillations at finite temperature. In addition, we have extracted from the exact representation an analytic dependence of LDOS on the distance from the impurity and shown how it crosses over to that for the pure LL.

On Majorization for Matrices

In this paper, we give several results for majorized matrices by using continuous convex function and Green function. We obtain mean value theorems for majorized matrices and also give corresponding Cauchy means, as well as prove that these means are monotonic. We prove positive semi-definiteness of matrices generated by differences deduced from majorized matrices which implies exponential convexity and log-convexity of these differences and also obtain Lypunov's and Dresher's type inequalities for these differences.