Sparse one-dimensional discrete Dirac operators II: Spectral properties

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

Estatística não-extensiva aplicada ao cálculo do calor específico eletrônico em estruturas quasiperiódicas

Systems whose spectra are fractals or multifractals have received a lot of attention in recent years. The complete understanding of the behavior of many physical properties of these systems is still far from being complete because of the complexity of such systems. Thus, new applications and new methods of study of their spectra have been proposed and consequently a light has been thrown on their properties, enabling a better understanding of these systems. We present in this work initially the basic and necessary theoretical framework regarding the calculation of energy spectrum of elementary excitations in some systems, especially in quasiperiodic ones. Later we show, by using the Schr¨odinger equation in tight-binding approximation, the results for the specific heat of electrons within the statistical mechanics of Boltzmann-Gibbs for one-dimensional quasiperiodic systems, growth by following the Fibonacci and Double Period rules. Structures of this type have already been exploited enough, however the use of non-extensive statistical mechanics proposed by Constantino Tsallis is well suited to systems that have a fractal profile, and therefore our main objective was to apply it to the calculation of thermodynamical quantities, by extending a little more the understanding of the properties of these systems. Accordingly, we calculate, analytical and numerically, the generalized specific heat of electrons in one-dimensional quasiperiodic systems (quasicrystals) generated by the Fibonacci and Double Period sequences. The electronic spectra were obtained by solving the Schr¨odinger equation in the tight-binding approach. Numerical results are presented for the two types of systems with different values of the parameter of nonextensivity q

Efeitos interfaciais em heteroestruturas quânticas nô-abruptas: GaAs/ALxGa1-xAs

Um minuncioso estudo das propriedades de confinamento em heterostructuras bidimensionais(poços quânticos) GaAs/AlxGa1_xAs, com interfaces graduais é realizado. Um modelo teórico que represente bem a variação da fração molar do alumínio nas interfaces, resultante do aparecimento de micro-rugosidades e ilhas durante os processos de crescimento e recozimento pós-crescimento da amostra, é elaborado. Vários perfis desta fração molar de alumínio nas interfaces são considerados. Soluções analíticas da equação de Schrodinger, na aproximação da massa efetiva constatne nas interfaces, resultando em equações transcendentais, que possibilitam a obtenção dos níveis de energia dos portadores, decorrentes do seu confinamento quântico, são apresentadas. Energias de ligação e de confinamento de excitons 2D, utilizando-se um método analítico e numerérico e a aproximação do potencial efetivo, são também calculadas. Resultados numéricos para os níveis de energia dos portadores e para as energias de ligação e de confinamento dos excitons 2D, em poços quânticos GaAs/Al0.35Ga0.65As não-abruptos, sem e com a presença de campo elétrico aplicado para vários perfis interfaciais da fração de molar, são mostrados. Para a obtenção desses resultados, faz-se uso do método dos degraus múltiplos e da técnica da matriz de transferência, e adota-se, como operador de energia cinética, o de Ben-Daniel e Duque para uma massa efetiva dependente da posição. Conclui-se que um modelo que leva em conta a existência de interfaces não-abruptas e seus diversos perfis é indispensável para uma melhor descrição das propriedades opto-eletrônicas de poços quânticos GaAs/AlxGa1-xAs, enquanto que a aproximação das interfaces abruptas apresenta-se bastante limitada

Position-dependent effective mass Dirac equations with PT-symmetric and non-PT-symmetric potentials

We present a new procedure to construct the one-dimensional non-Hermitian imaginary potential with a real energy spectrum in the context of the position-dependent effective mass Dirac equation with the vector-coupling scheme in 1 + 1 dimensions. In the first example, we consider a case for which the mass distribution combines linear and inversely linear forms, the Dirac problem with a PT-symmetric potential is mapped into the exactly solvable Schrodinger-like equation problem with the isotonic oscillator by using the local scaling of the wavefunction. In the second example, we take a mass distribution with smooth step shape, the Dirac problem with a non-PT-symmetric imaginary potential is mapped into the exactly solvable Schrodinger-like equation problem with the Rosen-Morse potential. The real relativistic energy levels and corresponding wavefunctions for the bound states are obtained in terms of the supersymmetric quantum mechanics approach and the function analysis method.

Orthogonality criterion for banishing hydrino states from standard quantum mechanics

Orthogonality criterion is used to show in a very simple and general way that anomalous bound-state solutions for the Coulomb potential (hydrino states) do not exist as bona fide solutions of the Schrodinger, Klein-Gordon and Dirac equations. (C) 2007 Elsevier B.V. All rights reserved.

Scattering and bound states of spinless particles in a mixed vector-scalar smooth step potential

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Real spectra for the non-Hermitian Dirac equation in 1+1 dimensions with the most general coupling

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Propriedades termo-eletrônicas da molécula do DNA

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Transporte eletrônico e propriedades termodinâmicas de nanobiomoléculas

We use a tight-binding formulation to investigate the transmissivity and the currentvoltage (I_V) characteristics of sequences of double-strand DNA molecules. In order to reveal the relevance of the underlying correlations in the nucleotides distribution, we compare theresults for the genomic DNA sequence with those of arti_cial sequences (the long-range correlated Fibonacci and RudinShapiro one) and a random sequence, which is a kind of prototype of a short-range correlated system. The random sequence is presented here with the same _rst neighbors pair correlations of the human DNA sequence. We found that the long-range character of the correlations is important to the transmissivity spectra, although the I_V curves seem to be mostly inuenced by the short-range correlations. We also analyze in this work the electronic and thermal properties along an _-helix sequence obtained from an _3 peptide which has the uni-dimensional sequence (Leu-Glu-Thr- Leu-Ala-Lys-Ala)3. An ab initio quantum chemical calculation procedure is used to obtain the highest occupied molecular orbital (HOMO) as well as their charge transfer integrals, when the _-helix sequence forms two di_erent variants with (the so-called 5Q variant) and without (the 7Q variant) _brous assemblies that can be observed by transmission electron microscopy. The di_erence between the two structures is that the 5Q (7Q) structure have Ala ! Gln substitution at the 5th (7th) position, respectively. We estimate theoretically the density of states as well as the electronic transmission spectra for the peptides using a tight-binding Hamiltonian model together with the Dyson's equation. Besides, we solve the time dependent Schrodinger equation to compute the spread of an initially localized wave-packet. We also compute the localization length in the _nite _-helix segment and the quantum especi_c heat. Keeping in mind that _brous protein can be associated with diseases, the important di_erences observed in the present vi electronic transport studies encourage us to suggest this method as a molecular diagnostic tool

MATHEMATICA notebook for computing tetrahedral finite element shape functions and matrices for the Helmholtz equation

A MATHEMATICA notebook to compute the elements of the matrices which arise in the solution of the Helmholtz equation by the finite element method (nodal approximation) for tetrahedral elements of any approximation order is presented. The results of the notebook enable a fast computational implementation of finite element codes for high order simplex 3D elements reducing the overheads due to implementation and test of the complex mathematical expressions obtained from the analytical integrations. These matrices can be used in a large number of applications related to physical phenomena described by the Poisson, Laplace and Schrodinger equations with anisotropic physical properties.

Thermodynamics of a Peyrard-Bishop One-Dimensional Lattice with On-site Hump Potential

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Solutions of the Fokker-Planck equation for a Morse isospectral potential

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Variational supersymmetric approach to evaluate Fokker-Planck probability

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A General Solution of the Fokker-Planck Equation

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A new type of confinement for the Morse potential

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