Energy spectrum and eigenfunctions through the Quantum Section Method

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

Confinement of spin-0 and spin-1/2 particles in a mixed vector-scalar coupling with unequal shapes for the potentials

The Klein - Gordon and the Dirac equations with vector and scalar potentials are investigated under a more general condition, V-v = V-s + constant. These isospectral problems are solved in the case of squared trigonometric potential functions and bound states for either particles or antiparticles are found. The eigenvalues and eigenfunctions are discussed in some detail. It is revealed that a spin-0 particle is better localized than a spin-1/2 particle when they have the same mass and are subjected to the same potentials.

Local dimension and finite time prediction in spatiotemporal chaotic systems

Predictability is related to the uncertainty in the outcome of future events during the evolution of the state of a system. The cluster weighted modeling (CWM) is interpreted as a tool to detect such an uncertainty and used it in spatially distributed systems. As such, the simple prediction algorithm in conjunction with the CWM forms a powerful set of methods to relate predictability and dimension.

Local dimension and finite time prediction in coupled map lattices

Forecasting, for obvious reasons, often become the most important goal to be achieved. For spatially extended systems (e.g. atmospheric system) where the local nonlinearities lead to the most unpredictable chaotic evolution, it is highly desirable to have a simple diagnostic tool to identify regions of predictable behaviour. In this paper, we discuss the use of the bred vector (BV) dimension, a recently introduced statistics, to identify the regimes where a finite time forecast is feasible. Using the tools from dynamical systems theory and Bayesian modelling, we show the finite time predictability in two-dimensional coupled map lattices in the regions of low BV dimension. © Indian Academy of Sciences.

Quasi-exactly-solvable confining solutions for spin-1 and spin-0 bosons in (1+1)-dimensions with a scalar linear potential

We point out a misleading treatment in the recent literature regarding confining solutions for a scalar potential in the context of the Duffin-Kemmer-Petiau theory. We further present the proper bound-state solutions in terms of the generalized Laguerre polynomials and show that the eigenvalues and eigenfunctions depend on the solutions of algebraic equations involving the potential parameter and the quantum number. (C) 2014 Elsevier Inc. All rights reserved.

Yang-Lee zeros of the two- and three-state Potts model defined on π3 Feynman diagrams

We present both analytical and numerical results on the position of partition function zeros on the complex magnetic field plane of the q=2 state (Ising) and the q=3 state Potts model defined on phi(3) Feynman diagrams (thin random graphs). Our analytic results are based on the ideas of destructive interference of coexisting phases and low temperature expansions. For the case of the Ising model, an argument based on a symmetry of the saddle point equations leads us to a nonperturbative proof that the Yang-Lee zeros are located on the unit circle, although no circle theorem is known in this case of random graphs. For the q=3 state Potts model, our perturbative results indicate that the Yang-Lee zeros lie outside the unit circle. Both analytic results are confirmed by finite lattice numerical calculations.

Estimation of genetic parameters for milk yield in Murrah buffaloes by Bayesian inference

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

General structures of Hamiltonian hierarchies

Three dimensional exactly solvable quantum potentials for which an extra term of form 1/r(2) has been added are shown to maintain their functional form which allows the construction of the Hamiltonian hierarchy and the determination of the spectra of eigenvalues and eigenfunctions within the Supersymmetric Quantum Mechanics formalism. For the specific cases of the harmonic oscillator and the Coulomb potentials, known as pseudo-harmonic oscillator and pseudo-Coulomb potentials, it is shown here that the inclusion of the new term corresponds to rescaling the angular momentum and it is responsible for maintaining their exact solvability.

Vibrational-rotational analysis of the Hulthen potential using hydrogenic eigenfunction bases

Hulthen's potential admits analytical solutions for its energy eigenvalues and eigenfunctions corresponding to zero orbital angular momentum stales, but its non zero angular momentum states are not equally known. This work presents a vibrational-rotational analy sis of Hulthen's potential using hydrogenic eigenfunction bases, which may be of interest and useful to students of quantum mechanics at different stages.

Rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a Lipschitz deformation

We analyze the behavior of solutions of nonlinear elliptic equations with nonlinear boundary conditions of type partial derivative u/partial derivative n + g( x, u) = 0 when the boundary of the domain varies very rapidly. We show that the limit boundary condition is given by partial derivative u/partial derivative n+gamma(x) g(x, u) = 0, where gamma(x) is a factor related to the oscillations of the boundary at point x. For the case where we have a Lipschitz deformation of the boundary,. is a bounded function and we show the convergence of the solutions in H-1 and C-alpha norms and the convergence of the eigenvalues and eigenfunctions of the linearization around the solutions. If, moreover, a solution of the limit problem is hyperbolic, then we show that the perturbed equation has one and only one solution nearby.

VERY RAPIDLY VARYING BOUNDARIES IN EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS. THE CASE of A NON UNIFORMLY LIPSCHITZ DEFORMATION

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

Patterns in parabolic problems with nonlinear boundary conditions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Interaction of pulses in the nonlinear Schrödinger model

A study was conducted on the interaction of two pulses in the nonlinear Schrodinger (NLS) model. The presence of different scenarios of the behavior depending on the initial parameters of the pulses, such as the pulse areas, the relative phase shift, the spatial and frequency separations were shown. It was observed that a pure real initial condition of the NLS equation can result in additional moving solitons.

Variational method for excited states from supersymmetric techniques

We suggest a method for constructing trial eigenfunctions for excited states to be used in the variational method. This method is a generalization of the one that uses a superpotential to obtain the trial functions for the ground state. The construction of an effective hierarchy of Hamiltonians is used to determine excited variational energies. The first four eigenvalues for a quartic double-well potential are calculated for several values of the potential parameter. The results are in very good agreement with the eigenvalues obtained by numerical integration.

Confined systems through variational supersymmetric quantum mechanics

The energy states of the confined harmonic oscillator and the Hulthén potentials are evaluated using the Variational Method associated to Supersymmetric Quantum Mechanics.