Morse basis expansion applied to diatomic molecules

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

Quantum rings of arbitrary shape and non-uniform width in a threading magnetic field

The electronic states of quantum rings with centerlines of arbitrary shape and non-uniform width in a threading magnetic field are calculated. The solutions of the Schrodinger equation with Dirichlet boundary conditions are obtained by a variational separation of variables in curvilinear coordinates. We obtain a width profile that compensates for the main effects of the curvature variations in the centerline. Numerical results are shown for circular, elliptical, and limacon-shaped quantum rings. We also show that smooth and tiny variations in the width may strongly affect the Aharonov-Bohm oscillations.

Modulational instability analysis of surface-waves in the Bénard-Marangoni phenomenon

By using the long-wave approximation, a system of coupled evolutions equations for the bulk velocity and the surface perturbations of a Bénard-Marangoni system is obtained. It includes nonlinearity, dispersion and dissipation, and it is interpreted as a dissipative generalization of the usual Boussinesq system of equations. Then, by considering that the Marangoni number is near the critical value M = -12, we show that the modulation of the Boussinesq waves is described by a perturbed Nonlinear Schrödinger Equation, and we study the conditions under which a Benjamin-Feir instability could eventually set in. The results give sufficient conditions for stability, but are inconclusive about the existence or not of a Benjamin-Feir instability in the long-wave limit. © 1995.

Liquid-gas phase transition in Bose-Einstein condensates with time evolution

We study the effects of a repulsive three-body interaction on a system of trapped ultracold atoms in a Bose-Einstein condensed state. The stationary solutions of the corresponding s-wave nonlinear Schrödinger equation suggest a scenario of first-order liquid-gas phase transition in the condensed state up to a critical strength of the effective three-body force. The time evolution of the condensate with feeding process and three-body recombination losses has a different characteristic pattern. Also, the decay time of the dense (liquid) phase is longer than expected due to strong oscillations of the mean-squared radius.

Chaos in collapsing Bose-condensed gas

We reinvestigate the dynamics of the grow and collapse of Bose-Einstein condensates in a system of trapped ultracold atoms with negative scattering lengths, and found a new behavior in the long time scale evolution: the number of atoms can go far beyond the static stability limit. The condensed state is described by the solution of the time-dependent nonlinear Schrödinger equation, in a model that includes atomic feeding and three-body dissipation. Our results for the model show that, by changing the feeding parameter and when a substantial depletion of the ground-state exists, a chaotic behavior is found. We consider a criterion proposed by Deissler and Kaneko [Phys. Lett. A 119, 397 (1987)] to diagnose spatiotemporal chaos. ©2000 The American Physical Society.

Array of Bose-Einstein condensates under time-periodic Feshbach-resonance management

The investigation of the dynamics of a discrete soliton in an array of Bose-Einstein condensates under the action of a periodically time-modulated atomic scattering length [Feshbach-resonance management (FRM)] was discussed. The slow and rapid modulations, in comparison with the tunneling frequency were considered. An averaged equation, which was a generalized discrete nonlinear Schrödinger equation, including higher-order effective nonlinearities and intersite nonlinear interactions was derived in the case of the rapid modulation. It was demonstrated that the modulations of sufficient strength results in splitting of the soliton by direct simulations.

Comportamento dinâmico não linear e controle de sistemas eletromecânicos em macro e micro escalas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estudo dos métodos de solução da equação de Fokker-Planck linear e não linear

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estudo de uma equação de onda não-linear

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Uma breve discussão sobre os possíveis estados ligados para uma classe de potenciais singulares

Investiga-se a equação de Schrödinger unidimensional com uma classe de potenciais V(|x|) que se anulam no infinito e apresentam singularidade dominante na origem na forma α/|x|β(0 < β < 2). A hermiticidade dos operadores associados com quantidades físicas observáveis é usada para determinar as condições de contorno apropriadas. Dupla degenerescência e exclusão de soluções simétricas, consoante o valor de β, são discutidas. Soluções explícitas para o átomo de hidrogênio e o potencial de Kratzer são apresentadas.

Wide vector solitons in systems with time- and space-modulated nonlinearities

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Mass-Imbalanced Three-Body Systems in 2D: Bound States and the Analytical Approach to the Adiabatic Potential

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

Mid-infrared supercontinuum generation in a suspended-core As2S3 chalcogenide microstructured optical fiber

We demonstrate the supercontinuum (SC) generation in a suspended-core As2S3 chalcogenide microstructured optical fiber (MOF). The variation of SC is investigated by changing the fiber length, pump peak power and pump wavelength. In the case of long fibers (20 and 40 cm), the SC ranges are discontinuous and stop at the wavelengths shorter than 3500 nm, due to the absorption of fiber. In the case of short fibers (1.3 and 2.4 cm), the SC ranges are continuous and can extend to the wavelengths longer than 4 μm. The SC broadening is observed when the pump peak power increases from 0.24 to 1.32 kW at 2500 nm. The SC range increases with the pump wavelength changing from 2200 to 2600 nm, corresponding to the dispersion of As2S3 MOF from the normal to anomalous region. The SC generation is simulated by the generalized nonlinear Schrödinger equation. The simulation includes the SC difference between 1.3 and 2.4 cm long fiber by 2500 nm pumping, the variation of SC with pump peak power in 2.4 cm long fiber, and the variation of SC with pump wavelength in 1.3 cm long fiber. The simulation agrees well with the experiment.

Um estudo sobre a equação de Schrödinger biharmônica

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Weakly bound states of two- and three-boson systems in the crossover from two to three dimensions

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