Mapping the Wigner distribution function of the Morse oscillator onto a semiclassical distribution function

The mapping of the Wigner distribution function (WDF) for a given bound state onto a semiclassical distribution function (SDF) satisfying the Liouville equation introduced previously by us is applied to the ground state of the Morse oscillator. The purpose of the present work is to obtain values of the potential parameters represented by the number of levels in the case of the Morse oscillator, for which the SDF becomes a faithful approximation of the corresponding WDF. We find that for a Morse oscillator with one level only, the agreement between the WDF and the mapped SDF is very poor but for a Morse oscillator of ten levels it becomes satisfactory. We also discuss the limit h --> 0 for fixed potential parameters.

Effects of oscillatory behavior of the dipole function on the dissociation dynamics of the classical driven Morse oscillator

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

The Morse oscillator generalised from supersymmetry

Using the factorisation method in supersymmetric quantum mechanics the author determines new potentials from the Morse oscillator. This method is applied although the ladder operators are not used.

O oscilador de Morse forçado e a influência do dipolo permanente na dissociação molecular

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Controle da dinâmica caótica do oscilador de morse forçado

In this work, the dissociation dynamics of heteronuclear diatomic molecules is investigated by means of the classical driven Morse oscillator. The interaction of the molecule and the laser field is represented through the product of the molecule dipole function and the electric field of the laser. This interaction may lead to the breaking of the chemical bound, that is, to the dissociation of the molecule. The work was developed in two parts. In the first part, we studied the dissociation as a function of the range of the permanent dipole. In the second part, we maximized the dissociation probability manipulating the parameters of the external field. We have observed that the dissociation can be controlled by means of variations of parameters associated with the range of the permanent dipole

Fotoassociação caótica no oscilador de Morse

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Role of the range of the dipole function in the classical dynamics of molecular dissociation

The dissociation dynamics of heteronuclear diatomic molecules induced by infrared laser pulses is investigated within the framework of the classical driven Morse oscillator. The interaction between the molecule and the laser field described in the dipole formulation is given by the product of a time-dependent external field with a position-dependent permanent dipole function. The effects of changing the spatial range of the dipole function in the classical dissociation dynamics of large ensembles of trajectories are studied. Numerical calculations have been performed for distinct amplitudes and carrier frequencies of the external pulses and also for ensembles with different initial energies. It is found that there exist a set of values of the dipole range for which the dissociation probability can be completely suppressed. The dependence of the dissociation on the dipole range is explained through the examination of the Fourier series coefficients of the dipole function in the angle variable of the free system. In particular, the suppression of dissociation corresponds to dipole ranges for which the Fourier coefficients associated with nonlinear resonances are null and the chaotic region in the phase space is reduced to thin layers. In this context, it is shown that the suppression of dissociation of heteronuclear molecules for certain frequencies of the external field is a consequence of the finite range of the corresponding permanent dipole. © 2013 American Physical Society.

Quantum-classical correspondence and the role of the dipole function in molecular dissociation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Controle de dissociação caótica de moléculas diatômicas

In this work we investigate the dissociation of heteronuclear diatomic molecules subjected to laser pulses. This phenomenon can be modeled by the classical forced Morse oscillator. This system presents a chaotic dynamics associated with the anharmonicity of the internuclear potential and with the coupling of permanent dipole of molecule with the electric field of laser. We want to verify how the dissociation probability evolves while we change the intensity and frequency of laser. We study the phase space of molecules to have a better understanding of system dynamics. We make the calculations changing two parameters of laser (intensity and frequency) and checking how this parameters influences on molecule dissociation. We compare the results of HF molecule (Fluoride acid) and CO molecule (Carbon monoxide) to check how the dipole moment of each molecule can influence on laser interaction

Controle e caos na formação de moléculas com pulso de laser

We investigate the formation of molecules under the action of external field acting during the atomic collision. To describe this process, the collision of atomic pairs, we use the Morse oscillator model driven The study was developed from the standpoint of classical mechanics by analyzing the sensitivity of the system with respect to initial conditions, the verification of chaotic dynamics associated with the process of formation of molecules with laser and analysis of system dynamics and the likelihood of photoassociation in response to the external field parameters

Estudo clássico e quântico da dissociação molecular induzida por laser

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Morse potential energy spectra through the variational method and supersymmetry

The Variational Method is applied within the context of Supersymmetric Quantum Mechanics to provide information about the energy and eigenfunction of the lowest levels of a Hamiltonian. The approach is illustrated by the case of the Morse potential applied to several diatomic molecules and the results are compared with stabilished results. (C) 2000 Elsevier Science B.V.

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)

Dynamic Morse decompositions for semigroups of homeomorphisms and control systems

In this paper, we introduce the concept of dynamic Morse decomposition for an action of a semigroup of homeomorphisms. Conley has shown in [5, Sec. 7] that the concepts of Morse decomposition and dynamic Morse decompositions are equivalent for flows in metric spaces. Here, we show that a Morse decomposition for an action of a semigroup of homeomorphisms of a compact topological space is a dynamic Morse decomposition. We also define Morse decompositions and dynamic Morse decompositions for control systems on manifolds. Under certain condition, we show that the concept of dynamic Morse decomposition for control system is equivalent to the concept of Morse decomposition.

On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator

The fractional generalized Langevin equation (FGLE) is proposed to discuss the anomalous diffusive behavior of a harmonic oscillator driven by a two-parameter Mittag-Leffler noise. The solution of this FGLE is discussed by means of the Laplace transform methodology and the kernels are presented in terms of the three-parameter Mittag-Leffler functions. Recent results associated with a generalized Langevin equation are recovered.