Expansion of a Bose-Einstein condensate formed on a joint harmonic and one-dimensional optical-lattice potential

We study the expansion of a Bose-Einstein condensate trapped in a combined optical-lattice and axially-symmetric harmonic potential using the numerical solution of the mean-field Gross-Pitaevskii equation. First, we consider the expansion of such a condensate under the action of the optical-lattice potential alone. In this case the result of numerical simulation for the axial and radial sizes during expansion is in agreement with two experiments by Morsch et al (2002 Phys. Rev. A 66 021601(R) and 2003 Laser Phys. 13 594). Finally, we consider the expansion under the action of the harmonic potential alone. In this case the oscillation, and the disappearance and revival of the resultant interference pattern is in agreement with the experiment by Muller et al (2003 J. Opt. B: Quantum Semiclass. Opt. 5 S38).

On energy transfer between linear and nonlinear oscillators

In this paper energy transfer in a dissipative mechanical system is analysed. Such system is composed of a linear and a nonlinear oscillator with a nonlinearizable cubic stiffness. Depending on initial conditions, we find energy transfer either from linear to nonlinear oscillator (energy pumping) or from nonlinear to linear. Such results are valid for two different potentials. However, under resonance and absence of external excitation, if the mass of the nonlinear oscillator is adequately small then the linear oscillator always loses energy. Our approach uses rigorous Regular Perturbation Theory. Besides, we have included the case of two linear oscillators under linear or cubic interactions. Comparisons with the earlier case are made. (c) 2008 Elsevier Ltd. All rights reserved.

On the effects of system parameters on the response of a harmonically excited system consisting of weakly coupled nonlinear and linear oscillators

This paper discusses the dynamic behaviour of a nonlinear two degree-of-freedom system consisting of a harmonically excited linear oscillator weakly connected to a nonlinear attachment having linear and cubic restoring forces. The effects of the system parameters on the shape of the frequency-response curve are investigated, in particular those yielding the appearance and disappearance of outer and inner detached resonance curves. In contrast to the case when the linear stiffness of the attachment is zero, it is found that multivaluedness occurs at low frequencies as the resonant peak bends to the right. It is also found that as the coefficient of the linear term increases, the range of parameters yielding detached curves reduces. Compared to the case when the attached system has no linear stiffness term, this range of parameters corresponds to smaller values of the damping and nonlinear coefficients. Approximate analytical expressions for the jump-up and jump-down frequencies of the system under investigation are also derived. (C) 2011 Elsevier Ltd. All rights reserved.

Exact propagator beyond and at caustics for isotropic time-dependent coupled and driven oscillators

Through a sequence of transformations we relate the propagator for the system of isotropic time-dependent, coupled and driven oscillators with time-varying mass, with those of free particles. We then derive the wave functions and the propagator beyond and at caustics. Finally we study a particular case which appears in quantum optics. © 1990.

On the quantum mechanical propagator for driven coupled harmonic oscillators

The exact propagator beyond and at caustics for a pair of coupled and driven oscillators with different frequencies and masses is calculated using the path-integral approach. The exact wavefunctions and energies are also presented. Finally the propagator is re-calculated through an alternative method, using the δfunction. © 1992 IOP Publishing Ltd.

A virtual experiment for the detection of specific features in the frequency response of a coupled nonlinear and linear oscillator

This paper presents an investigation into some practical issues that may be present in a real experiment, when trying to validate the theoretical frequency response curve of a two degree-of-freedom nonlinear system consisting of coupled linear and nonlinear oscillators. Some specific features, such as detached resonance curves, have been theoretically predicted in multi degree-of-freedom nonlinear oscillators, when subject to harmonic excitation, and the system parameters have been shown to be fundamental in achieving such features. When based on a simplified model, approximate analytical expression for the frequency response curves may be derived, which may be validated by the numerical solutions. In a real experiment, however, the practical achievability of such features was previously shown to be greatly affected by small disturbances induced by gravity and inertia, which led to some solutions becoming unstable which had been predicted to be stable. In this work a practical system configuration is proposed where such effects are reduced so that the previous limitations are overcome. A virtual experiment is carried out where a detailed multi-body model of the oscillator is assembled and the effects on the system response are investigated.

Harmonical oscillator and electro-mechanical analogy: an interdiscinary experiment to high precision mass variation measurements

De forma geral, os cursos de física clássica oferecidos nas universidades carecem de exemplos de aplicações nas áreas de química e biologia, o que por vezes desmotivam os alunos de graduação destas áreas a estudarem os conceitos físicos desenvolvidos em sala de aula. Neste texto, a analogia entre os osciladores elétrico e mecânico é explorada visando possívies aplicações em química e biologia, mostrando-se de grande valia devido ao seu uso em técnicas de medição de variação de massa com alta precisão, tanto de forma direta como indireta. Estas técnicas são conhecidas como técnicas eletrogravimétricas e são de especial importância em aplicações que envolvem biossensores. Desta forma, o texto explora o estudo da analogia eletromecânica de forma interdisciplinar envolvendo as áreas de física, química e biologia. Baseado nessa analogia é proposto um experimento que permite a sua aplicação em diferentes níveis conceituais dessas disciplinas, tanto em abordagem básica como mais profunda.

THE PARTITION-FUNCTION FOR AN ANYON-LIKE OSCILLATOR

We compute the partition function of an anyon-like harmonic oscillator. The well known results for both the bosonic and fermionic oscillators are then re-obtained as particular cases of our function. The technique we employ is a non-relativistic version of the Green function method used in the computation of one-loop effective actions of quantum field theory.

Mean-field model for Josephson oscillation in a Bose-Einstein condensate on an one-dimensional optical trap

Using the axially-symmetric time-dependent Gross-Pitaevskii equation we study the phase coherence in a repulsive Bose-Einstein condensate (BEC) trapped by a harmonic and an one-dimensional optical lattice potential to describe the experiment by Cataliotti et al. on atomic Josephson oscillation [Science 293, 843 (2001)]. The phase coherence is maintained after the BEC is set into oscillation by a small displacement of the magnetic trap along the optical lattice. The phase coherence in the presence of oscillating neutral current across an array of Josephson junctions manifests in an interference pattern formed upon free expansion of the BEC. The numerical response of the system to a large displacement of the magnetic trap is a classical transition from a coherent superfluid to an insulator regime and a subsequent destruction of the interference pattern in agreement With the more recent experiment by Cataliotti et al. [New J. Phys. 5, 71 (2003)].

On an Active Control for a Structurally Nonlinear Mechanical System, Taking Into Account an Energy Pumping

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

Forced oscillations with continuum models of atomic force microscopy

The dynamics of the AFM-atomic force microscope follows a model based in a Timoshenko cantilever beam with a tip attached at the free end and acting with the surface of a sample. General boundary conditions arise when the tip is either in contact or non-contact with the surface. The governing equations are given in matrix conservative form subject to localized loads. The eigenanalysis is done with a fundamental matrix response of a damped second-order matrix differential equation. Forced responses are found by using a Galerkin approximation of the matrix impulse response. Simulations results with harmonic and pulse forcing show the filtering character and the effects of the tip-sample interaction at the end of the beam. © 2012 American Institute of Physics.

A metáfora do Bogatyr: o corpo acrobata e a cena russa no início do século XX

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

Long-Lasting Oscillations in the Electro-Oxidation of Formic Acid on PtSn Intermetallic Surfaces

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Novel expert system for defining power quality compensators

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

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.