Fortran programs for the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

C programs for solving the time-dependent Gross-Pitaevskii equation in a fully anisotropic trap

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

Asymptotic solutions to the Gross-Pitaevskii gain equation: Growth of a Bose-Einstein condensate

We give an asymptotic analytic solution for the generic atom-laser system with gain in a D-dimensional trap, and show that this has a non-Thomas-Fermi behavior. The effect is due to Bose-enhanced condensate growth, which creates a local-density maximum and a corresponding outward momentum component. In addition, the solution predicts amplified center-of-mass oscillations, leading to enhanced center-of-mass temperature.

The problems of the european union film industry: an evolution from "subsidy trap" to the advent of "virtual print fee" model

Dissertação de Mestrado, Gestão de Empresa (MBA), 16 de Julho de 2013, Universidade dos Açores.

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)].

Relaxation algorithm to hyperbolic states in Gross-Pitaevskii equation

A new version of the relaxation algorithm is proposed in order to obtain the stationary ground-state solutions of nonlinear Schrodinger-type equations, including the hyperbolic solutions. In a first example, the method is applied to the three-dimensional Gross-Pitaevskii equation, describing a condensed atomic system with attractive two-body interaction in a non-symmetrical trap, to obtain results for the unstable branch. Next, the approach is also shown to be very reliable and easy to be implemented in a non-symmetrical case that we have bifurcation, with nonlinear cubic and quintic terms. (c) 2006 Elsevier B.V. All rights reserved.

Evolution of a collapsing and exploding Bose-Einstein condensate in different trap symmetries

Based on the time-dependent Gross-Pitaevskii equation we study the evolution of a collapsing and exploding Bose-Einstein condensate in different trap symmetries to see the effect of confinement on collapse and subsequent explosion, which can be verified in future experiments. We make a prediction for the evolution of the shape of the condensate and the number of atoms in it for different trap symmetries (cigar to pancake) as well as in the presence of an optical lattice potential. We also make a prediction for the jet formation in different cases when the collapse is suddenly terminated by changing the scattering length to zero via a Feshbach resonance. In addition to the usual global collapse to the center of the condensate, in the presence of an optical-lattice potential one could also have in certain cases independent collapse of parts of the condensate to local centers, which could be verified in experiments.

Numerical solution of the two-dimensional Gross-Pitaevskii equation for trapped interacting atoms

We present a numerical scheme for solving the time-independent nonlinear Gross-Pitaevskii equation in two dimensions describing the Bose-Einstein condensate of trapped interacting neutral atoms at zero temperature. The trap potential is taken to be of the harmonic-oscillator type and the interaction both attractive and repulsive. The Gross-Pitaevskii equation is numerically integrated consistent with the correct boundary conditions at the origin and in the asymptotic region. Rapid convergence is obtained in all cases studied. In the attractive case there is a limit Co the maximum number of atoms in the condensate. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

Mean-field model for the interference of matter-waves from a three-dimensional optical trap

Using the mean-field time-dependent Gross-Pitaevskii equation we study the formation of a repulsive Bose-Einstein condensate on a combined optical and harmonic traps in two and three dimensions and subsequent generation of the interference pattern upon the removal of the combined traps as in the experiment by, Greiner et al. [Nature (London 415 (2002) 39]. For optical traps of moderate strength, interference pattern of 27 (9) prominent bright spots is found to be formed in three. (two) dimensions on a cubic (square) lattice in agreement with experiment. Similar interference pattern can also be formed upon removal of the optical lattice trap only. The pattern so formed can oscillate for a long time in the harmonic trap which can be observed experimentally. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Collapse of attractive Bose-Einstein condensed vortex states in a cylindrical trap

The quantized vortex states of a weakly interacting Bose-Einstein condensate of atoms with attractive interatomic interaction in an axially symmetric harmonic oscillator trap are investigated using the numerical solution of the time-dependent Gross-Pitaevskii equation obtained by the semi-implicit Crank-Nicholson method. The collapse of the condensate is studied in the presence of deformed traps with the larger frequency along either the radial or the axial direction. The critical number of atoms for collapse is calculated as a function of the vortex quantum number L. The critical number increases with increasing angular momentum L of the cortex state but tends to saturate for large L.

Numerical study of the spherically symmetric Gross-Pitaevskii equation in two space dimensions

The Gross-Pitaevskii equation for Bose-Einstein condensation (BEC) in two space dimensions under the action of a harmonic oscillator trap potential for bosonic atoms with attractive and repulsive interparticle interactions was numerically studied by using time-dependent and time-independent approaches. In both cases, numerical difficulty appeared for large nonlinearity. Nonetheless, the solution of the time-dependent approach exhibited intrinsic oscillation with time iteration which is independent of space and time steps used in discretization.

The dynamics of bright matter wave solitons in a quasi one-dimensional Bose-Einstein condensate with a rapidly varying trap

The dynamics of a bright matter wave soliton in a quasi one-dimensional Bose-Einstein condensate (BEC) with a periodically rapidly varying time trap is considered. The governing equation is based on averaging the fast modulations of the Gross-Pitaevskii (GP) equation. This equation has the form of a GP equation with an effective potential of a more complicated structure than an unperturbed trap. In the case of an inverted (expulsive) quadratic trap corresponding to an unstable GP equation, the effective potential can be stable. For the bounded space trap potential it is showed that bifurcation exists, i.e. the single-well potential bifurcates to the triple-well effective potential. The stabilization of a BEC cloud on-site state in the temporary modulated optical lattice is found. This phenomenon is analogous to the Kapitza stabilization of an inverted pendulum. The analytical predictions of the averaged GP equation are confirmed by numerical simulations of the full GP equation with rapid perturbations.

Beyond the ‘Tomlinson Trap’: Analysing the Effectiveness of Section 1 of the Compensation Act 2006

One of the intentions underpinning section 1 of the Compensation Act 2006 was to provide reassurance to individual volunteers, and voluntary organisations, involved in what the provision called ‘desirable activities’ and including sport. The perception was that such volunteers, motivated by an apprehension about their increased vulnerability to negligence liability, and as driven by a fear of a wider societal compensation culture, were engaging excessively in risk-averse behaviour to the detriment of such socially desirable activities. Academic commentary on section 1 of the Compensation Act 2006 has largely regarded the provision as unnecessary and doing little more than restating existing common law practice. This article argues otherwise and, on critically reviewing the emerging jurisprudence, posits the alternative view that section 1, in practice, affords an enhanced level of protection and safeguarding for individuals undertaking functions in connection with a desirable activity. Nonetheless, the occasionally idiosyncratic judicial interpretation given to term ‘desirable activity’, potentially compounded by recent enactment of the Social Action, Responsibility and Heroism Act 2015, remains problematic. Two points of interest will be used to inform this debate. First, an analysis of the then House of Lords’ decision in Tomlinson and its celebrated ‘balancing exercise’ when assessing reasonableness in the context of negligence liability. Second, a fuller analysis of the application of section 1 in the specific context of negligence actions relating to the coaching of sport where it is argued that the, albeit limited, jurisprudence might support the practical utility of a heightened evidential threshold of gross negligence.

Gross anatomical features of the oropharyngeal cavity of the ostrich (Struthio camelus)

Most descriptions of the ostrich oropharynx and oesophagus are superficial and supply little meaningful morphological data. The aim of this investigation is describe the ostrich oropharingeal cavity, in order to supply the deficiency of macroscopic data about this important animal. Five heads of 12 to 14-month-old ostriches of either sex were anatomically dissected to expose the oropharynx. The ostrich oropharynx was "bell-shaped" composed by the maxillary and mandibular ramphoteca. The roof and floor presented two distinct regions different in colour of the mucosa. The rostral region was pale pink contrasting to creamy-pink coloured caudal region. The median longitudinal ridge extended rostrally from the apex of the choana to the tip of the beak in the roof and it is clearly more prominent and rigid than the homolog in the floor that appeared thin and stretched rostrally, continuing caudally surrounding the tongue and the laryngeal mound eventually merging with the oesophageal mucosa. The floor was formed by the interramal region, tongue and laryngeal mound containing shield-shaped glottis. It can be concluded that the present study, in addition to confirming the basic features of the oropharynx previously described for the ostrich, clarified the contradictory information presented in the literature and also provided new, unreported morphological data, some of which may be important when studying nutrition and health in these birds.

Trap-nesting bees (Hymenoptera: Apoidea) in forest fragments of the State of Sao Paulo, Brazil

We studied the community ecology of trap-nesting bees in two forest fragments of the State of Sao Paulo, Brazil, during two years, utilizing bamboo canes and tubes made of black cardboard as trap nests. The traps were inspected once a month with an otoscope. One hundred and fifteen nests were obtained at Estacao Ecologica de Paulo de Faria, Paulo de Faria (EEPF). These included nine species belonging to five genera and two families. At Santa Cecilia Farm (SCF), 12 species belonging to seven genera and three families built 392 nests. Natural enemies reared from nests of both areas included Hymenoptera, Diptera and Coleoptera. Species richness was similar between the areas but the communities differed considerably in species composition. The higher diversity found at EEPF was due to more even distribution of the species. No difference was observed between the numbers of nests built in each year in each area. Although the species richness was lower in the cool/dry season of both years at SCF, and in the first year at EEPF, the nesting frequencies did not differ between seasons for both the overall community but for each of the most abundant species. No annual fluctuation in the frequencies of nesting was observed. As temperature and precipitation were not found to be significantly different between the two years of study in each area, we concluded that climatic stability resulted in population stability.