Stability of Attractive Bose-Einstein Condensates in a Periodic Potential

Using a standing light wave trap, a stable quasi-one-dimensional attractive dilute-gas Bose-Einstein condensate can be realized. In a mean-field approximation, this phenomenon is modeled by the cubic nonlinear Schr\"odinger equation with attractive nonlinearity and an elliptic function potential of which a standing light wave is a special case. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schr\"odinger equation nor in the integrable nonlinear Schr\"odinger equation. Their stability is examined using analytic and numerical methods. Trivial-phase solutions are experimentally stable provided they have nodes and their density is localized in the troughs of the potential. Stable time-periodic solutions are also examined.Comment: 12 pages, 18 figure

Solutions of Gross-Pitaevskii equations beyond the hydrodynamic approximation: Application to the vortex problem

We develop the multiscale technique to describe excitations of a Bose-Einstein condensate (BEC) whose characteristic scales are comparable with the healing length, thus going beyond the conventional hydrodynamical approximation. As an application of the theory we derive approximate explicit vortex and other solutions. The dynamical stability of the vortex is discussed on the basis of the mathematical framework developed here, the result being that its stability is granted at least up to times of the order of seconds, which is the condensate lifetime. Our analytical results are confirmed by the numerical simulations.Comment: To appear in Phys. Rev.

Explorando Funcionamientos De La Lectura. Polémicas En El Discurso De La Física Y Sus Implicaciones Para La Enseñanza

A study of functioning of the polemic mechanism proposed by Dominique Maingueneau (1997) using divergent texts reading was held during Physics' teachers training course in a São Paulo's State University (Brazil). It has intended to mediate conceptual displacements in students' notions on Energy. In Discourse Analysis toward discursive heterogeneity, Maingueneau assume the polemic as a sort of correlation between discourses in interaction, in which theirs identities are reciprocally constituted. In this case a discourse builds a simulacrum of the other, emphasizing its' points where the interdiscoursiveness is based. Taking this theoretical supports, we have analyzed a situation on Physics and its teaching: the association between Classic Physic - Dynamic and Thermodynamic of equilibrium - and Physic of complexes systems implicated in Thermodynamic of no-equilibrium proposed by Prigogine. Our analysis and the students' work have been supported in two texts, one of which brings a discourse polemic to the other. We have shown that the text that expresses this polemic puts across the theory from which some elements are omitted in name of the disagreement in theory's teaching. We also discuss the implications of such communication of those hidden elements in scientific education associated to reading and comprehension of theory and concepts on Physics and on Science. So, we have found that the polemic mechanism constitute a synchronic representation valuable to describe the learning process through divergent reading in Physics classes.49SUPPL. 34043Bachelard, G., (1974) A Filosofia do Não. In: Os Pensadores. São Paulo: Abril SA., 38, p. 159. , Racionalismo aplicado, Rio de Janeiro: Zahar EditoresPrigogine, I., Stengers, I., (1997) A Nova Aliança, , Brasília: Editora UnBOrlandi, E., (1996) A Linguagem e Seu Funcionamento. As Formas do Discurso, , Campinas: PontesMaingueneau, D., (1997) Novas Tendências em Análise do Discurso, , Campinas/SP: Pontes: UNICAMPPêcheux, M., (1995) Semântica e Discurso. Uma Crítica à Afirmação do Óbvio, , Campinas: UNICAMPFeynmann, R., (1999) Física em Seis Lições, p. 115. , Rio de Janeiro, Editoria