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Dynamics of vortex dipoles in confined Bose-Einstein condensates |
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| Authors: | P.J. TorresP.G. Kevrekidis,D.J. FrantzeskakisR. Carretero-Gonzá lez,P. SchmelcherD.S. Hall |
| Affiliation: | a Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain b Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, USA c Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 157 84, Greece d Nonlinear Dynamical System Group,11http://nlds.sdsu.edu. Computational Science Research Center, and Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720, USA e Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany f Department of Physics, Amherst College, Amherst, MA 01002-5000, USA |
| Abstract: | We present a systematic theoretical analysis of the motion of a pair of straight counter-rotating vortex lines within a trapped Bose-Einstein condensate. We introduce the dynamical equations of motion, identify the associated conserved quantities, and illustrate the integrability of the ensuing dynamics. The system possesses a stationary equilibrium as a special case in a class of exact solutions that consist of rotating guiding-center equilibria about which the vortex lines execute periodic motion; thus, the generic two-vortex motion can be classified as quasi-periodic. We conclude with an analysis of the linear and nonlinear stability of these stationary and rotating equilibria. |
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