# American Institute of Mathematical Sciences

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November  2011, 10(6): 1589-1615. doi: 10.3934/cpaa.2011.10.1589

## Vortex interaction dynamics in trapped Bose-Einstein condensates

 1 Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada Campus de Fuentenueva s/n, 18071 Granada, Spain 2 Nonlinear Physics Group, Departamento de Física Aplicada I, Universidad de Sevilla, 41012 Sevilla, Spain 3 Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany, Germany 4 Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784, Greece 5 Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-9315, United States

Received  July 2010 Revised  May 2011 Published  May 2011

Motivated by recent experiments studying the dynamics of configurations bearing a small number of vortices in atomic Bose-Einstein condensates (BECs), we illustrate that such systems can be accurately described by ordinary differential equations (ODEs) incorporating the precession and interaction dynamics of vortices in harmonic traps. This dynamics is tackled in detail at the ODE level, both for the simpler case of equal charge vortices, and for the more complicated (yet also experimentally relevant) case of opposite charge vortices. In the former case, we identify the dynamics as being chiefly quasi-periodic (although potentially periodic), while in the latter, irregular dynamics may ensue when suitable external drive of the BEC cloud is also considered. Our analytical findings are corroborated by numerical computations of the reduced ODE system.
Citation: Pedro J. Torres, R. Carretero-González, S. Middelkamp, P. Schmelcher, Dimitri J. Frantzeskakis, P.G. Kevrekidis. Vortex interaction dynamics in trapped Bose-Einstein condensates. Communications on Pure & Applied Analysis, 2011, 10 (6) : 1589-1615. doi: 10.3934/cpaa.2011.10.1589
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