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Giant Vortex and the Breakdown of Strong Pinning in a Rotating Bose-Einstein Condensate
Authors:Email author" target="_blank">Amandine?AftalionEmail author  Stan?Alama  Lia?Bronsard
Institution:(1) Laboratoire Jacques-Louis Lions & CNRS Université Paris-VI, 175 rue du Chevaleret, 75013 Paris, France;(2) Dept. of Mathematics and Statistics, McMaster University, Hamilton Ontario, Canada, L8S 4K1
Abstract:We consider a two-dimensional model for a rotating Bose-Einstein condensate (BEC) in an anharmonic trap. The special shape of the trapping potential, negative in a central hole and positive in an annulus, favors an annular shape for the support of the wave function u. We study the minimizers of the energy in the Thomas-Fermi limit, where a small parameter ɛ tends to 0, for two different regimes of the rotational speed Ω. When Ω is independent of ɛ, we observe that the energy minimizers acquire vorticity beyond a critical Ω, but the vortices are strongly pinned in the central hole where the potential is negative. In this regime, minimizers exhibit no vortices in the annular bulk of the condensate. There is a critical rotational speed Ω=O(|lnɛ|) for which this strong pinning effect breaks down and vortices begin to appear in the annular bulk. We derive an asymptotic formula for the critical Ω, and determine precisely the location of nucleation of the vortices at the critical value. These results are related to very recent experimental and numerical observations on BEC.
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