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arXiv · 1508.07235

On the Third Critical Speed for Rotating Bose-Einstein Condensates

M. Correggi·D. Dimonte
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Abstract

We study a two-dimensional rotating Bose-Einstein condensate confined by an anharmonic trap in the framework of the Gross-Pitaevksii theory. We consider a rapid rotation regime close to the transition to a giant vortex state. It was proven in [M. Correggi {\it et al}, {\it J. Math. Phys. \textbf{53}(2012)] that such a transition occurs when the angular velocity is of order $ \varepsilon ^{-4}$, with $ \varepsilon ^{-2} $ denoting the coefficient of the nonlinear term in the Gross-Pitaevskii functional and $ \varepsilon \ll 1 $ (Thomas-Fermi regime). In this paper we identify a finite value $ Ω_{\mathrm{c}} $ such that, if $ Ω= Ω_0/\varepsilon ^4 $ with $ Ω_0 > Ω_{\mathrm{c}} $, the condensate is in the giant vortex phase. Under the same condition we prove a refined energy asymptotics and an estimate of the winding number of any Gross-Pitaevskii minimizer.

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M. Correggi, D. Dimonte. 2016-07-08. On the Third Critical Speed for Rotating Bose-Einstein Condensates. https://doi.org/10.1063/1.4954805

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