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On the third critical speed for rotating Bose-Einstein condensates (2016)

M. Correggi and D. Dimonte

American Institute of Physics (AIP)

In: Journal of Mathematical Physics

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Publication Date: 2016-07-13

Description: We study a two-dimensional rotating Bose-Einstein condensate confined by an anharmonic trap in the framework of the Gross-Pitaevskii theory. We consider a rapid rotation regime close to the transition to a giant vortex state. It was proven in Correggi et al. [J. Math. Phys. 53 , 095203 (2012)] that such a transition occurs when the angular velocity is of order ε −4 , with ε −2 denoting the coefficient of the nonlinear term in the Gross-Pitaevskii functional and ε ≪ 1 (Thomas-Fermi regime). In this paper, we identify a finite value Ω c such that if Ω = Ω 0 /ε 4 with Ω 0 〉 Ω 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.

Print ISSN: 0022-2488

Electronic ISSN: 1089-7658

Topics: Mathematics , Physics

Published by American Institute of Physics (AIP)

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