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 Ωc such that if Ω = Ω0/ε4 with Ω0 > Ωc, 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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July 2016
Research Article|
July 12 2016
On the third critical speed for rotating Bose-Einstein condensates
M. Correggi;
M. Correggi
1Dipartimento di Matematica e Fisica,
Università degli Studi Roma Tre
, L.go San Leonardo Murialdo, 1, 00146 Rome, Italy
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D. Dimonte
D. Dimonte
2
Scuola Internazionale Superiore di Studi Avanzati
, Via Bonomea, 265, 34136 Trieste, Italy
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J. Math. Phys. 57, 071901 (2016)
Article history
Received:
January 07 2016
Accepted:
June 13 2016
Citation
M. Correggi, D. Dimonte; On the third critical speed for rotating Bose-Einstein condensates. J. Math. Phys. 1 July 2016; 57 (7): 071901. https://doi.org/10.1063/1.4954805
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