%0 Journal Article %J Correggi, M., Dimonte, D., 2016. On the third critical speed for rotating Bose-Einstein condensates. J. Math. Phys. 57, 71901 %D 2016 %T On the third critical speed for rotating Bose-Einstein condensates %A Daniele Dimonte %A Michele Correggi %X 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. %B Correggi, M., Dimonte, D., 2016. On the third critical speed for rotating Bose-Einstein condensates. J. Math. Phys. 57, 71901 %I AIP Publisher %G en %U http://urania.sissa.it/xmlui/handle/1963/35246 %1 35557 %2 Mathematics %$ Submitted by ddimonte@sissa.it (ddimonte@sissa.it) on 2016-10-19T16:34:31Z No. of bitstreams: 1 1508.07235v4.pdf: 520340 bytes, checksum: e987bbeef8fe09e31b8ea970c4ae4b4b (MD5) %R 10.1063/1.4954805