@article {1809.03586, title = {On some rigorous aspects of fragmented condensation}, year = {2018}, url = {https://arxiv.org/abs/1809.03586}, author = {Daniele Dimonte and Marco Falconi and Alessandro Olgiati} } @article {2016, title = {On the third critical speed for rotating Bose-Einstein condensates}, journal = {Correggi, M., Dimonte, D., 2016. On the third critical speed for rotating Bose-Einstein condensates. J. Math. Phys. 57, 71901}, number = {Journal of Mathematical Physics;57}, year = {2016}, publisher = {AIP Publisher}, abstract = {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.}, doi = {10.1063/1.4954805}, url = {http://urania.sissa.it/xmlui/handle/1963/35246}, author = {Daniele Dimonte and Michele Correggi} }