In a previous article with A. Aftalion and X. Blanc, it was shown that the hypercontractivity property of the dilation semigroup in spaces of entire functions was a key ingredient in the study of the Lowest Landau Level model for fast rotating Bose–Einstein condensates. That former work was concerned with the stationary constrained variational problem. This article is about the nonlinear Hamiltonian dynamics and the spectral stability of the constrained minima with motivations arising from the description of Tkatchenko modes of Bose–Einstein condensates. Again the hypercontractivity property provides a very strong control of the nonlinear term in the dynamical analysis.
Exact lowest-Landau-level solutions for vortex precession in Bose-Einstein condensates