Computational and Applied Mathematics seminar

Abstract: Ground states of multicomponent Bose-Einstein condensates can be described as minimizers of the Gross-Pitaevskii energy functional on an infinite-dimensional manifold. For the computation of these minimizers, we investigate a family of Riemannian optimization methods with respect to different metrics. This allows a unified treatment of several algorithms under a common framework and enables us to prove global and local convergence guarantees for important cases. Finally, we also discuss extensions to rotating condensates, where uniqueness can no longer be guaranteed.