Speaker
Description
This talk addresses the computation of ground states of multicomponent Bose-Einstein condensates, defined as the global minimizer of an energy functional on an infinite -dimensional generalized oblique manifold. We establish the existence of the ground state and characterize it as the solution to a coupled nonlinear eigenvector problem. By equipping the manifold with several Riemannian metrics, we introduce a suite of Riemannian gradient descent and Riemannian Newton methods. Metrics that incorporate first- or second-order information about the energy are particularly advantageous, effectively preconditioning the resulting methods. For a Riemannian gradient descent method with an energy-adaptive metric, we provide a qualitative global and quantitative local convergence analysis, confirming its reliability and robustness with respect to the choice of spatial discretization. Numerical experiments highlight the computational efficiency of both the Riemannian gradient descent and Newton methods.
