Computation of Ground States of the Gross--Pitaevskii Functional via Riemannian Optimization

In this paper we combine concepts from Riemannian optimization [P.-A. Absil, R. Mahony, and R. Sepulchre, Optimization Algorithms on Matrix Manifolds, Princeton University Press, 2008] and the theory of Sobolev gradients [J. W. Neuberger, Sobolev Gradients and Differential Equation, 2nd ed., Springer, 2010] to derive a new conjugate gradient method for direct minimization of the Gross--Pitaevskii energy functional with rotation. The …