Small-time bilinear control of Schrödinger equations with application to rotating linear molecules

Abstract

In Duca and Nersesyan (2023), a small-time controllability property of nonlinear Schrödinger equations is proved on a d-dimensional torus Td. In this paper we study a similar property, in the linear setting, starting from a closed Riemannian manifold. We then focus on the 2-dimensional sphere S2, which models the bilinear control of a rotating linear top: as a corollary, we obtain the approximate controllability in arbitrarily small times among particular eigenfunctions of the Laplacian of S2.