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arXiv · 2207.03818

Small-time bilinear control of Schr\"odinger equations with application to rotating linear molecules

Thomas Chambrion·Eugenio Pozzoli
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Abstract

In [14] Duca and Nersesyan proved a small-time controllability property of nonlinear Schr\"odinger equations on a d-dimensional torus $\mathbb{T}^d$. 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 $S^2$, 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 $S^2$.

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Thomas Chambrion, Eugenio Pozzoli. 2022-07-08. Small-time bilinear control of Schr\"odinger equations with application to rotating linear molecules. https://arxiv.org/abs/2207.03818

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