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

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

URL: http://arxiv.org/abs/2207.03818v2
Date: Tue, 12 Jul 2022 18:02:41 GMT
Title: Small-time bilinear control of Schr\"odinger equations with application to rotating linear molecules
Authors: Thomas Chambrion and Eugenio Pozzoli
Abstract summary: We prove a small-time controllability property of nonlinear Schr"odinger equations on a d-dimensional torus $mathbbTd$. We focus on the 2-dimensional sphere $S2$, which models the bilinear control of a rotating linear top.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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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