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arXiv · 1401.6828

Minimal time for the bilinear control of Schrödinger equations

Karine Beauchard·Jean-Michel Coron·Holger Teismann
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Abstract

We consider a quantum particle in a potential V (x) (x in R^N) subject to a (spatially homogeneous) time-dependent electric field E(t), which plays the role of the control. Under generic assumptions on V, this system is approximately controllable on the L2(R^N;C)-sphere, in su ffiently large times T, as proved by Boscain, Caponigro, Chambrion and Sigalotti. In the present article, we show that this approximate controllability result is false in small time. As a consequence, the result by Boscain et al. is, in some sense, optimal with respect to the control time T.

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Karine Beauchard, Jean-Michel Coron, Holger Teismann. 2014-01-27. Minimal time for the bilinear control of Schrödinger equations. https://arxiv.org/abs/1401.6828

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