Minimal time for the bilinear control of Schrödinger equations

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...

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Bibliographic Details
Main Authors Beauchard, Karine, Coron, Jean-Michel, Teismann, Holger
Format Journal Article
LanguageEnglish
Published 27.01.2014
Subjects
Mathematics - Analysis of PDEs
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DOI10.48550/arxiv.1401.6828

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Summary: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.
DOI:10.48550/arxiv.1401.6828