Minimal time for the bilinear control of Schrödinger equations

We consider a quantum particle in a potential V(x) (x∈RN) 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(RN,C)-sphere, in sufficiently large times T, as...

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Bibliographic Details
Published inSystems & control letters Vol. 71; pp. 1 - 6
Main Authors Beauchard, Karine, Coron, Jean-Michel, Teismann, Holger
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.09.2014
Elsevier
Subjects
Analysis of PDEs
Mathematics
Minimal time
Quantum control
Schrödinger equation
Minimal time
Schrödinger equation
Quantum control
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ISSN0167-6911
1872-7956
1872-7956
DOI10.1016/j.sysconle.2014.06.009

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Summary:We consider a quantum particle in a potential V(x) (x∈RN) 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(RN,C)-sphere, in sufficiently large times T, as proved by Boscain, Caponigro, Chambrion and Sigalotti (2012). 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.
ISSN:0167-6911
1872-7956
1872-7956
DOI:10.1016/j.sysconle.2014.06.009