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Article Dans Une Revue Systems and Control Letters Année : 2014

Minimal time for the bilinear control of Schrödinger equations

Résumé

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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Dates et versions

hal-00936546 , version 1 (26-01-2014)

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Karine Beauchard, Jean-Michel Coron, Holger Teismann. Minimal time for the bilinear control of Schrödinger equations. Systems and Control Letters, 2014, 71, pp.1-6. ⟨10.1016/j.sysconle.2014.06.009⟩. ⟨hal-00936546⟩
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