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Article Dans Une Revue Journal de Mathématiques Pures et Appliquées Année : 2015

Simultaneous global exact controllability of an arbitrary number of 1D bilinear Schrödinger equations

Résumé

We consider a system of an arbitrary number of \textsc{1d} linear Schrödinger equations on a bounded interval with bilinear control. We prove global exact controllability in large time of these $N$ equations with a single control. This result is valid for an arbitrary potential with generic assumptions on the dipole moment of the considered particle. Thus, even in the case of a single particle, this result extends the available literature. The proof combines local exact controllability around finite sums of eigenstates, proved with Coron's return method, a global approximate controllability property, proved with Lyapunov strategy, and a compactness argument.
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hal-00837645 , version 1 (24-06-2013)

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Morgan Morancey, Vahagn Nersesyan. Simultaneous global exact controllability of an arbitrary number of 1D bilinear Schrödinger equations. Journal de Mathématiques Pures et Appliquées, 2015, 103 (1), ⟨10.1016/j.matpur.2014.04.002⟩. ⟨hal-00837645⟩
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