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arXiv · 1306.5851

Simultaneous global exact controllability of an arbitrary number of 1D bilinear Schr\"odinger equations

Morgan Morancey·Vahagn Nersesyan
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Abstract

We consider a system of an arbitrary number of \textsc{1d} linear Schr\"odinger 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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Morgan Morancey, Vahagn Nersesyan. 2013-06-25. Simultaneous global exact controllability of an arbitrary number of 1D bilinear Schr\"odinger equations. https://arxiv.org/abs/1306.5851

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