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Local controllability of 1D Schrödinger equations with bilinear control and minimal time

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  • We consider a linear Schrödinger equation, on a bounded interval, with bilinear control.
        In [10], Beauchard and Laurent prove that, under an appropriate non degeneracy assumption, this system is controllable, locally around the ground state, in arbitrary time. In [18], Coron proves that a positive minimal time is required for this controllability result, on a particular degenerate example.
        In this article, we propose a general context for the local controllability to hold in large time, but not in small time. The existence of a positive minimal time is closely related to the behaviour of the second order term, in the power series expansion of the solution.
    Mathematics Subject Classification: 93B05, 93C20, 81Q93.


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