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

We consider a system of an arbitrary number of 1D linear Schrodinger 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. (C) 2014 Elsevier Masson SAS. All rights reserved.