2013/06/25 by Morgan Morancey, Morancey, Morgan, Vahagn Nersesyan +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC) #Quantum chaos and dynamical systems #math.AP #math.OC
paper · pdf · doi:10.48550/arxiv.1306.5851
arxiv created 2013/06/25 · openalex publication_date 2013/06/25 · arxiv updated 2013/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a system of an arbitrary number of 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.