2013/02/18 by Ugo Boscain, Boscain, Ugo, Marco Caponigro +3 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #FOS: Mathematics #Laser-Matter Interactions and Applications #Optimization and Control (math.OC) #Quantum optics and atomic interactions #math.OC
paper · pdf · doi:10.48550/arxiv.1302.4173
arxiv created 2013/02/18 · openalex publication_date 2013/02/18 · arxiv updated 2013/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a sufficient condition for approximate controllability of the bilinear discrete-spectrum Schrödinger equation exploiting the use of several controls. The controllability result extends to simultaneous controllability, approximate controllability in Hs, and tracking in modulus. The result is more general than those present in the literature even in the case of one control and permits to treat situations in which the spectrum of the uncontrolled operator is very degenerate (e.g. it has multiple eigenvalues or equal gaps among different pairs of eigenvalues). We apply the general result to a rotating polar linear molecule, driven by three orthogonal external fields. A remarkable property of this model is the presence of infinitely many degeneracies and resonances in the spectrum preventing the application of the results in the literature.