An obstruction to small-time controllability of the bilinear Schrödinger equation

Ivan Beschastnyi (1, 2) , Ugo Boscain (3, 1, 2) , Mario Sigalotti (1, 2)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 CaGE - Control And GEometry
3 CNRS - Centre National de la Recherche Scientifique

In this article we discuss which controllability properties of classical Hamiltonian systems are preserved after quantization. We discuss some necessary and some sufficient conditions for small-time controllability of classical systems and quantum systems using the WKB method. In particular, we investigate the conjecture that if the classical system is not small-time controllable, then the corresponding quantum system is not small-time controllable either.

Domaines: Optimisation et contrôle [math.OC]; Physique mathématique [math-ph]

Ivan Beschastnyi, Ugo Boscain, Mario Sigalotti. An obstruction to small-time controllability of the bilinear Schrödinger equation. Journal of Mathematical Physics, 2021, 62, ⟨10.1063/5.0003524⟩. ⟨hal-02385244v2⟩