On the \(K+P\) problem for a three-level quantum system: Optimality implies resonance. (English) Zbl 1022.53028

Boscain, U.; Chambrion, T.; Gauthier, J.-P.

J. Dyn. Control Syst. 8, No. 4, 547-572 (2002).

The authors develop a geometric approach in studying an optimal control problem whose general complex setting is related to the time dependent Schrödinger equation. The main result shows that the optimality implies resonance. Optimal trajectories reaching the final target and satisfying transversality conditions are computed by using methods of sub-Riemannian geometry on Lie groups.

Reviewer: Dumitru Motreanu (Perpignan)

MSC:

53C17	Sub-Riemannian geometry
49J15	Existence theories for optimal control problems involving ordinary differential equations
22E70	Applications of Lie groups to the sciences; explicit representations

Keywords:

sub-Riemannian geometry; Lie groups; quantum control