Weakly Coupled Systems in Quantum Control

Weakly coupled systems are a class of infinite dimensional conservative bilinear control systems with discrete spectrum. An important feature of these systems is that they can be precisely approached by finite dimensional Galerkin approximations. This property is of particular interest for the approximation of quantum system dynamics and the control of the bilinear Schrödinger equation. The present study provides rigorous definitions and analysis of the dynamics of weakly coupled systems and gives sufficient conditions for an infinite dimensional quantum control system to be weakly coupled. As an illustration we provide examples chosen among common physical systems.