Controllability of bilinear quantum systems in explicit times via explicit control fields

ABSTRACT

We consider the bilinear Schrödinger equation on a bounded one-dimensional domain and we provide explicit times such that the global exact controllability is verified. In addition, we show how to construct controls for the global approximate controllability.

Keywords:

• Schrödinger equation
• global exact controllability
• bilinear quantum systems
• explicit controls
• explicit times

AMS subject classifications:

• 35Q41
• 93C20
• 93B05

Acknowledgments

The author thanks Thomas Chambrion for suggesting him the problem and for the explanations provided on the work (Chambrion, 2012). He is also grateful to the colleagues Nabile Boussaïd, Lorenzo Tentarelli and Riccardo Adami for the fruitful discussions.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work has been partially supported by the ISDEEC project by Agence Nationale de la Recherche (ANR) 16-CE40-0013.