Energy estimates for low regularity bilinear Schrödinger equations

Nabile Boussaid (1) , Marco Caponigro (2) , Thomas Chambrion (3, 4)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 M2N - Modélisation mathématique et numérique
3 CORIDA - Robust control of infinite dimensional systems and applications
4 IECL - Institut Élie Cartan de Lorraine

This paper presents an energy estimate in terms of the total variation of the control for bilinear infinite dimensional quantum systems with unbounded potentials. These estimates allow a rigorous construction of propagators associated with controls of bounded variation. Moreover, upper bounds of the error made when replacing the infinite dimensional system by its finite dimensional Galerkin approximations is presented.

Mots clés: approximation.; Bilinear systems; quantum systems; well-posedness; approximation

Domaines: Optimisation et contrôle [math.OC]

Nabile Boussaid, Marco Caponigro, Thomas Chambrion. Energy estimates for low regularity bilinear Schrödinger equations. 1st IFAC Workshop on Control of Systems Governed by Partial Differential Equations (2013), Sep 2013, Paris, France. pp.25-30, ⟨10.3182/20130925-3-FR-4043.00046⟩. ⟨hal-00784876v2⟩