Global exact controllability of 1D Schrödinger equations with a polarizability term

Morgan Morancey (1, 2) , Vahagn Nersesyan (3)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 CMLA - Centre de Mathématiques et de Leurs Applications
3 LMV - Laboratoire de Mathématiques de Versailles

We consider a quantum particle in a 1D interval submitted to a potential. The evolution of this particle is controlled using an external electric field. Taking into account the so-called polarizability term in the model (quadratic with respect to the control), we prove global exact controllability in a suitable space for arbitrary potential and arbitrary dipole moment. This term is relevant both from the mathematical and physical points of view. The proof uses tools from the bilinear setting and a perturbation argument.

Domaines: Optimisation et contrôle [math.OC]

Morgan Morancey, Vahagn Nersesyan. Global exact controllability of 1D Schrödinger equations with a polarizability term. Comptes rendus de l'Académie des sciences. Série I, Mathématique, 2014, 352 (5), http://dx.doi.org/10.1016/j.crma.2014.03.013. ⟨10.1016/j.crma.2014.03.013⟩. ⟨hal-00866642⟩