Explicit approximate controllability of the Schrödinger equation with a polarizability term - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Mathematics of Control, Signals, and Systems Année : 2013

Explicit approximate controllability of the Schrödinger equation with a polarizability term

Résumé

We consider a controlled Schrödinger equation with a dipolar and a polarizability term, used when the dipolar approximation is not valid. The control is the amplitude of the external electric field, it acts non linearly on the state. We extend in this infinite dimensional framework previous techniques used by Coron, Grigoriu, Lefter and Turinici for stabilization in finite dimension. We consider a highly oscillating control and prove the semi-global weak $H^2$ stabilization of the averaged system using a Lyapunov function introduced by Nersesyan. Then it is proved that the solutions of the Schrödinger equation and of the averaged equation stay close on every finite time horizon provided that the control is oscillating enough. Combining these two results, we get approximate controllability to the ground state for the polarizability system.
Fichier principal
Vignette du fichier
Morancey_polarisability.pdf (828.55 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00826188 , version 1 (13-11-2014)

Identifiants

Citer

Morgan Morancey. Explicit approximate controllability of the Schrödinger equation with a polarizability term. Mathematics of Control, Signals, and Systems, 2013, 25 (3), pp.407-432. ⟨10.1007/s00498-012-0102-2⟩. ⟨hal-00826188⟩
149 Consultations
107 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More