Local controllability of a 1D Schrödinger equation

Karine Beauchard (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We consider a nonrelativistic charged particle in a 1-D box of potential. This quantum system is subject to a control, which is a uniform electric field. It is represented by a complex probability amplitude solution of a Schrödinger equation. We prove the local controllability of this nonlinear system around the ground state. Our proof uses the return method, a Nash-Moser implicit function theorem and moment theory.

Mots clés: Controllability; Schrödinger equation; Nash-Moser theorem; Moment theory

Domaines: Equations aux dérivées partielles [math.AP]

Karine Beauchard. Local controllability of a 1D Schrödinger equation. Journal de Mathématiques Pures et Appliquées, 2005, 84, pp.851-956. ⟨hal-00825514⟩