Controllability of the rotation of a quantum planar molecule

Abstract— We consider the simplest model for controlling the rotation of a molecule by the action of an electric field, namely a quantum planar pendulum. This problem consists in characterizing the controllability of a PDE (the Schr¨odinger equation) on a manifold with nontrivial topology (the circle S1 ). The drift has discrete spectrum and its eigenfunctions are trigonometric functions. Some controllability results for the Schr¨odinger equation can be applied in this context. We tackle the problem by adapting the general method proposed by some of the authors in a recent paper. This requires, in particular, proving, by perturbation arguments, the non-resonance of the spectrum of the differential operator corresponding to a small constant control. The spectrum of this operator is given by the Mathieu characteristic values and its eigenfunctions are the Mathieu sinus and cosinus. Our main result says that we have simultaneous approximate controllability separately for the even and...

• Type: Conference
• Year: 2009
• Where: CDC
• Authors: Ugo V. Boscain, Thomas Chambrion, Paolo Mason, Mario Sigalotti, Dominique Sugny
• Keywords: CDC 2009, Control Systems, Molecular Dynamics, Quantum Planar Pendulum, Schr¨odinger Equation