Generic controllability properties for the bilinear Schrödinger equation

In a recent paper we proposed a set of sufficient conditions for the approximate controllability of a discrete-spectrum bilinear Schrodinger equation on a fixed domain. These conditions are expressed in terms of the controlled potential and of the eigenpairs of the uncontrolled Schrodinger operator. The aim of this presentation is to show that these conditions are generic with respect to the uncontrolled or the controlled potential. The results are obtained by analytic perturbation arguments and through the study of asymptotic properties of eigenfunctions.