Generic controllability properties for the bilinear Schrödinger equation

Abstract

In [15] we proposed a set of sufficient conditions for the approximate controllability of a discrete-spectrum bilinear Schrödinger equation. These conditions are expressed in terms of the controlled potential and of the eigenpairs of the uncontrolled Schrödinger operator. The aim of this paper is to show that these conditions are generic with respect to the uncontrolled and the controlled potential, denoted respectively by $V$ and $W$. More precisely, we prove that the Schrödinger equation is approximately controllable generically with respect to $W$ when $V$ is fixed and also generically with respect to $V$ when $W$ is fixed and non-constant. The results are obtained by analytic perturbation arguments and through the study of asymptotic properties of eigenfunctions.

References in corpus (3)

• Controllability of the discrete-spectrum Schrodinger equation driven by an external field
• Lyapunov control of a quantum particle in a decaying potential
• Global approximate controllability for Schrödinger equation in higher Sobolev norms and applications