# Bilinear control of discrete spectrum Schrödinger operators

1 IRMAR - Institut de Recherche Mathématique de Rennes 2 FSM - Faculté des Sciences de Monastir

Abstract : The bilinear control problem of the Schrödinger equation $i\frac{\partial}{\partial t}\psit$ $= A+ut B\psit$, where $ut$ is the control function, is investigated through topological irreducibility of the set $\mathfrak{M}=\{ e^{-it A+u B}, u\in \mathbb{R}, t>0\}$ of bounded operators. Under an appropriate assumption on $B$, this allows to prove the approximate controllability of such systems when the uncontrolled Hamiltonian $A$ has a simple discrete spectrum.

Keywords : Bilinear control Approximate controllability Schrödinger operators Invariant subspaces Topological irreducibility

Author: Zied Ammari - Kais Ammari -

Source: https://hal.archives-ouvertes.fr/