26450 articles – 20327 references  [version française]
Detailed view Preprint, Working Paper, ...
Attached file list to this document: 
PDF
schrod-bilinear.pdf(213.2 KB)
Bilinear control of discrete spectrum Schrödinger operators
Zied Ammari1, Kais Ammari2

The bilinear control problem of the Schrödinger equation $i\frac{\partial}{\partial t}\psi(t)$ $=( A+u(t) B)\psi(t)$, where $u(t)$ 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.
1:  IRMAR - Institut de Recherche Mathématique de Rennes
2:  FSM - Faculté des Sciences de Monastir
Bilinear control – Approximate controllability – Schrödinger operators – Invariant subspaces – Topological irreducibility