CONTROLLABILITY OF PERIODIC BILINEAR QUANTUM SYSTEMS ON INFINITE GRAPHS
Résumé
In this work, we study the controllability of the bilinear Schrödinger equation on infinite graphs for periodic quantum states. We consider the equation (BSE) $i\partial_t\psi = −\Delta \psi+ u(t)B\psi$ in the Hilbert space $L^2_p$ composed by functions defined on an infinite graph $\mathcal{G}$ verifying periodic boundary conditions on the infinite edges. The Laplacian $−\Delta$ is equipped with specific boundary conditions, $B$ is a bounded symmetric operator and $u \in L^2 ((0, T), \mathbb{R})$ with $T > 0$. We present the well-posedness of the (BSE) in suitable subspaces of $L^2_p$. In such spaces, we study the global exact controllability and we provide examples involving tadpole graphs and star graphs with infinite spokes.
Origine | Fichiers produits par l'(les) auteur(s) |
---|
Loading...