CONTROLLABILITY OF PERIODIC BILINEAR QUANTUM SYSTEMS ON INFINITE GRAPHS - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Mathematical Physics Année : 2020

CONTROLLABILITY OF PERIODIC BILINEAR QUANTUM SYSTEMS ON INFINITE GRAPHS

Kaïs Ammari
Alessandro Duca

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.
Fichier principal
Vignette du fichier
grafi_period_v1.pdf (349.25 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02169344 , version 1 (01-07-2019)
hal-02169344 , version 2 (07-09-2020)

Identifiants

Citer

Kaïs Ammari, Alessandro Duca. CONTROLLABILITY OF PERIODIC BILINEAR QUANTUM SYSTEMS ON INFINITE GRAPHS. Journal of Mathematical Physics, 2020, 61 (10), ⟨10.1063/5.0010579⟩. ⟨hal-02169344v2⟩
104 Consultations
100 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More