Controllability of localised quantum states on infinite graphs through bilinear control fields. Issue 7 (3rd July 2021)

• Record Type: Journal Article
• Authors: Ammari, Kaïs; Duca, Alessandro
• Is Part Of: International journal of control. Volume 94:Issue 7(2021)
• Page Start: 1824
• Page End: 1837
• Publication Date: 2021-07-03
• Subjects: Bilinear control -- infinite graph -- Schrödinger equation; 35Q40 -- 93B05 -- 93C05; Automatic control -- Periodicals; Electronic journals; 629.8
• DOI: 10.1080/00207179.2019.1680868
• Languages: English
• ISSNs: 0020-7179

Abstract

Abstract : In this work, we consider the bilinear Schrödinger equation (BSE) i ∂ t ψ = − Δ ψ + u ( t ) B ψ in the Hilbert space L 2 ( G, C ) with G an infinite graph. The Laplacian − Δ is equipped with self-adjoint boundary conditions, B is a bounded symmetric operator and u ∈ L 2 ( ( 0, T ), R ) with T >0. We study the well-posedness of the (BSE) in suitable subspaces of D ( | Δ | 3 / 2 ) preserved by the dynamics despite the dispersive behaviour of the equation. In such spaces, we study the global exact controllability and the 'energetic controllability'. We provide examples involving for instance infinite tadpole graphs.