In this paper we prove an approximate controllability result for the bilinear Schrodinger equation. This result requires less restrictive non-resonance hypotheses on the spectrum of the uncontrolled Schrodinger operator than those present in the literature. The control operator is not required to be bounded and we are able to extend the controllability result to the density matrices. The proof is based on fine controllability properties of the finite dimensional Galerkin approximations and allows to get estimates for the L (1) norm of the control. The general controllability result is applied to the problem of controlling the rotation of a bipolar rigid molecule confined on a plane by means of two orthogonal external fields.

Boscain, U., Caponigro, M., Chambrion, T., Sigalotti, M. (2012). A weak spectral condition for the controllability of the bilinear Schroedinger equation with application to the control of a rotating planar molecule. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 311(2), 423-455 [10.1007/s00220-012-1441-z].

A weak spectral condition for the controllability of the bilinear Schroedinger equation with application to the control of a rotating planar molecule

Caponigro, Marco;
2012-01-01

Abstract

In this paper we prove an approximate controllability result for the bilinear Schrodinger equation. This result requires less restrictive non-resonance hypotheses on the spectrum of the uncontrolled Schrodinger operator than those present in the literature. The control operator is not required to be bounded and we are able to extend the controllability result to the density matrices. The proof is based on fine controllability properties of the finite dimensional Galerkin approximations and allows to get estimates for the L (1) norm of the control. The general controllability result is applied to the problem of controlling the rotation of a bipolar rigid molecule confined on a plane by means of two orthogonal external fields.
2012
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Boscain, U., Caponigro, M., Chambrion, T., Sigalotti, M. (2012). A weak spectral condition for the controllability of the bilinear Schroedinger equation with application to the control of a rotating planar molecule. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 311(2), 423-455 [10.1007/s00220-012-1441-z].
Boscain, U; Caponigro, M; Chambrion, T; Sigalotti, M
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/313622
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