DocumentCode :
3300949
Title :
Controllability of the rotation of a quantum planar molecule
Author :
Boscain, U. ; Chambrion, T. ; Mason, P. ; Sigalotti, M. ; Sugny, D.
Author_Institution :
CNRS, Paris, France
fYear :
2009
fDate :
15-18 Dec. 2009
Firstpage :
369
Lastpage :
374
Abstract :
We consider the simplest model for controlling the rotation of a molecule by the action of an electric field, namely a quantum planar pendulum. This problem consists in characterizing the controllability of a PDE (the Schrodinger equation) on a manifold with nontrivial topology (the circle S1). The drift has discrete spectrum and its eigenfunctions are trigonometric functions. Some controllability results for the Schrodinger equation can be applied in this context. We tackle the problem by adapting the general method proposed by some of the authors in a recent paper. This requires, in particular, proving, by perturbation arguments, the non-resonance of the spectrum of the differential operator corresponding to a small constant control. The spectrum of this operator is given by the Mathieu characteristic values and its eigenfunctions are the Mathieu sinus and cosinus. Our main result says that we have simultaneous approximate controllability separately for the even and odd components of the wave function.
Keywords :
Schrodinger equation; controllability; eigenvalues and eigenfunctions; motion control; rotational states; topology; Mathieu characteristic values; Mathieu cosinus; Mathieu sinus; Schrodinger equation; eigenfunctions; molecule rotation controllability; nontrivial topology; quantum planar molecule; quantum planar pendulum; trigonometric functions; Azimuthal angle; Controllability; Eigenvalues and eigenfunctions; Frequency; Laplace equations; Laser modes; Polarization; Tensile stress; Topology; Wave functions;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on
Conference_Location :
Shanghai
ISSN :
0191-2216
Print_ISBN :
978-1-4244-3871-6
Electronic_ISBN :
0191-2216
Type :
conf
DOI :
10.1109/CDC.2009.5399942
Filename :
5399942
Link To Document :
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