Approximate controllability via adiabatic techniques for the three-inputs controlled Schrödinger equation

Abstract : We consider a system described by a controlled bilinear Schrödinger equation with three external inputs. We provide a constructive method to approximately steer the system from a given energy level to a superposition of energy levels corresponding to a given probability distribution. The method is based on adiabatic techniques and works if the spectrum of the Hamiltonian admits eigenvalue intersections, with respect to variations of the controls, and if the latter are conical. We provide sharp estimates of the relation between the error and the controllability time, and we show how to improve these estimates by selecting special control paths.
Type de document :
Pré-publication, Document de travail
2015
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https://hal.archives-ouvertes.fr/hal-01117828
Contributeur : Francesca Carlotta Chittaro <>
Soumis le : mercredi 18 février 2015 - 08:39:19
Dernière modification le : samedi 18 février 2017 - 01:20:30
Document(s) archivé(s) le : mardi 19 mai 2015 - 10:11:47

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adiabatic-threecontrols.pdf
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  • HAL Id : hal-01117828, version 1
  • ARXIV : 1502.06814

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Francesca Chittaro, Paolo Mason. Approximate controllability via adiabatic techniques for the three-inputs controlled Schrödinger equation. 2015. <hal-01117828>

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