Practical stabilization of a quantum particle in a one-dimensional infinite square potential well

Karine Beauchard; Mazyar Mirrahimi

doi:10.1137/070704204

Practical stabilization of a quantum particle in a one-dimensional infinite square potential well

Karine Beauchard
, Mazyar Mirrahimi

ENS Paris-Saclay
INRIA Rocquencourt

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

33 Citations (Scopus)

Résumé

We consider a nonrelativistic charged particle in a one-dimensional infinite square potential well. This quantum system is subjected to a control, which is a uniform (in space) timedepending electric field. It is represented by a complex probability amplitude solution of a Schrödinger equation on a one-dimensional bounded domain, with Dirichlet boundary conditions. We prove the almost global practical stabilization of the eigenstates by explicit feedback laws.

langue originale	Anglais
Pages (de - à)	1179-1205
Nombre de pages	27
journal	SIAM Journal on Control and Optimization
Volume	48
Numéro de publication	2
Les DOIs	https://doi.org/10.1137/070704204
état	Publié - 1 déc. 2009
Modification externe	Oui

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10.1137/070704204

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abstract = "We consider a nonrelativistic charged particle in a one-dimensional infinite square potential well. This quantum system is subjected to a control, which is a uniform (in space) timedepending electric field. It is represented by a complex probability amplitude solution of a Schr{\"o}dinger equation on a one-dimensional bounded domain, with Dirichlet boundary conditions. We prove the almost global practical stabilization of the eigenstates by explicit feedback laws.",

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KW - Bilinear schrödinger equation

KW - Control of partial differential equations

KW - Lyapunov stabilization

KW - Quantum systems

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Practical stabilization of a quantum particle in a one-dimensional infinite square potential well

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