Lyapunov control of a particle in a finite quantum potential well

Author

Mirrahimi, Mazyar

Author_Institution

Centre Automatique et Syst., Ecole des Mines de Paris

fYear

2006

fDate

13-15 Dec. 2006

Firstpage

3962

Lastpage

3967

Abstract

A Lyapunov-based approach for the trajectory generation of a Schrodinger equation is proposed. For the case of a quantum particle in a 3-dimensional finite potential well with an arbitrary shape the convergence is precisely analyzed. Similar assumptions to those formerly used for the finite dimensional configurations ensure the quasi-global approximate stabilization of the partial differential equation around an isolated eigenstate of the free system. Dispersive estimates of Strichartz type are widely used for the proof of the convergence result

Keywords

Lyapunov methods; Schrodinger equation; convergence of numerical methods; eigenvalues and eigenfunctions; partial differential equations; quantum theory; stability; Lyapunov control; Schrodinger equation; Strichartz type; finite quantum potential well; isolated eigenstate; partial differential equation; quantum particle; quasiglobal approximate stabilization; trajectory generation; Controllability; Convergence; Cost function; Dispersion; Eigenvalues and eigenfunctions; Feedback; Open loop systems; Partial differential equations; Potential well; USA Councils;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2006 45th IEEE Conference on

Conference_Location

San Diego, CA

Print_ISBN

1-4244-0171-2

Type

conf

DOI

10.1109/CDC.2006.377356

Filename

4177128