Title :
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
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;
Conference_Titel :
Decision and Control, 2006 45th IEEE Conference on
Conference_Location :
San Diego, CA
Print_ISBN :
1-4244-0171-2
DOI :
10.1109/CDC.2006.377356
