Controllability of the discrete-spectrum Schrodinger equation driven by an external field

被引：103

作者：

Chambrion, Thomas ^{[1
]}

Mason, Paolo ^{[1
,2
]}

Sigalotti, Mario ^{[1
]}

Boscain, Ugo ^{[3
]}

机构：

[1] Nancy Univ, CNRS, INRIA, Inst Elie Cartan,UMR 7502, F-54506 Vandoeuvre Les Nancy, France

[2] CNR, IAC, I-00161 Rome, Italy

[3] Univ Bourgogne, CNRS, Le2i, F-21078 Dijon, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2009年 / 26卷 / 01期

关键词：

Quantum control; Control of PDE; Approximate controllability; Bilinear Schrodinger equation; Galerkin approximation; Density matrix; QUANTUM-MECHANICAL SYSTEMS; TIME; RESONANCE;

D O I：

10.1016/j.anihpc.2008.05.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove approximate controllability of the bilinear Schrodinger equation in the case in which the uncontrolled Hamiltonian has discrete non-resonant spectrum. The results that are obtained apply both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. The method relies on finite-dimensional techniques applied to the Galerkin approximations and permits, in addition, to get some controllability properties for the density matrix. Two examples are presented: the harmonic oscillator and the 3D well of potential, both controlled by suitable potentials. (c) 2008 Elsevier Masson SAS. All rights reserved.

引用

页码：329 / 349

页数：21

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