Approximate controllability by adiabatic methods of the Schrodinger equation with nonlinear Hamiltonian.

被引：0
|
作者：
Chittaro, Francesca Carlotta [1 ,2 ]
Mason, Paolo [3 ]
机构：
[1] Aix Marseille Univ, CNRS, ENSAM, LSIS UMR 7296, F-13397 Marseille, France
[2] Univ Toulon & Var, CNRS, LSIS UMR 7296, F-83957 La Garde, France
[3] Univ Paris Sud, CNRS, Cent Supelec, L2S,UMR 8506, F-91192 Gif Sur Yvette, France
来源：
2015 54TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC) | 2015年
关键词：
D O I：
暂无
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We consider quantum systems described by a controlled Schrodinger equation, where the Hamiltonian depends smoothly on three external inputs. We use adiabatic techniques to provide a constructive controllability result in some portion of the discrete spectrum, provided that it is conically connected. The case of Schrodinger Hamiltonians with electromagnetic fields fits the nonlinear setting studied in this paper.
引用
收藏
页码：7771 / 7776
页数：6
相关论文
共 50 条
  • [21] THE HAMILTONIAN STRUCTURES OF THE NONLINEAR SCHRODINGER-EQUATION IN THE CLASSICAL LIMIT
    VEROSKY, J
    JOURNAL OF MATHEMATICAL PHYSICS, 1987, 28 (05) : 1094 - 1096
  • [22] Multiplicative Controllability for the Schrodinger Equation
    Khapalov, Alexander Y.
    CONTROLLABILITY OF PARTIAL DIFFERENTIAL EQUATIONS GOVERNED BY MULTIPLICATIVE CONTROLS, 2010, 1995 : 265 - 274
  • [23] Exact controllability of the Schrodinger equation
    Aassila, M
    APPLIED MATHEMATICS AND COMPUTATION, 2003, 144 (01) : 89 - 106
  • [24] LOCAL EXACT CONTROLLABILITY AND STABILIZABILITY OF THE NONLINEAR SCHRODINGER EQUATION ON A BOUNDED INTERVAL
    Rosier, Lionel
    Zhang, Bing-Yu
    SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2009, 48 (02) : 972 - 992
  • [25] LOCAL EXACT CONTROLLABILITY OF A ONE-DIMENSIONAL NONLINEAR SCHRODINGER EQUATION
    Beauchard, Karine
    Lange, Horst
    Teismann, Holger
    SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2015, 53 (05) : 2781 - 2818
  • [26] SYMPLECTIC METHODS FOR THE NONLINEAR SCHRODINGER-EQUATION
    HERBST, BM
    VARADI, F
    ABLOWITZ, MJ
    MATHEMATICS AND COMPUTERS IN SIMULATION, 1994, 37 (4-5) : 353 - 369
  • [27] Explicit Symplectic Methods for the Nonlinear Schrodinger Equation
    Guan, Hua
    Jiao, Yandong
    Liu, Ju
    Tang, Yifa
    COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2009, 6 (03) : 639 - 654
  • [28] Numerical Methods for the Derivative Nonlinear Schrodinger Equation
    Li, Shu-Cun
    Li, Xiang-Gui
    Shi, Fang-Yuan
    INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2018, 19 (3-4) : 239 - 249
  • [29] A class of energy-conserving Hamiltonian boundary value methods for nonlinear Schrodinger equation with wave operator
    Brugnano, Luigi
    Zhang, Chengjian
    Li, Dongfang
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2018, 60 : 33 - 49
  • [30] Adiabatic midpoint rule for the dispersion-managed nonlinear Schrodinger equation
    Jahnke, Tobias
    Mikl, Marcel
    NUMERISCHE MATHEMATIK, 2018, 138 (04) : 975 - 1009
12345