@article{AIHPC_2009__26_1_329_0,
author = {Chambrion, Thomas and Mason, Paolo and Sigalotti, Mario and Boscain, Ugo},
title = {Controllability of the Discrete-Spectrum Schr\"odinger Equation Driven by an External Field},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
volume = {26},
year = {2009},
pages = {329-349},
doi = {10.1016/j.anihpc.2008.05.001},
mrnumber = {2483824},
zbl = {1161.35049},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPC_2009__26_1_329_0}
}
Chambrion, Thomas; Mason, Paolo; Sigalotti, Mario; Boscain, Ugo. Controllability of the Discrete-Spectrum Schrödinger Equation Driven by an External Field. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) pp. 329-349. doi : 10.1016/j.anihpc.2008.05.001. http://gdmltest.u-ga.fr/item/AIHPC_2009__26_1_329_0/
[1] R. Adami, U. Boscain, Controllability of the Schrödinger equation via intersection of eigenvalues, in: Proceedings of the 44th IEEE Conference on Decision and Control, December 12-15, 2005, pp. 1080-1085.
[2] , , An Estimation of the Controllability Time for Single-Input Systems on Compact Lie Groups, ESAIM Control Optim. Calc. Var. 12 (3) (2006) 409-441. | Numdam | MR 2224821 | Zbl 1106.93006
[3] , , , , On Finite-Dimensional Projections of Distributions for Solutions of Randomly Forced 2D Navier-Stokes Equations, Ann. Inst. H. Poincaré Probab. Statist. 43 (4) (2007) 399-415. | Numdam | MR 2329509 | Zbl 1177.60059
[4] , , Control Theory From the Geometric Viewpoint, Encyclopaedia of Mathematical Sciences, vol. 87, Springer-Verlag, Berlin, 2004, Control Theory and Optimization, II. | MR 2062547 | Zbl 1062.93001
[5] , , Controllability of 2D Euler and Navier-Stokes Equations by Degenerate Forcing, Commun. Math. Phys. 265 (3) (2006) 673-697. | MR 2231685 | Zbl 1105.93008
[6] , Genericity of Simple Eigenvalues for Elliptic PDE's, Proc. Amer. Math. Soc. 48 (1975) 413-418. | MR 385934 | Zbl 0302.35071
[7] , , Notions of Controllability for Bilinear Multilevel Quantum Systems, IEEE Trans. Automat. Control 48 (8) (2003) 1399-1403. | MR 2004373
[8] , Controllability of Quantum Mechanical Systems by Root Space Decomposition of , J. Math. Phys. 43 (5) (2002) 2051-2062. | MR 1893660 | Zbl 1059.93016
[9] , Controllability Properties for Finite Dimensional Quantum Markovian Master Equations, J. Math. Phys. 44 (6) (2003) 2357-2372. | MR 1979090 | Zbl 1062.82033
[10] , , , Controllability for Distributed Bilinear Systems, SIAM J. Control Optim. 20 (4) (1982) 575-597. | MR 661034 | Zbl 0485.93015
[11] , , , Regularity for a Schrödinger Equation With Singular Potentials and Application to Bilinear Optimal Control, J. Differential Equations 216 (1) (2005) 188-222. | MR 2158922 | Zbl 1109.35094
[12] , Local Controllability of a 1-D Schrödinger Equation, J. Math. Pures Appl. (9) 84 (7) (2005) 851-956. | MR 2144647 | Zbl 1124.93009
[13] , , Controllability of a Quantum Particle in a Moving Potential Well, J. Funct. Anal. 232 (2) (2006) 328-389. | MR 2200740 | Zbl 1188.93017 | Zbl pre05017416
[14] , , Analysis of a Leap-Frog Pseudospectral Scheme for the Schrödinger Equation, J. Comput. Appl. Math. 193 (1) (2006) 65-88. | MR 2228707 | Zbl 1118.65107
[15] , , , Nonisotropic 3-Level Quantum Systems: Complete Solutions for Minimum Time and Minimum Energy, Discrete Contin. Dyn. Syst. Ser. B 5 (4) (2005) 957-990, (electronic). | MR 2170218 | Zbl 1084.81083
[16] , , Resonance of Minimizers for N-Level Quantum Systems With an Arbitrary Cost, ESAIM Control Optim. Calc. Var. 10 (4) (2004) 593-614, (electronic). | Numdam | MR 2111082 | Zbl 1072.49002
[17] , , Time Minimal Trajectories for a Spin 1/2 Particle in a Magnetic Field, J. Math. Phys. 47 (6) (2006) 29, 062101. | MR 2239948 | Zbl 1112.81098
[18] , Control and Nonlinearity, Mathematical Surveys and Monographs, vol. 136, American Mathematical Society, Providence, RI, 2007. | MR 2302744 | Zbl 1140.93002
[19] , Introduction to Quantum Control and Dynamics, Applied Mathematics and Nonlinear Science Series, Chapman, Hall/CRC, Boca Raton, FL, 2008. | MR 2357229 | Zbl 1139.81001
[20] , Spectral Theory and Differential Operators, Cambridge Studies in Advanced Mathematics, vol. 42, Cambridge University Press, Cambridge, 1995. | MR 1349825 | Zbl 0893.47004
[21] , Extremum Problems for Eigenvalues of Elliptic Operators, Frontiers in Mathematics, Birkhäuser Verlag, Basel, 2006. | MR 2251558 | Zbl 1109.35081
[22] , , , Nuclear Magnetic Resonance Quantum Computing Exploiting the Pure Spin State of Para Hydrogen, J. Chem. Phys. 113 (6) (2000) 2056-2059.
[23] , , Optimal Bilinear Control of an Abstract Schrödinger Equation, SIAM J. Control Optim. 46 (1) (2007) 274-287, (electronic). | MR 2299629 | Zbl 1136.35089
[24] , , Control Systems on Lie Groups, J. Differential Equations 12 (1972) 313-329. | MR 331185 | Zbl 0237.93027
[25] , Perturbation Theory for Linear Operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag, New York, 1966. | MR 203473 | Zbl 0148.12601
[26] , , , Sub-Riemannian Geometry and Time Optimal Control of Three Spin Systems: Quantum Gates and Coherence Transfer, Phys. Rev. A 65 (3) (2002) 11, 032301. | MR 1891763
[27] M. Mirrahimi, Lyapunov control of a particle in a finite quantum potential well, in: Proceedings of the 45th IEEE Conference on Decision and Control, December 13-15, 2006.
[28] , , Controllability of Quantum Harmonic Oscillators, IEEE Trans. Automat. Control 49 (5) (2004) 745-747. | MR 2057808
[29] , , , Optimal Control of Quantum Mechanical Systems: Existence, Numerical Approximations, and Applications, Phys. Rev. A 37 (1988) 4950-4964. | MR 949169
[30] , Strichartz Estimates for the Schrödinger and Heat Equations Perturbed With Singular and Time Dependent Potentials, Asymptotic Anal. 47 (1-2) (2006) 1-18. | MR 2224403 | Zbl 1100.35020
[31] , , , , Wither the Future of Controlling Quantum Phenomena?, Science 288 (2000) 824-828.
[32] , , Methods of Modern Mathematical Physics. IV. Analysis of Operators, Academic Press (Harcourt Brace Jovanovich Publishers), New York, 1978. | MR 493421 | Zbl 0401.47001
[33] , Perturbation Theory of Eigenvalue Problems, Assisted by J. Berkowitz. With a preface by Jacob T. Schwartz, Gordon Breach Science Publishers, New York, 1969. | MR 240668 | Zbl 0181.42002
[34] , , Time Decay for Solutions of Schrödinger Equations With Rough and Time-Dependent Potentials, Invent. Math. 155 (3) (2004) 451-513. | MR 2038194 | Zbl 1063.35035
[35] , Navier-Stokes Equation on the Rectangle Controllability by Means of Low Mode Forcing, J. Dynam. Control Syst. 12 (4) (2006) 517-562. | MR 2253360 | Zbl 1105.35085
[36] P. Rouchon, Control of a quantum particle in a moving potential well, in: Lagrangian and Hamiltonian Methods for Nonlinear Control 2003, IFAC, Laxenburg, 2003, pp. 287-290. | MR 2082989
[37] , Controllability of Invariant Systems on Lie Groups and Homogeneous Spaces, Dynamical systems, 8, J. Math. Sci. (New York) 100 (4) (2000) 2355-2427. | MR 1776551 | Zbl 1073.93511
[38] , , Principles of the Quantum Control of Molecular Processes, Wiley-VCH, 2003, pp. 250.
[39] G. Tenenbaum, M. Tucsnak, K. Ramdani, T. Takahashi, A spectral approach for the exact observability of infinite dimensional systems with skew-adjoint generator, J. Funct. Anal., 2007. | MR 2158180 | Zbl 1140.93395
[40] , On the Controllability of Bilinear Quantum Systems, in: , (Eds.), Mathematical Models and Methods for Ab Initio Quantum Chemistry, Lecture Notes in Chemistry, vol. 74, Springer, 2000. | MR 1857459 | Zbl 1007.81019
[41] , Remarks on the Controllability of the Schrödinger Equation, in: Quantum Control: Mathematical and Numerical Challenges, CRM Proc. Lecture Notes, vol. 33, Amer. Math. Soc., Providence, RI, 2003, pp. 193-211. | MR 2043529