Approximate Controllability for a System of Schrödinger Equations Modeling a Single Trapped Ion
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2111-2136.
@article{AIHPC_2009__26_6_2111_0,
     author = {Ervedoza, Sylvain and Puel, Jean-Pierre},
     title = {Approximate {Controllability} for a {System} of {Schr\"odinger} {Equations} {Modeling} a {Single} {Trapped} {Ion}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {2111--2136},
     publisher = {Elsevier},
     volume = {26},
     number = {6},
     year = {2009},
     doi = {10.1016/j.anihpc.2009.01.005},
     mrnumber = {2569888},
     zbl = {1180.35437},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2009.01.005/}
}
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Ervedoza, Sylvain; Puel, Jean-Pierre. Approximate Controllability for a System of Schrödinger Equations Modeling a Single Trapped Ion. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 6, pp. 2111-2136. doi : 10.1016/j.anihpc.2009.01.005. http://archive.numdam.org/articles/10.1016/j.anihpc.2009.01.005/

[1] R. Adami, U. Boscain, Controllability of the Schroedinger equation via intersection of eigenvalues, in: Proc. of the 44rd IEEE Conf. on Decision and Control, 2005.

[2] Ball J. M., Marsden J. E., Slemrod M., Controllability for Distributed Bilinear Systems, SIAM J. Control Optim. 20 (4) (1982) 575-597. | MR | Zbl

[3] Baudouin L., A Bilinear Optimal Control Problem Applied to a Time Dependent Hartree-Fock Equation Coupled With Classical Nuclear Dynamics, Portugal Math. (N.S.) 63 (3) (2006) 293-325. | EuDML | MR | Zbl

[4] Baudouin L., Kavian O., Puel J.-P., Regularity for a Schrödinger Equation With Singular Potentials and Application to Bilinear Optimal Control, J. Differential Equations 216 (1) (2005) 188-222. | MR | Zbl

[5] Baudouin L., Salomon J., Constructive Solution of a Bilinear Control Problem, C. R. Math. Acad. Sci. Paris, Ser. I 342 (2) (2006) 119-124. | MR | Zbl

[6] Beauchard K., Local Controllability of a 1-D Schrödinger Equation, J. Math. Pures Appl. (9) 84 (7) (2005) 851-956. | MR | Zbl

[7] Beauchard K., Controllability of a Quantum Particle in a 1D Variable Domain, ESAIM Control Optim. Calc. Var. 14 (1) (2008) 105-147. | EuDML | Numdam | MR | Zbl

[8] Beauchard K., Coron J.-M., Controllability of a Quantum Particle in a Moving Potential Well, J. Funct. Anal. 232 (2) (2006) 328-389. | MR | Zbl

[9] Beauchard K., Coron J.-M., Mirrahimi M., Rouchon P., Implicit Lyapunov Control of Finite Dimensional Schrödinger Equations, Systems Control Lett. 56 (5) (2007) 388-395. | MR | Zbl

[10] K. Beauchard, M. Mirrahimi, Approximate stabilization of a quantum particle in a 1D infinite potential well, in: IFAC World Congress, Seoul, 2008.

[11] A.M. Bloch, R.W. Brockett, C. Rangan, The controllability of infinite quantum systems and closed subspace criteria, IEEE Trans. Automat. Control, submitted for publication.

[12] Brezis H., Analyse Fonctionnelle, Collection Mathématiques Appliquées pour la Maîtrise, Masson, Paris, 1983, Théorie et applications (Theory and applications). | MR | Zbl

[13] Chambrion T., Mason P., Sigalotti M., Boscain U., Controllability of the Discrete-Spectrum Schrödinger Equation Driven by an External Field, Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (1) (2009) 329-349. | Numdam | MR | Zbl

[14] Coron J.-M., On the Small-Time Local Controllability of a Quantum Particle in a Moving One-Dimensional Infinite Square Potential Well, C. R. Acad. Sci. Paris, Ser. I 342 (2) (2006) 103-108. | MR | Zbl

[15] Coron J.-M., Control and Nonlinearity, Mathematical Surveys and Monographs, vol. 136, American Mathematical Society, Providence, RI, 2007. | MR | Zbl

[16] Ito K., Kunisch K., Optimal Bilinear Control of an Abstract Schrödinger Equation, SIAM J. Control Optim. 46 (1) (2007) 274-287, (electronic). | MR | Zbl

[17] Law C. K., Eberly J. H., Arbitrary Control of a Quantum Electromagnetic Field, Phys. Rev. Lett. 76 (7) (1996) 1055-1058.

[18] Mirrahimi M., Lyapunov Control of a Quantum Particle in a Decaying Potential, Ann. Inst. H. Poincaré Anal. Non Linéaire 26 (5) (2009) 1743-1765. | Numdam | MR | Zbl

[19] M. Mirrahimi, Lyapunov control of a particle in a finite quantum potential well, in: IEEE Conf. on Decision and Control, 2006.

[20] Mirrahimi M., Rouchon P., Controllability of Quantum Harmonic Oscillators, IEEE Trans. Automat. Control 49 (5) (2004) 745-747. | MR

[21] Mirrahimi M., Rouchon P., Turinici G., Lyapunov Control of Bilinear Schrödinger Equations, Automatica J. IFAC 41 (11) (2005) 1987-1994. | MR | Zbl

[22] V. Nersesyan, Growth of Sobolev norms and controllability of Schrödinger equation, Preprint, 2008. | MR | Zbl

[23] Rangan C., Bloch A. M., Control of Finite-Dimensional Quantum Systems: Application to a Spin-1 2 Particle Coupled With a Finite Quantum Harmonic Oscillator, J. Math. Phys. 46 (3) (2005) 032106. | MR | Zbl

[24] Reed M., Simon B., Methods of Modern Mathematical Physics. I. Functional Analysis, second ed., Academic Press Inc. (Harcourt Brace Jovanovich Publishers), New York, 1980. | MR | Zbl

[25] Rouchon P., Quantum Systems and Control, Arima 9 (2008) 325-357. | MR

[26] Turinici G., On the Controllability of Bilinear Quantum Systems, in: Mathematical Models and Methods for Ab Initio Quantum Chemistry, Lecture Notes in Chem., vol. 74, Springer, Berlin, 2000, pp. 75-92. | MR | Zbl

[27] Turinici G., Rabitz H., Wavefunction Controllability for Finite-Dimensional Bilinear Quantum Systems, J. Phys. A 36 (10) (2003) 2565-2576. | MR | Zbl

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