@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 = {https://www.numdam.org/articles/10.1016/j.anihpc.2009.01.005/} }
TY - JOUR AU - Ervedoza, Sylvain AU - Puel, Jean-Pierre TI - Approximate Controllability for a System of Schrödinger Equations Modeling a Single Trapped Ion JO - Annales de l'I.H.P. Analyse non linéaire PY - 2009 SP - 2111 EP - 2136 VL - 26 IS - 6 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2009.01.005/ DO - 10.1016/j.anihpc.2009.01.005 LA - en ID - AIHPC_2009__26_6_2111_0 ER -
%0 Journal Article %A Ervedoza, Sylvain %A Puel, Jean-Pierre %T Approximate Controllability for a System of Schrödinger Equations Modeling a Single Trapped Ion %J Annales de l'I.H.P. Analyse non linéaire %D 2009 %P 2111-2136 %V 26 %N 6 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2009.01.005/ %R 10.1016/j.anihpc.2009.01.005 %G en %F AIHPC_2009__26_6_2111_0
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. https://www.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] Controllability for Distributed Bilinear Systems, SIAM J. Control Optim. 20 (4) (1982) 575-597. | MR | Zbl
, , ,[3] 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] 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] Constructive Solution of a Bilinear Control Problem, C. R. Math. Acad. Sci. Paris, Ser. I 342 (2) (2006) 119-124. | MR | Zbl
, ,[6] Local Controllability of a 1-D Schrödinger Equation, J. Math. Pures Appl. (9) 84 (7) (2005) 851-956. | MR | Zbl
,[7] 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] Controllability of a Quantum Particle in a Moving Potential Well, J. Funct. Anal. 232 (2) (2006) 328-389. | MR | Zbl
, ,[9] 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] Analyse Fonctionnelle, Collection Mathématiques Appliquées pour la Maîtrise, Masson, Paris, 1983, Théorie et applications (Theory and applications). | MR | Zbl
,[13] 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] 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] Control and Nonlinearity, Mathematical Surveys and Monographs, vol. 136, American Mathematical Society, Providence, RI, 2007. | MR | Zbl
,[16] Optimal Bilinear Control of an Abstract Schrödinger Equation, SIAM J. Control Optim. 46 (1) (2007) 274-287, (electronic). | MR | Zbl
, ,[17] Arbitrary Control of a Quantum Electromagnetic Field, Phys. Rev. Lett. 76 (7) (1996) 1055-1058.
, ,[18] 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] Controllability of Quantum Harmonic Oscillators, IEEE Trans. Automat. Control 49 (5) (2004) 745-747. | MR
, ,[21] 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] Control of Finite-Dimensional Quantum Systems: Application to a Spin-
[24] Methods of Modern Mathematical Physics. I. Functional Analysis, second ed., Academic Press Inc. (Harcourt Brace Jovanovich Publishers), New York, 1980. | MR | Zbl
, ,[25] Quantum Systems and Control, Arima 9 (2008) 325-357. | MR
,[26] 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] Wavefunction Controllability for Finite-Dimensional Bilinear Quantum Systems, J. Phys. A 36 (10) (2003) 2565-2576. | MR | Zbl
, ,- Examples of Small-Time Controllable Schrödinger Equations, Annales Henri Poincaré (2025) | DOI:10.1007/s00023-025-01559-x
- Switching Controls for Conservative Bilinear Quantum Systems with Discrete Spectrum, SIAM Journal on Control and Optimization, Volume 63 (2025) no. 1, p. S1 | DOI:10.1137/23m1588494
- On a sharper bound on the stability of non-autonomous Schrödinger equations and applications to quantum control, Journal of Functional Analysis, Volume 287 (2024) no. 8, p. 110563 | DOI:10.1016/j.jfa.2024.110563
- On Global Approximate Controllability of a Quantum Particle in a Box by Moving Walls, SIAM Journal on Control and Optimization, Volume 62 (2024) no. 2, p. 826 | DOI:10.1137/22m1518980
- Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions, Journal of Physics A: Mathematical and Theoretical, Volume 56 (2023) no. 32, p. 325201 | DOI:10.1088/1751-8121/ace505
- Stabilization of the weakly coupled Schrödinger system, Applicable Analysis, Volume 101 (2022) no. 2, p. 733 | DOI:10.1080/00036811.2020.1758309
- Bilinear Control of Schrödinger PDEs, Encyclopedia of Systems and Control (2021), p. 144 | DOI:10.1007/978-3-030-44184-5_12
- Approximate controllability of the Jaynes-Cummings dynamics, Journal of Mathematical Physics, Volume 59 (2018) no. 7 | DOI:10.1063/1.5023587
- Controllability in projection of the simple spectrum bilinear Schrödinger equation, IFAC-PapersOnLine, Volume 50 (2017) no. 1, p. 5592 | DOI:10.1016/j.ifacol.2017.08.1104
- Multiplicative controllability for semilinear reaction–diffusion equations with finitely many changes of sign, Journal de Mathématiques Pures et Appliquées, Volume 108 (2017) no. 4, p. 425 | DOI:10.1016/j.matpur.2017.07.002
- Approximate Controllability, Exact Controllability, and Conical Eigenvalue Intersections for Quantum Mechanical Systems, Communications in Mathematical Physics, Volume 333 (2015) no. 3, p. 1225 | DOI:10.1007/s00220-014-2195-6
- On the control of spin-boson systems, Journal of Mathematical Physics, Volume 56 (2015) no. 9 | DOI:10.1063/1.4929543
- Approximate controllability of the two trapped ions system, Quantum Information Processing, Volume 14 (2015) no. 7, p. 2397 | DOI:10.1007/s11128-015-0991-3
- Simultaneous local exact controllability of 1D bilinear Schrödinger equations, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 31 (2014) no. 3, p. 501 | DOI:10.1016/j.anihpc.2013.05.001
- Multi-input Schrödinger equation: Controllability, tracking, and application to the quantum angular momentum, Journal of Differential Equations, Volume 256 (2014) no. 11, p. 3524 | DOI:10.1016/j.jde.2014.02.004
- Local controllability of 1D Schrödinger equations with bilinear control and minimal time, Mathematical Control Related Fields, Volume 4 (2014) no. 2, p. 125 | DOI:10.3934/mcrf.2014.4.125
- On the Controllability of Quantum Transport in an Electronic Nanostructure, SIAM Journal on Applied Mathematics, Volume 74 (2014) no. 6, p. 1870 | DOI:10.1137/130939328
- Bilinear Control of Schrödinger PDEs, Encyclopedia of Systems and Control (2013), p. 1 | DOI:10.1007/978-1-4471-5102-9_12-1
- Weakly Coupled Systems in Quantum Control, IEEE Transactions on Automatic Control, Volume 58 (2013) no. 9, p. 2205 | DOI:10.1109/tac.2013.2255948
- Exact controllability for stochastic Schrödinger equations, Journal of Differential Equations, Volume 255 (2013) no. 8, p. 2484 | DOI:10.1016/j.jde.2013.06.021
- Explicit approximate controllability of the Schrödinger equation with a polarizability term, Mathematics of Control, Signals, and Systems, Volume 25 (2013) no. 3, p. 407 | DOI:10.1007/s00498-012-0102-2
- , 2012 IEEE 51st IEEE Conference on Decision and Control (CDC) (2012), p. 3038 | DOI:10.1109/cdc.2012.6426289
- A Weak Spectral Condition for the Controllability of the Bilinear Schrödinger Equation with Application to the Control of a Rotating Planar Molecule, Communications in Mathematical Physics, Volume 311 (2012) no. 2, p. 423 | DOI:10.1007/s00220-012-1441-z
- Controllability properties for the one-dimensional Heat equation under multiplicative or nonnegative additive controls with local mobile support, ESAIM: Control, Optimisation and Calculus of Variations, Volume 18 (2012) no. 4, p. 1207 | DOI:10.1051/cocv/2012004
- Local controllability and non-controllability for a 1D wave equation with bilinear control, Journal of Differential Equations, Volume 250 (2011) no. 4, p. 2064 | DOI:10.1016/j.jde.2010.10.008
- On the problem of quantum control in infinite dimensions, Journal of Physics A: Mathematical and Theoretical, Volume 44 (2011) no. 13, p. 135302 | DOI:10.1088/1751-8113/44/13/135302
- Global approximate controllability for Schrödinger equation in higher Sobolev norms and applications, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 27 (2010) no. 3, p. 901 | DOI:10.1016/j.anihpc.2010.01.004
- Generic Controllability Properties for the Bilinear Schrödinger Equation, Communications in Partial Differential Equations, Volume 35 (2010) no. 4, p. 685 | DOI:10.1080/03605300903540919
- Local controllability of 1D linear and nonlinear Schrödinger equations with bilinear control, Journal de Mathématiques Pures et Appliquées, Volume 94 (2010) no. 5, p. 520 | DOI:10.1016/j.matpur.2010.04.001
Cité par 29 documents. Sources : Crossref