Free Access
Issue
ESAIM: COCV
Volume 12, Number 4, October 2006
Page(s) 615 - 635
DOI https://doi.org/10.1051/cocv:2006014
Published online 11 October 2006
  1. F.Kh. Abdullaev and J. Garnier, Collective oscillations of one-dimensional Bose-Einstein gas under varying in time trap potential and atomic scattering length. Phys. Rev. A 70 (2004) 053604. [CrossRef] [Google Scholar]
  2. G. Bachman and N. Narici, Functional Analysis. Academic Press, N.Y. (1966). [Google Scholar]
  3. J. Ball, J. Marsden and M. Slemrod, Controllability for distributed bilinear systems. SIAM J. Contr. Opt. 20 (1982) 575-597. [CrossRef] [MathSciNet] [Google Scholar]
  4. C. Bardos, G. Lebeau and J. Rauch, Sharp sufficient conditions for the observation, control, and stabilization of waves from the boundary. SIAM J. Contr. Opt. 30 (1992) 1024-1065. [CrossRef] [MathSciNet] [Google Scholar]
  5. L. Baudouin, A bilinear optimal control problem applied to a time dependent Hartree-Fock equation coupled with classical nuclear dynamics. Portugaliae Mat. (To appear). [Google Scholar]
  6. L. Baudouin, Existence and regularity of the solution of a time dependent Hartree-Fock equation coupled with a classical nuclear dynamics. Rev. Mat. Complut. 18 (2005) 285-314. [MathSciNet] [Google Scholar]
  7. L. Baudouin and J.-P. Puel, Bilinear optimal control problem on a Schrödinger equation with singular potentials. Preprint (2004). [Google Scholar]
  8. K. Beauchard, Local controllability of a 1-D Schrödinger equation, J. Math. Pures Appl. 84 (2005) 851-956. [Google Scholar]
  9. K. Beauchard and J.M. Coron, Controllability of a quantum particle in a moving potential well. J. Funct. Anal. 232 (2006) 328-389. [CrossRef] [MathSciNet] [Google Scholar]
  10. P.W. Brumer and M. Shapiro, Principles of the Quantum Control of Molecular Processes. Wiley-VCH, Berlin (2003). [Google Scholar]
  11. R. Carles, Linear vs. nonlinear effects for nonlinear Schrödinger equations with potential. Commun. Contemp. Math. 7(4) (2005) 483-508. [Google Scholar]
  12. E. Cancès and C. LeBris, On the time-dependent Hartree-Fock equations coupled with classical nuclear dynamics. Math. Mod. Meth. Appl. Sci. 9 (1999) 963-990. [CrossRef] [Google Scholar]
  13. E. Cancès, C. LeBris and M. Pilot, Contrôle optimale bilinéaire d'une équation de Schrödinger. C. R. Acad. Sci. Paris, Sér. 1 330 (2000) 567-571. [Google Scholar]
  14. J.W. Clark, D.G. Lucarelli and T.J. Tarn, Control of quantum systems. Int. J. Mod. Phys. B 17 (2003) 5397-5412. [CrossRef] [Google Scholar]
  15. C. Fabre, Résultats de contrôlabilité exacte interne pour l'équation de Schrödinger at leurs limites asymptotiques, Application à certaines équations de plaques vibrantes. Asymptotic Analysis 5 (1992) 343-379. [MathSciNet] [Google Scholar]
  16. H. Helson, Harmonic Analysis. Addison-Wesley, Reading (1983). [Google Scholar]
  17. M. Holthaus and S. Stenholm, Coherent control of self-trapping transition. Eur. Phys. J. B 20 (2001) 451-467. [CrossRef] [EDP Sciences] [Google Scholar]
  18. G.M Huang, Tarn T.J and J.W. Clark, On the controllability of quantum-mechanical systems. J. Math. Phys. 24 (1983) 2608-2618. [CrossRef] [MathSciNet] [Google Scholar]
  19. H. Husimi, Miscellanea in elementary quantum mechanics II. Prog. Theor. Phys. 9 (1953) 381-402. [CrossRef] [Google Scholar]
  20. R. Illner, H. Lange and H. Teismann, A note on the exact internal control of nonlinear Schrödinger equations. CRM Proc. Lecture Notes 33 (2003) 127-137. [Google Scholar]
  21. A.E. Ingham, Some trigonometric inequalities with applications to the theory of series. Math. Z. 41 (1936) 367. [CrossRef] [MathSciNet] [Google Scholar]
  22. J.L. Journé, A. Soffer and C.D. Sogge, Decay estimates for Schrödinger operators. Commun. Pure Appl. Math. 44 (1991) 573-604. [CrossRef] [Google Scholar]
  23. K.H. Kerner, Note on the forced and damped oscillator in quantum mechanics. Can. J. Phys. 36 (1958) 371-377. [Google Scholar]
  24. C. Lan, T.J. Tarn, Q.-S. Chi and J.W. Clark, Analytic controllability of time-dependent quantum control systems. J. Math. Phys. 46 (2005) 052102 [CrossRef] [MathSciNet] [Google Scholar]
  25. I. Lasiecka and R. Triggiani, Optimal regularity, exact controllability and uniform stabilization of Schrödinger equations with Dirichlet controls. Differ. Int. Equ. 5 (1992) 571-535. [Google Scholar]
  26. I. Lasiecka and R. Triggiani, Control theory for partial differential equations, continuous and approximation theories. I & II. Cambridge University Press, Cambridge (2000). [Google Scholar]
  27. I. Lasiecka, R. Triggiani and X. Zhang, Global uniqueness, observability and stabilization of nonconservative Schrödinger equations via pointwise Carleman estimates. I. Formula -estimates. J. Inverse Ill-Posed Probl. 12 (2004) 43-123. [MathSciNet] [Google Scholar]
  28. I. Lasiecka, R. Triggiani and X. Zhang, Global uniqueness, observability and stabilization of nonconservative Schrödinger equations via pointwise Carleman estimates. II. Formula -estimates. J. Inverse Ill-Posed Probl. 12 (2004) 183-231. [MathSciNet] [Google Scholar]
  29. G. Lebeau, Contrôle de l'équation de Schrödinger. Jour. Math. Pures Appl. 71 (1992) 267-291. [Google Scholar]
  30. C. LeBris, Control theory applied to quantum chemistry, some tracks, in Conf. Int. contrôle des systèmes gouvernés par des équations aux derivées partielles. ESAIM Proc. 8 (2000) 77-94. [Google Scholar]
  31. C. LeBris, Computational Chemistry, in Handbook of Numerical Analysis, C. LeBris, Ph.G. Ciarlet Eds. North-Holland, Amsterdam (2003). [Google Scholar]
  32. J.-L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués. Tome 1 & 2. Masson, Paris (1988). [Google Scholar]
  33. E. Machtyngier, Exact controllability for the Schrödinger equation. SIAM J. Contr. Opt. 32 (1994) 24-34. [Google Scholar]
  34. E. Machtyngier and E. Zuazua, Stabilization of the Schrödinger equation. Portugaliae Mat. 51 (1994) 243-256. [Google Scholar]
  35. M. Mirrahimi and P. Rouchon, Controllability of quantum harmonic oscillators. IEEE Trans. Automatic Control 49 (2004) 745-747. [CrossRef] [MathSciNet] [Google Scholar]
  36. K.-D. Phung, Observability and control of Schrödinger equations. SIAM J. Contr. Opt. 40 (2001) 211-230. [CrossRef] [MathSciNet] [Google Scholar]
  37. S.A. Rice and M. Zhao, Optical Control of Molecular Dynamics. John Wiley & Sons, New York (2000). [Google Scholar]
  38. D.L. Russell, Controllability and stabilizability theory for linear partial differential equations, recent progress and open questions. SIAM Rev. (1978) 20 639-739. [Google Scholar]
  39. S.G. Schirmer, J.V. Leahy and A.I. Solomon, Degrees of controllability for quantum systems and application to atomic systems. J. Phys. A 35 (2002) 4125-4141. [CrossRef] [MathSciNet] [Google Scholar]
  40. A.P. Shustov, Coherent states and energy spectrum of the anharmonic osciallator. J. Phys. A 11 (1978) 1771-1780. [CrossRef] [Google Scholar]
  41. E.M. Stein, Singular Integrals and Differentiability Properties of Functions. Princeton University Press (1974). [Google Scholar]
  42. G. Turinici, Analyse de méthodes numériques de simulation et contrôle en chimie quantique. Ph.D. Thesis, Univ. Paris VI (2000). [Google Scholar]
  43. G. Turinici, Controllable quantities for bilinear quantum systems, in Proc. of the 39th IEEE Conference on Decision and Control, Sydney, Australia (2000) 1364-1369. [Google Scholar]
  44. R.M. Young, An Introduction to Nonharmonic Fourier Series. Academic Press, New York (1980). [Google Scholar]
  45. J. Zabczyk, Introduction to Control Theory. Birkhäuser, Basel (1994). [Google Scholar]
  46. E. Zuazua, Remarks on the controllability of the Schrödinger equation. CRM Proc. Lecture Notes 33 (2003) 193-211. [Google Scholar]

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