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Volumn 27, Issue 3, 2010, Pages 901-915

Global approximate controllability for Schrödinger equation in higher Sobolev norms and applications

Author keywords

[No Author keywords available]

Indexed keywords

CONTROLLABILITY;

EID: 77951253441     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2010.01.004     Document Type: Article
Times cited : (77)

References (38)
  • 1
    • 33745808312 scopus 로고    scopus 로고
    • An estimation of the controllability time for single-input systems on compact Lie groups
    • Agrachev A., and Chambrion T. An estimation of the controllability time for single-input systems on compact Lie groups. J. ESAIM Control Optim. Calc. Var. 12 3 (2006) 409-441
    • (2006) J. ESAIM Control Optim. Calc. Var. , vol.12 , Issue.3 , pp. 409-441
    • Agrachev, A.1    Chambrion, T.2
  • 2
    • 84968483685 scopus 로고
    • Genericity of simple eigenvalues for elliptic PDE's
    • Albert J.H. Genericity of simple eigenvalues for elliptic PDE's. Proc. Amer. Math. Soc. 48 (1975) 413-418
    • (1975) Proc. Amer. Math. Soc. , vol.48 , pp. 413-418
    • Albert, J.H.1
  • 3
    • 0042883845 scopus 로고    scopus 로고
    • Notions of controllability for bilinear multilevel quantum systems
    • Albertini F., and D'Alessandro D. Notions of controllability for bilinear multilevel quantum systems. IEEE Trans. Automat. Control 48 8 (2003) 1399-1403
    • (2003) IEEE Trans. Automat. Control , vol.48 , Issue.8 , pp. 1399-1403
    • Albertini, F.1    D'Alessandro, D.2
  • 4
    • 0035981789 scopus 로고    scopus 로고
    • Controllability of quantum mechanical systems by root space decomposition of su (n)
    • Altafini C. Controllability of quantum mechanical systems by root space decomposition of su (n). J. Math. Phys. 43 5 (2002) 2051-2062
    • (2002) J. Math. Phys. , vol.43 , Issue.5 , pp. 2051-2062
    • Altafini, C.1
  • 5
    • 0000107228 scopus 로고
    • Controllability for distributed bilinear systems
    • Ball J.M., Marsden J.E., and Slemrod M. Controllability for distributed bilinear systems. SIAM J. Control Optim. 20 4 (1982) 575-597
    • (1982) SIAM J. Control Optim. , vol.20 , Issue.4 , pp. 575-597
    • Ball, J.M.1    Marsden, J.E.2    Slemrod, M.3
  • 6
    • 0036906375 scopus 로고    scopus 로고
    • Uniqueness and stability in an inverse problem for the Schrödinger equation
    • Baudouin L., and Puel J.-P. Uniqueness and stability in an inverse problem for the Schrödinger equation. Inverse Problems 18 6 (2001) 1537-1554
    • (2001) Inverse Problems , vol.18 , Issue.6 , pp. 1537-1554
    • Baudouin, L.1    Puel, J.-P.2
  • 7
    • 20044377637 scopus 로고    scopus 로고
    • Local controllability of a 1D Schrödinger equation
    • Beauchard K. Local controllability of a 1D Schrödinger equation. J. Math. Pures Appl. 84 7 (2005) 851-956
    • (2005) J. Math. Pures Appl. , vol.84 , Issue.7 , pp. 851-956
    • Beauchard, K.1
  • 8
    • 77951256307 scopus 로고    scopus 로고
    • Local controllability of a 1D bilinear Schrödinger equation: A simpler proof
    • Preprint
    • K. Beauchard, Local controllability of a 1D bilinear Schrödinger equation: a simpler proof, Preprint, 2009
    • (2009)
    • Beauchard, K.1
  • 9
    • 31744450577 scopus 로고    scopus 로고
    • Controllability of a quantum particle in a moving potential well
    • Beauchard K., and Coron J.-M. Controllability of a quantum particle in a moving potential well. J. Funct. Anal. 232 2 (2006) 328-389
    • (2006) J. Funct. Anal. , vol.232 , Issue.2 , pp. 328-389
    • Beauchard, K.1    Coron, J.-M.2
  • 10
    • 33947213375 scopus 로고    scopus 로고
    • Implicit Lyapunov control of finite dimensional Schrödinger equations
    • Beauchard K., Coron J.-M., Mirrahimi M., and Rouchon P. Implicit Lyapunov control of finite dimensional Schrödinger equations. Systems Control Lett. 56 5 (2007) 388-395
    • (2007) Systems Control Lett. , vol.56 , Issue.5 , pp. 388-395
    • Beauchard, K.1    Coron, J.-M.2    Mirrahimi, M.3    Rouchon, P.4
  • 11
    • 77950961578 scopus 로고    scopus 로고
    • Practical stabilization of a quantum particle in a one-dimensional infinite square potential well
    • Beauchard K., and Mirrahimi M. Practical stabilization of a quantum particle in a one-dimensional infinite square potential well. SIAM J. Control Optim. 48 2 (2009) 1179-1205
    • (2009) SIAM J. Control Optim. , vol.48 , Issue.2 , pp. 1179-1205
    • Beauchard, K.1    Mirrahimi, M.2
  • 12
    • 21844511925 scopus 로고
    • Periodic nonlinear Schrödinger equation and invariant measures
    • Bourgain J. Periodic nonlinear Schrödinger equation and invariant measures. Comm. Math. Phys. 166 1 (1994) 1-26
    • (1994) Comm. Math. Phys. , vol.166 , Issue.1 , pp. 1-26
    • Bourgain, J.1
  • 14
  • 15
    • 26844527772 scopus 로고    scopus 로고
    • Ergodicity for a weakly damped stochastic nonlinear Schrödinger equations
    • Debussche A., and Odasso C. Ergodicity for a weakly damped stochastic nonlinear Schrödinger equations. J. Evol. Eq. 3 5 (2005) 317-356
    • (2005) J. Evol. Eq. , vol.3 , Issue.5 , pp. 317-356
    • Debussche, A.1    Odasso, C.2
  • 16
    • 33749642834 scopus 로고    scopus 로고
    • Stabilization and control for the nonlinear Schrödinger equation on a compact surface
    • Dehman B., Gérard P., and Lebeau G. Stabilization and control for the nonlinear Schrödinger equation on a compact surface. Math. Z. 254 4 (2006) 729-749
    • (2006) Math. Z. , vol.254 , Issue.4 , pp. 729-749
    • Dehman, B.1    Gérard, P.2    Lebeau, G.3
  • 17
    • 71849105789 scopus 로고    scopus 로고
    • Approximate controllability for a system of Schrödinger equations modeling a single trapped ion
    • Ervedoza S., and Puel J.-P. Approximate controllability for a system of Schrödinger equations modeling a single trapped ion. Ann. Inst. H. Poincaré Anal. Non Linéaire 26 6 (2009) 2111-2136
    • (2009) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.26 , Issue.6 , pp. 2111-2136
    • Ervedoza, S.1    Puel, J.-P.2
  • 19
    • 0001226256 scopus 로고
    • Unique continuation and absence of positive eigenvalues for Schrödinger operators (with an appendix by E.M. Stein)
    • Jerison D., and Kenig C.E. Unique continuation and absence of positive eigenvalues for Schrödinger operators (with an appendix by E.M. Stein). Ann. of Math. 121 3 (1985) 463-494
    • (1985) Ann. of Math. , vol.121 , Issue.3 , pp. 463-494
    • Jerison, D.1    Kenig, C.E.2
  • 22
    • 0001505224 scopus 로고    scopus 로고
    • Ergodicity for the randomly forced 2D Navier-Stokes equations
    • Kuksin S., and Shirikyan A. Ergodicity for the randomly forced 2D Navier-Stokes equations. Math. Phys. Anal. Geom. 4 2 (2001) 147-195
    • (2001) Math. Phys. Anal. Geom. , vol.4 , Issue.2 , pp. 147-195
    • Kuksin, S.1    Shirikyan, A.2
  • 23
    • 1842683021 scopus 로고    scopus 로고
    • Randomly forced CGL equation: stationary measures and the inviscid limit
    • Kuksin S., and Shirikyan A. Randomly forced CGL equation: stationary measures and the inviscid limit. J. Phys. A: Math. Gen. 37 12 (2004) 3805-3822
    • (2004) J. Phys. A: Math. Gen. , vol.37 , Issue.12 , pp. 3805-3822
    • Kuksin, S.1    Shirikyan, A.2
  • 24
    • 0000977450 scopus 로고
    • Contrôle de l'équation de Schrödinger
    • Lebeau G. Contrôle de l'équation de Schrödinger. J. Math. Pures Appl. 71 3 (1992) 267-291
    • (1992) J. Math. Pures Appl. , vol.71 , Issue.3 , pp. 267-291
    • Lebeau, G.1
  • 25
    • 32544439582 scopus 로고
    • Stabilization of the Schrödinger equation
    • Machtyngier E., and Zuazua E. Stabilization of the Schrödinger equation. Portugaliae Matematica 51 2 (1994) 243-256
    • (1994) Portugaliae Matematica , vol.51 , Issue.2 , pp. 243-256
    • Machtyngier, E.1    Zuazua, E.2
  • 26
    • 39749085219 scopus 로고    scopus 로고
    • Lyapunov control of a particle in a finite quantum potential well
    • San Diego
    • M. Mirrahimi, Lyapunov control of a particle in a finite quantum potential well, in: IEEE Conf. on Decision and Control, San Diego, 2006
    • (2006) IEEE Conf. on Decision and Control
    • Mirrahimi, M.1
  • 27
    • 70349820722 scopus 로고    scopus 로고
    • Exponential mixing for finite-dimensional approximations of the Schrödinger equation with multiplicative noise
    • Nersesyan V. Exponential mixing for finite-dimensional approximations of the Schrödinger equation with multiplicative noise. Dynam. PDE 6 2 (2009) 167-183
    • (2009) Dynam. PDE , vol.6 , Issue.2 , pp. 167-183
    • Nersesyan, V.1
  • 28
    • 70349678394 scopus 로고    scopus 로고
    • Growth of Sobolev norms and controllability of the Schrödinger equation
    • Nersesyan V. Growth of Sobolev norms and controllability of the Schrödinger equation. Comm. Math. Phys. 290 1 (2009) 371-387
    • (2009) Comm. Math. Phys. , vol.290 , Issue.1 , pp. 371-387
    • Nersesyan, V.1
  • 30
    • 0007325010 scopus 로고    scopus 로고
    • An inverse Sturm-Liouville problem by three spectra
    • Pivovarchik V.N. An inverse Sturm-Liouville problem by three spectra. Integr. Equ. Oper. Theory 34 2 (1999) 234-243
    • (1999) Integr. Equ. Oper. Theory , vol.34 , Issue.2 , pp. 234-243
    • Pivovarchik, V.N.1
  • 31
    • 77951256834 scopus 로고    scopus 로고
    • The squares of Laplacian-Dirichlet eigenfunctions are generically linearly independent
    • Preprint
    • Y. Privat, M. Sigalotti, The squares of Laplacian-Dirichlet eigenfunctions are generically linearly independent, Preprint, 2008
    • (2008)
    • Privat, Y.1    Sigalotti, M.2
  • 34
    • 0033469793 scopus 로고    scopus 로고
    • How rare are multiple eigenvalues?
    • Teytel M. How rare are multiple eigenvalues?. Comm. Pure Appl. Math. 52 8 (1999) 917-934
    • (1999) Comm. Pure Appl. Math. , vol.52 , Issue.8 , pp. 917-934
    • Teytel, M.1
  • 35
    • 84975903381 scopus 로고    scopus 로고
    • G. Turinici, On the Controllability of Bilinear Quantum Systems, Lecture Notes in Chem., 74, 2000
    • G. Turinici, On the Controllability of Bilinear Quantum Systems, Lecture Notes in Chem., vol. 74, 2000
  • 36
    • 0035371423 scopus 로고    scopus 로고
    • Quantum wavefunction controllability
    • Turinici G., and Rabitz H. Quantum wavefunction controllability. Chem. Phys. 267 1 (2001) 1-9
    • (2001) Chem. Phys. , vol.267 , Issue.1 , pp. 1-9
    • Turinici, G.1    Rabitz, H.2
  • 37
    • 48449103020 scopus 로고    scopus 로고
    • Invariant measures for the nonlinear Schrödinger equation on the disc
    • Tzvetkov N. Invariant measures for the nonlinear Schrödinger equation on the disc. Dynam. PDE 3 2 (2006) 111-160
    • (2006) Dynam. PDE , vol.3 , Issue.2 , pp. 111-160
    • Tzvetkov, N.1
  • 38
    • 31744446192 scopus 로고    scopus 로고
    • Remarks on the controllability of the Schrödinger equation
    • Zuazua E. Remarks on the controllability of the Schrödinger equation. CRM Proc. Lecture Notes 33 (2003) 193-211
    • (2003) CRM Proc. Lecture Notes , vol.33 , pp. 193-211
    • Zuazua, E.1


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