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Volumn 26, Issue 5, 2009, Pages 1743-1765

Lyapunov control of a quantum particle in a decaying potential

Author keywords

Approximate stabilization; Dispersive estimates; Lyapunov techniques; Nonlinear control of PDEs; Pre compactness

Indexed keywords

AIRCRAFT ENGINES; STABILIZATION;

EID: 69949096628     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2008.09.006     Document Type: Article
Times cited : (76)

References (52)
  • 1
    • 0000815745 scopus 로고
    • Spectral properties of Schrödinger operators and scattering theory
    • Agmon S. Spectral properties of Schrödinger operators and scattering theory. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 4 2 (1975) 151-218
    • (1975) Ann. Scuola Norm. Sup. Pisa Cl. Sci. , vol.4 , Issue.2 , pp. 151-218
    • Agmon, S.1
  • 2
    • 0003308723 scopus 로고
    • Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigenfunctions of N-body Schrödinger Operators
    • Princeton University Press
    • Agmon S. Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigenfunctions of N-body Schrödinger Operators. Mathematical Notes vol. 29 (1982), Princeton University Press
    • (1982) Mathematical Notes , vol.29
    • Agmon, S.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
    • 0033471912 scopus 로고    scopus 로고
    • Adiabatic theorem without a gap condition
    • Avron J.E., and Elgart A. Adiabatic theorem without a gap condition. Comm. Math. Phys. 203 (1999) 445-463
    • (1999) Comm. Math. Phys. , vol.203 , pp. 445-463
    • Avron, J.E.1    Elgart, A.2
  • 6
    • 23644461902 scopus 로고    scopus 로고
    • Regularity for a Schrödinger equation with singular potentials and application to bilinear optimal control
    • Baudouin L., Puel J.P., and Kavian O. Regularity for a Schrödinger equation with singular potentials and application to bilinear optimal control. J. Differential Equations 216 (2005) 188-222
    • (2005) J. Differential Equations , vol.216 , pp. 188-222
    • Baudouin, L.1    Puel, J.P.2    Kavian, O.3
  • 7
    • 29944435252 scopus 로고    scopus 로고
    • Constructive solutions of a bilinear control problem
    • Baudouin L., and Salomon J. Constructive solutions of a bilinear control problem. C. R. Acad. Sci. Paris, Ser. I 342 2 (2006) 119-124
    • (2006) C. R. Acad. Sci. Paris, Ser. I , vol.342 , Issue.2 , pp. 119-124
    • Baudouin, L.1    Salomon, J.2
  • 8
    • 20044377637 scopus 로고    scopus 로고
    • Local controllability of a 1-D Schrödinger equation
    • Beauchard K. Local controllability of a 1-D Schrödinger equation. J. Math. Pures Appl. 84 (2005) 851-956
    • (2005) J. Math. Pures Appl. , vol.84 , pp. 851-956
    • Beauchard, K.1
  • 9
    • 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 (2007) 388-395
    • (2007) Systems Control Lett. , vol.56 , pp. 388-395
    • Beauchard, K.1    Coron, J.-M.2    Mirrahimi, M.3    Rouchon, P.4
  • 10
    • 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 (2006) 328-389
    • (2006) J. Funct. Anal. , vol.232 , pp. 328-389
    • Beauchard, K.1    Coron, J.M.2
  • 12
    • 58249137155 scopus 로고    scopus 로고
    • Controllability of the discrete-spectrum Schrödinger equation driven by an external field
    • Chambrion T., Mason P., Sigalotti M., and Boscain U. Controllability of the discrete-spectrum Schrödinger equation driven by an external field. Ann. I. H. Poincaré - AN 26 (2009) 329-349
    • (2009) Ann. I. H. Poincaré - AN , vol.26 , pp. 329-349
    • Chambrion, T.1    Mason, P.2    Sigalotti, M.3    Boscain, U.4
  • 13
    • 36449001503 scopus 로고
    • Competitive tracking of molecular objectives described by quantum mechanics
    • Chen Y., Gross P., Ramakrishna V., Rabitz H., and Mease K. Competitive tracking of molecular objectives described by quantum mechanics. J. Chem. Phys. 102 (1995) 8001-8010
    • (1995) J. Chem. Phys. , vol.102 , pp. 8001-8010
    • Chen, Y.1    Gross, P.2    Ramakrishna, V.3    Rabitz, H.4    Mease, K.5
  • 14
    • 0032075414 scopus 로고    scopus 로고
    • Stabilization of a rotating body-beam without damping
    • Coron J.-M., and d'Andréa Novel B. Stabilization of a rotating body-beam without damping. IEEE Trans. Automat. Control 43 5 (1998) 608-618
    • (1998) IEEE Trans. Automat. Control , vol.43 , Issue.5 , pp. 608-618
    • Coron, J.-M.1    d'Andréa Novel, B.2
  • 15
    • 33847379688 scopus 로고    scopus 로고
    • A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws
    • Coron J.-M., d'Andrá Novel B., and Bastin G. A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws. IEEE Trans. Automat. Control 52 1 (2007) 2-11
    • (2007) IEEE Trans. Automat. Control , vol.52 , Issue.1 , pp. 2-11
    • Coron, J.-M.1    d'Andrá Novel, B.2    Bastin, G.3
  • 16
    • 0026626117 scopus 로고
    • Global stabilization for controllable systems without drift
    • Coron J.M. Global stabilization for controllable systems without drift. Math. Control Signals Systems 5 (1992) 295-312
    • (1992) Math. Control Signals Systems , vol.5 , pp. 295-312
    • Coron, J.M.1
  • 17
    • 0033184240 scopus 로고    scopus 로고
    • On the null asymptotic stabilization of the two-dimensional incompressible Euler equations in a simply connected domain
    • Coron J.M. On the null asymptotic stabilization of the two-dimensional incompressible Euler equations in a simply connected domain. SIAM J. Control Optim. 37 (1999) 1874-1896
    • (1999) SIAM J. Control Optim. , vol.37 , pp. 1874-1896
    • Coron, J.M.1
  • 18
    • 49249127518 scopus 로고    scopus 로고
    • Control and Nonlinearity
    • American Mathematica Society, USA
    • Coron J.M. Control and Nonlinearity. Mathematical Surveys and Monographs vol. 136 (2007), American Mathematica Society, USA
    • (2007) Mathematical Surveys and Monographs , vol.136
    • Coron, J.M.1
  • 19
    • 33646581689 scopus 로고    scopus 로고
    • Asymptotic stabilizability by stationary feedback of the two-dimensional Euler equation: The multiconnected case
    • Glass O. Asymptotic stabilizability by stationary feedback of the two-dimensional Euler equation: The multiconnected case. SIAM J. Control Optim. 44 3 (2005) 1105-1147
    • (2005) SIAM J. Control Optim. , vol.44 , Issue.3 , pp. 1105-1147
    • Glass, O.1
  • 20
    • 55549113656 scopus 로고    scopus 로고
    • Controllability and asymptotic stabilization of the Camassa-Holm equation
    • preprint
    • O. Glass, Controllability and asymptotic stabilization of the Camassa-Holm equation, preprint, 2007
    • (2007)
    • Glass, O.1
  • 21
    • 33746746992 scopus 로고    scopus 로고
    • Dispersive bounds for the three-dimensional Schrödinger equation with almost critical potentials
    • Goldberg M. Dispersive bounds for the three-dimensional Schrödinger equation with almost critical potentials. Geom. Funct. Anal. 16 3 (2006) 517-536
    • (2006) Geom. Funct. Anal. , vol.16 , Issue.3 , pp. 517-536
    • Goldberg, M.1
  • 22
    • 7544222374 scopus 로고    scopus 로고
    • Dispersive estimates for Schrödinger operators in dimensions one and three
    • Goldberg M., and Schlag W. Dispersive estimates for Schrödinger operators in dimensions one and three. Comm. Math. Phys. 251 (2004) 157-178
    • (2004) Comm. Math. Phys. , vol.251 , pp. 157-178
    • Goldberg, M.1    Schlag, W.2
  • 24
    • 33745623103 scopus 로고    scopus 로고
    • A counterexample to dispersive estimates for Schrödinger operators in higher dimensions
    • Goldberg M., and Visan M. A counterexample to dispersive estimates for Schrödinger operators in higher dimensions. Comm. Math. Phys. 266 1 (2006) 211-238
    • (2006) Comm. Math. Phys. , vol.266 , Issue.1 , pp. 211-238
    • Goldberg, M.1    Visan, M.2
  • 25
    • 25644449551 scopus 로고    scopus 로고
    • Modeling and feedback control design for quantum state preparation
    • Special issue on quantum control
    • Van Handel R., Stockton J.K., and Mabuchi H. Modeling and feedback control design for quantum state preparation. J. Opt. B: Quant. Semiclass. Opt. 7 (2005) S179-S197 Special issue on quantum control
    • (2005) J. Opt. B: Quant. Semiclass. Opt. , vol.7
    • Van Handel, R.1    Stockton, J.K.2    Mabuchi, H.3
  • 27
    • 84972568716 scopus 로고
    • Spectral properties of Schrödinger operators and time-decay of the wave functions
    • Jensen A., and Kato T. Spectral properties of Schrödinger operators and time-decay of the wave functions. Duke Math. J. 46 3 (1979) 583-611
    • (1979) Duke Math. J. , vol.46 , Issue.3 , pp. 583-611
    • Jensen, A.1    Kato, T.2
  • 28
    • 0036103535 scopus 로고    scopus 로고
    • p-boundedness of wave operators for two-dimensional Schrödinger operators
    • p-boundedness of wave operators for two-dimensional Schrödinger operators. Comm. Math. Phys. 225 3 (2002) 633-637
    • (2002) Comm. Math. Phys. , vol.225 , Issue.3 , pp. 633-637
    • Jensen, A.1    Yajima, K.2
  • 31
    • 0001138601 scopus 로고    scopus 로고
    • Endpoint Strichartz estimates
    • Keel M., and Tao T. Endpoint Strichartz estimates. Amer. J. Math. 5 (1998) 955-980
    • (1998) Amer. J. Math. , vol.5 , pp. 955-980
    • Keel, M.1    Tao, T.2
  • 32
    • 0037158946 scopus 로고    scopus 로고
    • Optimal dynamic discrimination of similar molecules through quantum learning control
    • Li B., Turinici G., Ramakrishna V., and Rabitz H. Optimal dynamic discrimination of similar molecules through quantum learning control. J. Phys. Chem. B 106 33 (2002) 8125-8131
    • (2002) J. Phys. Chem. B , vol.106 , Issue.33 , pp. 8125-8131
    • Li, B.1    Turinici, G.2    Ramakrishna, V.3    Rabitz, H.4
  • 33
    • 84975903449 scopus 로고    scopus 로고
    • M. Mirrahimi, Lyapunov control of a particle in a finite quantum potential well, in: CDC, San Diego, 2006
    • M. Mirrahimi, Lyapunov control of a particle in a finite quantum potential well, in: CDC, San Diego, 2006
  • 34
    • 24944551258 scopus 로고    scopus 로고
    • Lyapunov control of bilinear Schrödinger equations
    • Mirrahimi M., Rouchon P., and Turinici G. Lyapunov control of bilinear Schrödinger equations. Automatica 41 (2005) 1987-1994
    • (2005) Automatica , vol.41 , pp. 1987-1994
    • Mirrahimi, M.1    Rouchon, P.2    Turinici, G.3
  • 35
    • 15744392972 scopus 로고    scopus 로고
    • Reference trajectory tracking for locally designed coherent quantum controls
    • Mirrahimi M., Turinici G., and Rouchon P. Reference trajectory tracking for locally designed coherent quantum controls. J. Phys. Chem. A 109 (2005) 2631-2637
    • (2005) J. Phys. Chem. A , vol.109 , pp. 2631-2637
    • Mirrahimi, M.1    Turinici, G.2    Rouchon, P.3
  • 36
    • 34548854458 scopus 로고    scopus 로고
    • Stabilizing feedback controls for quantum systems
    • Mirrahimi M., and Van Handel R. Stabilizing feedback controls for quantum systems. SIAM J. Control Optim. 46 2 (2007) 445-467
    • (2007) SIAM J. Control Optim. , vol.46 , Issue.2 , pp. 445-467
    • Mirrahimi, M.1    Van Handel, R.2
  • 38
    • 0039687341 scopus 로고
    • Local decay of scattering solutions to Schrödinger's equation
    • Rauch J. Local decay of scattering solutions to Schrödinger's equation. Comm. Math. Phys. 61 2 (1978) 149-168
    • (1978) Comm. Math. Phys. , vol.61 , Issue.2 , pp. 149-168
    • Rauch, J.1
  • 40
    • 1542508715 scopus 로고    scopus 로고
    • Time decay for solutions of Schrödinger equations with rough and time-dependent potentials
    • Rodnianski I., and Schlag W. Time decay for solutions of Schrödinger equations with rough and time-dependent potentials. Invent. Math. 155 (2004) 451-513
    • (2004) Invent. Math. , vol.155 , pp. 451-513
    • Rodnianski, I.1    Schlag, W.2
  • 41
    • 18844449404 scopus 로고    scopus 로고
    • Dispersive estimates for Schrödinger operators in two dimensions
    • Schlag W. Dispersive estimates for Schrödinger operators in two dimensions. Comm. Math. Phys. 257 1 (2005) 87-117
    • (2005) Comm. Math. Phys. , vol.257 , Issue.1 , pp. 87-117
    • Schlag, W.1
  • 42
    • 36549097008 scopus 로고
    • Optimal control of selective vibrational excitation in harmonic linear chain molecules
    • Shi S., Woody A., and Rabitz H. Optimal control of selective vibrational excitation in harmonic linear chain molecules. J. Chem. Phys. 88 11 (1988) 6870-6883
    • (1988) J. Chem. Phys. , vol.88 , Issue.11 , pp. 6870-6883
    • Shi, S.1    Woody, A.2    Rabitz, H.3
  • 43
    • 1642336432 scopus 로고    scopus 로고
    • An estimate for the number of bound states of the Schrödinger operator in two dimensions
    • Stoiciu M. An estimate for the number of bound states of the Schrödinger operator in two dimensions. Proc. Amer. Math. Soc. 132 4 (2004) 1143-1151
    • (2004) Proc. Amer. Math. Soc. , vol.132 , Issue.4 , pp. 1143-1151
    • Stoiciu, M.1
  • 44
    • 84972553620 scopus 로고
    • Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
    • Strichartz R. Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations. Duke Math. J. 44 3 (1977) 705-714
    • (1977) Duke Math. J. , vol.44 , Issue.3 , pp. 705-714
    • Strichartz, R.1
  • 45
    • 0038298901 scopus 로고    scopus 로고
    • General formulation of locally designed coherent control theory for quantum systems
    • Sugawara M. General formulation of locally designed coherent control theory for quantum systems. J. Chem. Phys. 118 15 (2003) 6784-6800
    • (2003) J. Chem. Phys. , vol.118 , Issue.15 , pp. 6784-6800
    • Sugawara, M.1
  • 47
    • 84975898125 scopus 로고    scopus 로고
    • T.J. Tarn, J.W. Clark, D.G. Lucarelli, Controllability of quantum mechanical systems with continuous spectra, in: CDC, Sydney, 2000
    • T.J. Tarn, J.W. Clark, D.G. Lucarelli, Controllability of quantum mechanical systems with continuous spectra, in: CDC, Sydney, 2000
  • 49
    • 0037436743 scopus 로고    scopus 로고
    • Wavefunction controllability in quantum systems
    • Turinici G., and Rabitz H. Wavefunction controllability in quantum systems. J. Phys. A 36 (2003) 2565-2576
    • (2003) J. Phys. A , vol.36 , pp. 2565-2576
    • Turinici, G.1    Rabitz, H.2
  • 50
    • 0002283169 scopus 로고    scopus 로고
    • ′ estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential
    • ′ estimates for the Schrödinger equation on the line and inverse scattering for the nonlinear Schrödinger equation with a potential. J. Funct. Anal. 170 1 (2000) 37-68
    • (2000) J. Funct. Anal. , vol.170 , Issue.1 , pp. 37-68
    • Weder, R.1
  • 51
    • 84972559697 scopus 로고
    • k, p-continuity of wave operators for Schrödinger operators
    • k, p-continuity of wave operators for Schrödinger operators. J. Math. Soc. Japan 47 3 (1995) 551-581
    • (1995) J. Math. Soc. Japan , vol.47 , Issue.3 , pp. 551-581
    • Yajima, K.1
  • 52
    • 0033235580 scopus 로고    scopus 로고
    • p-boundedness of wave operators for two-dimensional Schrödinger operators
    • p-boundedness of wave operators for two-dimensional Schrödinger operators. Comm. Math. Phys. 208 1 (1999) 125-152
    • (1999) Comm. Math. Phys. , vol.208 , Issue.1 , pp. 125-152
    • Yajima, K.1


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