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Volumn 14, Issue 1, 2008, Pages 105-147

Controllablity of a quantum particle in a 1D variable domain

Author keywords

Controllability; Moment theory; Nash Moser theorem; Schr dinger equation

Indexed keywords

CONTROLLABILITY; EIGENVALUES AND EIGENFUNCTIONS; NONLINEAR CONTROL SYSTEMS; ONE DIMENSIONAL; THEOREM PROVING;

EID: 38149044222     PISSN: 12928119     EISSN: 12623377     Source Type: Journal    
DOI: 10.1051/cocv:2007047     Document Type: Article
Times cited : (33)

References (38)
  • 1
    • 0042883845 scopus 로고    scopus 로고
    • Notions of controllability for bilinear multilevel quantum systems
    • F. Albertini and D. D'Alessandro, Notions of controllability for bilinear multilevel quantum systems. IEEE Trans. Automat. Control 48 (2003) 1399-1403.
    • (2003) IEEE Trans. Automat. Control , vol.48 , pp. 1399-1403
    • Albertini, F.1    D'Alessandro, D.2
  • 3
    • 0035981789 scopus 로고    scopus 로고
    • Controllability of quantum mechanical systems by root space decomposition of su(n)
    • C. Altafini, Controllability of quantum mechanical systems by root space decomposition of su(n). J. Math. Phys. 43 (2002) 2051-2062.
    • (2002) J. Math. Phys , vol.43 , pp. 2051-2062
    • Altafini, C.1
  • 5
    • 38149014790 scopus 로고    scopus 로고
    • A bilinear optimal control problem applied to a time dependent Hartree-Fock equation coupled with classical nuclear dynamics
    • L. Baudouin, A bilinear optimal control problem applied to a time dependent Hartree-Fock equation coupled with classical nuclear dynamics. Portugaliae Matematica (NS.) 63 (2006) 293-325.
    • (2006) Portugaliae Matematica (NS.) , vol.63 , pp. 293-325
    • Baudouin, L.1
  • 6
    • 29944435252 scopus 로고    scopus 로고
    • Constructive solution of a bilinear control problem
    • L. Baudouin and J. Salomon, Constructive solution of a bilinear control problem. C.R. Math. Acad. Sci. Paris 342 (2006) 119-124.
    • (2006) C.R. Math. Acad. Sci. Paris , vol.342 , pp. 119-124
    • Baudouin, L.1    Salomon, J.2
  • 7
    • 23644461902 scopus 로고    scopus 로고
    • Regularity for a Schrödinger equation with singular potential and application to bilinear optimal control
    • L. Baudouin, O. Kavian and J.-P. Puel, Regularity for a Schrödinger equation with singular potential 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    Kavian, O.2    Puel, J.-P.3
  • 8
    • 38149066070 scopus 로고    scopus 로고
    • Local controllability of a 1-D beam equation
    • to appear
    • K. Beauchard, Local controllability of a 1-D beam equation. SIAM J. Control Optim. (to appear).
    • SIAM J. Control Optim
    • Beauchard, K.1
  • 9
    • 20044377637 scopus 로고    scopus 로고
    • Local Controllability of a 1-D Schrödinger equation
    • K. Beauchard, 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
  • 10
    • 31744450577 scopus 로고    scopus 로고
    • Controllability of a quantum particle in a moving potential well
    • K. Beauchard and J.-M. Coron, Controllability of a quantum particle in a moving potential well. J. Functional Analysis 232 (2006) 328-389.
    • (2006) J. Functional Analysis , vol.232 , pp. 328-389
    • Beauchard, K.1    Coron, J.-M.2
  • 11
    • 0000871390 scopus 로고
    • Lie theory and control systems defined on spheres
    • R. Brockett, Lie theory and control systems defined on spheres. SIAM J. Appl. Math. 25 (1973) 213-225.
    • (1973) SIAM J. Appl. Math , vol.25 , pp. 213-225
    • Brockett, R.1
  • 12
    • 0034165527 scopus 로고    scopus 로고
    • Contrôle optimal bilinéaire d'une équation de Schrödinger
    • E. Cancès, C. Le Bris and M. Pilot, Contrôle optimal bilinéaire d'une équation de Schrödinger. C.R. Acad. Sci. Paris, Série 1330 (2000) 567-571.
    • (2000) C.R. Acad. Sci. Paris, Série , vol.1 , Issue.330 , pp. 567-571
    • Cancès, E.1    Le Bris, C.2    Pilot, M.3
  • 13
    • 0026626117 scopus 로고
    • Global asymptotic stabilization for controllable systems without drift
    • J.-M. Coron, Global asymptotic 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
  • 14
    • 0000590239 scopus 로고
    • Contrôlabilité exacte frontière de l'équation d'Euler des fluides parfaits incompressibles bidimensionnels
    • J.-M. Coron, Contrôlabilité exacte frontière de l'équation d'Euler des fluides parfaits incompressibles bidimensionnels. C. R. Acad. Sci. Paris 317 (1993) 271-276.
    • (1993) C. R. Acad. Sci. Paris , vol.317 , pp. 271-276
    • Coron, J.-M.1
  • 15
    • 0000731294 scopus 로고    scopus 로고
    • On the controllability of 2-D incompressible perfect fluids
    • J.-M. Coron, On the controllability of 2-D incompressible perfect fluids. J. Math. Pures Appl. 75 (1996) 155-188.
    • (1996) J. Math. Pures Appl , vol.75 , pp. 155-188
    • Coron, J.-M.1
  • 16
    • 2442663960 scopus 로고    scopus 로고
    • Local Controllability of a 1-D Tank Containing a Fluid Modeled by the shallow water equations
    • J.-M. Coron, Local Controllability of a 1-D Tank Containing a Fluid Modeled by the shallow water equations. ESAIM: COCV 8 (2002) 513-554.
    • (2002) ESAIM: COCV , vol.8 , pp. 513-554
    • Coron, J.-M.1
  • 17
    • 29944433591 scopus 로고    scopus 로고
    • On the small-time local controllability of a quantum particule in a moving one-dimensional infinite square potential well
    • J.-M. Coron, On the small-time local controllability of a quantum particule in a moving one-dimensional infinite square potential well. C.R. Acad. Sci., Série 1342 (2006) 103-108.
    • (2006) C.R. Acad. Sci., Série , vol.1342 , pp. 103-108
    • Coron, J.-M.1
  • 18
    • 3042583135 scopus 로고    scopus 로고
    • Exact boundary controllability of a nonlinear KdV equation with critical lengths
    • J.-M. Coron and E. Crépeau, Exact boundary controllability of a nonlinear KdV equation with critical lengths. J. Eur. Math. Soc. 6 (2004) 367-398.
    • (2004) J. Eur. Math. Soc , vol.6 , pp. 367-398
    • Coron, J.-M.1    Crépeau, E.2
  • 19
    • 0030313177 scopus 로고    scopus 로고
    • Global exact controllability of the 2D Navier-Stokes equation on a manifold without boundary
    • J.-M. Coron and A. Fursikov, Global exact controllability of the 2D Navier-Stokes equation on a manifold without boundary. Russ. J. Math. Phys. 4 (1996) 429-448.
    • (1996) Russ. J. Math. Phys , vol.4 , pp. 429-448
    • Coron, J.-M.1    Fursikov, A.2
  • 20
    • 0002427074 scopus 로고    scopus 로고
    • Exact controllability of the Navier-Stokes and Boussinesq equations
    • A.V. Fursikov and O.Yu. Imanuvilov, Exact controllability of the Navier-Stokes and Boussinesq equations. Russian Math. Surveys 54 (1999) 565-618.
    • (1999) Russian Math. Surveys , vol.54 , pp. 565-618
    • Fursikov, A.V.1    Imanuvilov, O.Y.2
  • 21
    • 34250317414 scopus 로고    scopus 로고
    • On the controllability of the ID isentropic Euler equation
    • O. Glass, On the controllability of the ID isentropic Euler equation. J. European Mathematical Society 9 (2007) 427-486.
    • (2007) J. European Mathematical Society , vol.9 , pp. 427-486
    • Glass, O.1
  • 22
    • 0034425491 scopus 로고    scopus 로고
    • Exact boundary controllability of 3-D Euler equation
    • O. Glass, Exact boundary controllability of 3-D Euler equation. ESAIM: COCV 5 (2000) 1-14.
    • (2000) ESAIM: COCV , vol.5 , pp. 1-14
    • Glass, O.1
  • 23
    • 0345547748 scopus 로고    scopus 로고
    • On the controllability of the Vlasov-Poisson system
    • O. Glass, On the controllability of the Vlasov-Poisson system. J. Differential Equations 195 (2003) 332-379.
    • (2003) J. Differential Equations , vol.195 , pp. 332-379
    • Glass, O.1
  • 25
    • 0000089068 scopus 로고
    • Séries lacunaires et contrôle semi-interne des vibrations d'une plaque rectangulaire
    • A. Haraux, Séries lacunaires et contrôle semi-interne des vibrations d'une plaque rectangulaire. J. Math. Pures Appl. 68 (1989) 457-465.
    • (1989) J. Math. Pures Appl , vol.68 , pp. 457-465
    • Haraux, A.1
  • 27
    • 84996138194 scopus 로고    scopus 로고
    • On the controllability of the Burgers equation
    • T. Horsin, On the controllability of the Burgers equation. ESAIM: COCV 3 (1998) 83-95.
    • (1998) ESAIM: COCV , vol.3 , pp. 83-95
    • Horsin, T.1
  • 28
    • 33749682238 scopus 로고    scopus 로고
    • Limitations on the control of Schrödinger equations
    • R. Ilner, H. Lange and H. Teismann, Limitations on the control of Schrödinger equations. ESAIM: COCV 12 (2006) 615-635.
    • (2006) ESAIM: COCV , vol.12 , pp. 615-635
    • Ilner, R.1    Lange, H.2    Teismann, H.3
  • 31
    • 84972514083 scopus 로고
    • Optimal regularity, exact controllability and uniform stabilization of Schrödinger equations with Dirichlet controls
    • I. Lasiecka and R. Triggiani, Optimal regularity, exact controllability and uniform stabilization of Schrödinger equations with Dirichlet controls. Differential Integral Equations 5 (1992) 571-535.
    • (1992) Differential Integral Equations , vol.5 , pp. 571-535
    • Lasiecka, I.1    Triggiani, R.2
  • 32
    • 2942683404 scopus 로고    scopus 로고
    • Global uniqueness, observability and stabilization of nonconservative Schrödinger equations via pointwise Carlemann estimates
    • I. Lasiecka, R. Triggiani and X. Zhang, Global uniqueness, observability and stabilization of nonconservative Schrödinger equations via pointwise Carlemann estimates. J. Inverse III Posed-Probl. 12 (2004) 183-231.
    • (2004) J. Inverse III Posed-Probl , vol.12 , pp. 183-231
    • Lasiecka, I.1    Triggiani, R.2    Zhang, X.3
  • 33
    • 0000977450 scopus 로고
    • Contrôle de l'équation de Schrödinger
    • G. Lebeau, Contrôle de l'équation de Schrödinger. J. Math. Pures Appl. 71 (1992) 267-291.
    • (1992) J. Math. Pures Appl , vol.71 , pp. 267-291
    • Lebeau, G.1
  • 34
    • 0028257122 scopus 로고
    • Exact controllability for the Schrödinger equation
    • Machtyngier, Exact controllability for the Schrödinger equation. SIAM J. Contr. Opt. 32 (1994) 24-34.
    • (1994) SIAM J. Contr. Opt , vol.32 , pp. 24-34
    • Machtyngier1
  • 35
    • 2942557186 scopus 로고    scopus 로고
    • Controllability of quantum harmonic oscillators
    • M. Mirrahimi and P. Rouchon, Controllability of quantum harmonic oscillators. IEEE Trans. Automat. Control 49 (2004) 745-747.
    • (2004) IEEE Trans. Automat. Control , vol.49 , pp. 745-747
    • Mirrahimi, M.1    Rouchon, P.2
  • 36
    • 0029342141 scopus 로고
    • Control of systems without drift via generic loops
    • E. Sontag, Control of systems without drift via generic loops. IEEE Trans. Automat. Control 40 (1995) 1210-1219.
    • (1995) IEEE Trans. Automat. Control , vol.40 , pp. 1210-1219
    • Sontag, E.1
  • 37
    • 38149058304 scopus 로고    scopus 로고
    • G. Turinici, On the controllability of bilinear quantum systems, in Mathematical Models and Methods for Ab Initio Quantum Chemistry, C. Le Bris and M. Defranceschi Eds., Lect. Notes Chemistry 74, Springer (2000).
    • G. Turinici, On the controllability of bilinear quantum systems, in Mathematical Models and Methods for Ab Initio Quantum Chemistry, C. Le Bris and M. Defranceschi Eds., Lect. Notes Chemistry 74, Springer (2000).
  • 38
    • 31744446192 scopus 로고    scopus 로고
    • Remarks on the controllability of the Schrödinger equation
    • E. Zuazua, Remarks on the controllability of the Schrödinger equation. CRM Proc. Lect. Notes 33 (2003) 193-211.
    • (2003) CRM Proc. Lect. Notes , vol.33 , pp. 193-211
    • Zuazua, E.1


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