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Volumn 30, Issue 1, 2007, Pages 441-462

Multigrid optimization schemes for solving Bose-Einstein condensate control problems

Author keywords

Bose Einstein condensates; Cascadic acceleration; Gross Pitaevskii equation; Multigrid method; Nonlinear conjugate gradient method; Optimal control theory; Optimality conditions

Indexed keywords

BOSE-EINSTEIN CONDENSATION; COMPUTATION THEORY; CONJUGATE GRADIENT METHOD; CONTROL THEORY; NONLINEAR EQUATIONS; NONLINEAR PROGRAMMING; OPTIMAL CONTROL SYSTEMS; QUANTUM CHEMISTRY; STATISTICAL MECHANICS;

EID: 55549091084     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/070686135     Document Type: Article
Times cited : (20)

References (40)
  • 1
    • 55549143121 scopus 로고    scopus 로고
    • A. D. BANDRAUK, M. C. DELFOUR, AND C. LE BRIS, EDS., Quantum Control: Mathematical and Numerical Challenges, CRM Proc. Lecture Notes 33, American Mathematical Society, Providence, RI, 2004.
    • A. D. BANDRAUK, M. C. DELFOUR, AND C. LE BRIS, EDS., Quantum Control: Mathematical and Numerical Challenges, CRM Proc. Lecture Notes 33, American Mathematical Society, Providence, RI, 2004.
  • 2
    • 6344289363 scopus 로고    scopus 로고
    • Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow
    • W. BAO AND Q. DU, Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow, SIAM J. Sci. Comput., 25 (2004), pp. 1674-1697.
    • (2004) SIAM J. Sci. Comput , vol.25 , pp. 1674-1697
    • BAO, W.1    DU, Q.2
  • 3
    • 0037408314 scopus 로고    scopus 로고
    • Numerical solution of the Gross-Pitaevskii Equation for Bose-Einstein condensation
    • W. BAO, D. JAKSCH, AND P. A. MARKOWICH, Numerical solution of the Gross-Pitaevskii Equation for Bose-Einstein condensation, J. Comput. Phys., 187 (2003), pp. 318-342.
    • (2003) J. Comput. Phys , vol.187 , pp. 318-342
    • BAO, W.1    JAKSCH, D.2    MARKOWICH, P.A.3
  • 4
    • 0037138007 scopus 로고    scopus 로고
    • On time-splitting spectral approximation for the Schrödinger equation in the semiclassical regime
    • W. BAO, S. JIN, AND P. A. MARKOWIOH, On time-splitting spectral approximation for the Schrödinger equation in the semiclassical regime, J. Comput. Phys., 175 (2002), pp. 487-524.
    • (2002) J. Comput. Phys , vol.175 , pp. 487-524
    • BAO, W.1    JIN, S.2    MARKOWIOH, P.A.3
  • 5
    • 0030369254 scopus 로고    scopus 로고
    • The cascadic multigrid method for elliptic problems
    • F. A. BORNEMANN AND P. DEUFLHARD, The cascadic multigrid method for elliptic problems, Numer. Math., 75 (1996), pp. 135-152.
    • (1996) Numer. Math , vol.75 , pp. 135-152
    • BORNEMANN, F.A.1    DEUFLHARD, P.2
  • 7
    • 33747884718 scopus 로고    scopus 로고
    • Analysis of a leap-frog pseudospectral scheme for the Schroedinger equation
    • A. BORZÌ AND E. DECKER, Analysis of a leap-frog pseudospectral scheme for the Schroedinger equation, J. Comput. Appl. Math., 193 (2006), pp. 65-88.
    • (2006) J. Comput. Appl. Math , vol.193 , pp. 65-88
    • BORZÌ, A.1    DECKER, E.2
  • 8
    • 41449096046 scopus 로고    scopus 로고
    • Formulation and numerical solution of finite-level quantam optimal control problems
    • to appear
    • A. BORZÌ, J. SALOMON, AND S. VOLKWEIN, Formulation and numerical solution of finite-level quantam optimal control problems, J. Comput. Appl. Math., to appear.
    • J. Comput. Appl. Math
    • BORZÌ, A.1    SALOMON, J.2    VOLKWEIN, S.3
  • 9
    • 0036877299 scopus 로고    scopus 로고
    • Optimal quantum control in nanostructures: Theory and application to a generic three-level system
    • A. BORZÌ, G. STADLER, AND U. HOHENESTER, Optimal quantum control in nanostructures: Theory and application to a generic three-level system, Phys. Rev. A, 66 (2002), 053811.
    • (2002) Phys. Rev. A , vol.66 , pp. 053811
    • BORZÌ, A.1    STADLER, G.2    HOHENESTER, U.3
  • 10
    • 84966233568 scopus 로고
    • Multi-level adaptive solutions to boundary-value problems
    • A. BRANDT, Multi-level adaptive solutions to boundary-value problems, Math. Comp., 31 (1977), pp. 333-390.
    • (1977) Math. Comp , vol.31 , pp. 333-390
    • BRANDT, A.1
  • 12
    • 55549127702 scopus 로고    scopus 로고
    • A. G. BUTKOVSKIY AND YU. I. SAMOILENKO, Control of Quantum-Mechanical Processes and Systems, Kluwer, Norwell, MA, 1990.
    • A. G. BUTKOVSKIY AND YU. I. SAMOILENKO, Control of Quantum-Mechanical Processes and Systems, Kluwer, Norwell, MA, 1990.
  • 13
    • 33745829083 scopus 로고    scopus 로고
    • Theoretical analysis of the implementation of a quantum phase gate with neutral atoms on atom. chips
    • E. CHARRON, M. CIRONE, A. NEGRETTI. J. SCHMIEDMAYER, AND T. CALARCO, Theoretical analysis of the implementation of a quantum phase gate with neutral atoms on atom. chips, Phys. Rev. A, 74 (2006), 012308.
    • (2006) Phys. Rev. A , vol.74 , pp. 012308
    • CHARRON, E.1    CIRONE, M.2    NEGRETTI, A.3    SCHMIEDMAYER, J.4    CALARCO, T.5
  • 14
    • 0033266804 scopus 로고    scopus 로고
    • A nonlinear conjugate gradient method with a strong global convergence property
    • Y. H. DAI AND Y. YUAN, A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optim., 10 (1999), pp. 177-182.
    • (1999) SIAM J. Optim , vol.10 , pp. 177-182
    • DAI, Y.H.1    YUAN, Y.2
  • 18
    • 0002824920 scopus 로고
    • Global convergence properties of conjugate gradient methods for optimization
    • J. C. GILBERT AND J. NOCEDAL, Global convergence properties of conjugate gradient methods for optimization, SIAM J. Optim., 2 (1992), pp. 21-42.
    • (1992) SIAM J. Optim , vol.2 , pp. 21-42
    • GILBERT, J.C.1    NOCEDAL, J.2
  • 21
    • 0001654023 scopus 로고
    • Analysis of a damped nonlinear multilevel method
    • W. HACKBUSCH AND A. REUSKEN, Analysis of a damped nonlinear multilevel method, Numer. Math., 55 (1989), pp. 225-246.
    • (1989) Numer. Math , vol.55 , pp. 225-246
    • HACKBUSCH, W.1    REUSKEN, A.2
  • 22
    • 33747876503 scopus 로고    scopus 로고
    • Optical properties of semiconductor nanostructures: Decoherence versus quantum control
    • M. Rieth and W. Schommers, eds, American Scientific Publishers, Valencia, CA
    • U. HOHENESTER, Optical properties of semiconductor nanostructures: Decoherence versus quantum control, in Handbook of Theoretical and Computational Nanotechnology, M. Rieth and W. Schommers, eds., American Scientific Publishers, Valencia, CA, 2005.
    • (2005) Handbook of Theoretical and Computational Nanotechnology
    • HOHENESTER, U.1
  • 23
    • 33846840518 scopus 로고    scopus 로고
    • Optimal quantum control of Bose Einstein condensates in magnetic microtraps
    • U. HOHENESTER, P.-K. REKDAL, A. BORZÌ, AND J. SCHMIEDMAYER, Optimal quantum control of Bose Einstein condensates in magnetic microtraps, Phys. Rev. A, 75 (2007), 023602.
    • (2007) Phys. Rev. A , vol.75 , pp. 023602
    • HOHENESTER, U.1    REKDAL, P.-K.2    BORZÌ, A.3    SCHMIEDMAYER, J.4
  • 25
    • 19844364417 scopus 로고    scopus 로고
    • Model problems for the multigrid optimization of systems governed by differential equations
    • R. M. LEWIS AND S. G. NASH, Model problems for the multigrid optimization of systems governed by differential equations, SIAM J. Sci. Comput., 26 (2005), pp. 1811-1837.
    • (2005) SIAM J. Sci. Comput , vol.26 , pp. 1811-1837
    • LEWIS, R.M.1    NASH, S.G.2
  • 26
    • 33645498549 scopus 로고    scopus 로고
    • Monotonic time-discretized schemes in quantum control
    • Y. MADAY, J. SALOMON, AND G. TURINICI, Monotonic time-discretized schemes in quantum control, Numer. Math., 103 (2006), pp. 323-338.
    • (2006) Numer. Math , vol.103 , pp. 323-338
    • MADAY, Y.1    SALOMON, J.2    TURINICI, G.3
  • 27
    • 0034452269 scopus 로고    scopus 로고
    • A multigrid approach to discretized optimization problems
    • S. G. NASH, A multigrid approach to discretized optimization problems, Optim. Methods Softw., 14 (2000), pp. 99-116.
    • (2000) Optim. Methods Softw , vol.14 , pp. 99-116
    • NASH, S.G.1
  • 29
    • 0037191441 scopus 로고    scopus 로고
    • Quantum computing by an optimal control algorithm for unitary transformations
    • J. P. PALAO AND R. KOSLOFF, Quantum computing by an optimal control algorithm for unitary transformations, Phys. Rev. Lett., 89 (2002), 188301.
    • (2002) Phys. Rev. Lett , vol.89 , pp. 188301
    • PALAO, J.P.1    KOSLOFF, R.2
  • 30
    • 18144377812 scopus 로고    scopus 로고
    • Nonlinear resonant transport of Bose-Einstein condensates
    • T. PAUL, K. RICHTER, AND P. SCHLAGHECK, Nonlinear resonant transport of Bose-Einstein condensates, Phys. Rev. Lett., 94 (2005), 020404.
    • (2005) Phys. Rev. Lett , vol.94 , pp. 020404
    • PAUL, T.1    RICHTER, K.2    SCHLAGHECK, P.3
  • 31
    • 35949011561 scopus 로고
    • Optimal control of quantum-mechanical systems: Existence, numerical approximation, and applications
    • A. P. PEIRCE, M. A. DAHLEH, AND H. RABITZ, Optimal control of quantum-mechanical systems: Existence, numerical approximation, and applications, Phys. Rev. A, 37 (1988), pp. 4950-4964.
    • (1988) Phys. Rev. A , vol.37 , pp. 4950-4964
    • PEIRCE, A.P.1    DAHLEH, M.A.2    RABITZ, H.3
  • 32
    • 4644304362 scopus 로고    scopus 로고
    • H. RABITZ, G. TURINICI, AND E. BROWN, Control of molecular motion: Concepts, procedures, and future prospects, in Handb. Numer. Anal. 10, P. Ciarlet and J. Lions, eds., Elsevier, Amsterdam, 2003.
    • H. RABITZ, G. TURINICI, AND E. BROWN, Control of molecular motion: Concepts, procedures, and future prospects, in Handb. Numer. Anal. 10, P. Ciarlet and J. Lions, eds., Elsevier, Amsterdam, 2003.
  • 33
    • 4444321157 scopus 로고    scopus 로고
    • Nonlinear time-dependent one-dimensional Schrödinger equation with doublewell potential
    • A. SACCHETTI, Nonlinear time-dependent one-dimensional Schrödinger equation with doublewell potential, SIAM J. Math. Anal., 35 (2004), pp. 1160-1176.
    • (2004) SIAM J. Math. Anal , vol.35 , pp. 1160-1176
    • SACCHETTI, A.1
  • 34
    • 0002609579 scopus 로고    scopus 로고
    • Some estimates of the rate of convergence of the cascadic conjugate gradient method
    • V. V. SHAIDUROV, Some estimates of the rate of convergence of the cascadic conjugate gradient method, Comput. Math. Appl., 31 (1996), pp. 161-171.
    • (1996) Comput. Math. Appl , vol.31 , pp. 161-171
    • SHAIDUROV, V.V.1
  • 35
    • 0000618748 scopus 로고
    • Conjugate gradient methods with inexact, searches
    • D. F. SHANNO, Conjugate gradient methods with inexact, searches, Math. Oper. Res., 3 (1978), pp. 244-256.
    • (1978) Math. Oper. Res , vol.3 , pp. 244-256
    • SHANNO, D.F.1
  • 37
    • 33646916388 scopus 로고
    • On using shaped light pulses to control the selectivity of product formation in a chemical reaction: An application to a multiple level system
    • S. H. TERSIGNI, P. GASPARD, AND S. A. RICE, On using shaped light pulses to control the selectivity of product formation in a chemical reaction: An application to a multiple level system, J. Chem. Phys., 93 (1990), pp. 1670-1680.
    • (1990) J. Chem. Phys , vol.93 , pp. 1670-1680
    • TERSIGNI, S.H.1    GASPARD, P.2    RICE, S.A.3
  • 40
    • 33846850560 scopus 로고    scopus 로고
    • Magnetic microtraps for ultracold atoms
    • J. FORTAGH AND C. ZIMMERMANN, Magnetic microtraps for ultracold atoms, Rev. Modern Phys., 79 (2007), pp. 235-289.
    • (2007) Rev. Modern Phys , vol.79 , pp. 235-289
    • FORTAGH, J.1    ZIMMERMANN, C.2


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