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Volumn 25, Issue 6, 2004, Pages 2145-2164

Long-time-step integrators for almost-adiabatic quantum dynamics

Author keywords

Highly oscillatory problem; Multiple time scales; Numerical integrator; Singularly perturbed Schr dinger equation

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; ELECTRONS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; NUMERICAL METHODS; TIME AND MOTION STUDY; VIBRATING CONVEYORS;

EID: 10244226833     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827502411316     Document Type: Article
Times cited : (18)

References (22)
  • 1
    • 0034676955 scopus 로고    scopus 로고
    • Splitting methods for the time-dependent Schrödinger equation
    • S. BLANES AND P. C. MOAN, Splitting methods for the time-dependent Schrödinger equation, Phys. Lett. A, 265 (2000), pp. 35-42.
    • (2000) Phys. Lett. A , vol.265 , pp. 35-42
    • Blanes, S.1    Moan, P.C.2
  • 2
    • 34250915197 scopus 로고
    • Beweis des Adiabatensatzes
    • M. BORN AND V. FOCK, Beweis des Adiabatensatzes, 1. Phys., 51 (1928), pp. 165-180.
    • (1928) J. Phys. , vol.51 , pp. 165-180
    • Born, M.1    Fock, V.2
  • 3
    • 0000563788 scopus 로고    scopus 로고
    • Quantum-classical molecular dynamics as an approximation to full quantum dynamics
    • F. A. BORNEMANN, P. NETTESHEIM, AND CH. SCHÜTTE, Quantum-classical molecular dynamics as an approximation to full quantum dynamics, J. Chem. Phys., 105 (1996), pp. 1074-1083.
    • (1996) J. Chem. Phys. , vol.105 , pp. 1074-1083
    • Bornemann, F.A.1    Nettesheim, P.2    Schütte, Ch.3
  • 4
    • 0344286523 scopus 로고    scopus 로고
    • On the singular limit of the quantum-classical molecular dynamics model
    • F. A. BORNEMANN AND CH. SCHÜTTE, On the singular limit of the quantum-classical molecular dynamics model, SIAM J. Appl. Math., 59 (1999), pp. 1208-1224.
    • (1999) SIAM J. Appl. Math. , vol.59 , pp. 1208-1224
    • Bornemann, F.A.1    Schütte, Ch.2
  • 6
    • 0009482155 scopus 로고    scopus 로고
    • Nonadiabatic dynamics: Mean-field and surface hopping
    • J. Grotendorst, D. Marx, and A. Muramatsu, eds., John von Neumann Institute for Computing, Forschungszentrum Jülich, Jülich
    • N. L. DOLTSINIS, Nonadiabatic Dynamics: Mean-Field and Surface Hopping, in Quantum Simulations of Complex Many-Body Systems: From Theory to Algorithms, J. Grotendorst, D. Marx, and A. Muramatsu, eds., John von Neumann Institute for Computing, Forschungszentrum Jülich, Jülich, 2002, pp. 377-397.
    • (2002) Quantum Simulations of Complex Many-body Systems: From Theory to Algorithms , pp. 377-397
    • Doltsinis, N.L.1
  • 7
    • 0012987210 scopus 로고    scopus 로고
    • First principles molecular dynamics involving excited states and nonadiabatic transitions
    • N. L. DOLTSINIS AND D. MARX, First principles molecular dynamics involving excited states and nonadiabatic transitions, J. Theor. Comp. Chem., 1 (2002), pp. 319-349.
    • (2002) J. Theor. Comp. Chem. , vol.1 , pp. 319-349
    • Doltsinis, N.L.1    Marx, D.2
  • 8
    • 0001206738 scopus 로고
    • Proof of the Landau-Zener formula in an adiabatic limit with small eigen-value gaps
    • G. A. HAGEDORN, Proof of the Landau-Zener formula in an adiabatic limit with small eigen-value gaps, Comm. Math. Phys., 136 (1991), pp. 433-449.
    • (1991) Comm. Math. Phys. , vol.136 , pp. 433-449
    • Hagedorn, G.A.1
  • 9
    • 0041887727 scopus 로고    scopus 로고
    • A bunch of time integrators for quantum/classical molecular dynamics
    • Computational Molecular Dynamics: Challenges, Methods, Ideas, Springer-Verlag, Berlin
    • M. HOCHBRUCK AND CH. LUBICH, A bunch of time integrators for quantum/classical molecular dynamics, in Computational Molecular Dynamics: Challenges, Methods, Ideas, Lecture Notes in Comput. Sci. Engrg. 4, Springer-Verlag, Berlin, 1999, pp. 421-432.
    • (1999) Lecture Notes in Comput. Sci. Engrg. , vol.4 , pp. 421-432
    • Hochbruck, M.1    Lubich, Ch.2
  • 10
    • 0043228271 scopus 로고    scopus 로고
    • Exponential integrators for quantum-classical molecular dynamics
    • M. HOCHBRUCK AND CH. LUBICH, Exponential integrators for quantum-classical molecular dynamics, BIT, 39 (1999), pp. 620-645.
    • (1999) BIT , vol.39 , pp. 620-645
    • Hochbruck, M.1    Lubich, Ch.2
  • 11
    • 2942576160 scopus 로고    scopus 로고
    • On Magnus integrators for time-dependent Schrödinger equations
    • M. HOCHBRUCK AND CH. LUBICH, On Magnus integrators for time-dependent Schrödinger equations, SIAM J. Numer. Anal., 41 (2003), pp. 945-963.
    • (2003) SIAM J. Numer. Anal. , vol.41 , pp. 945-963
    • Hochbruck, M.1    Lubich, Ch.2
  • 12
    • 0042735340 scopus 로고    scopus 로고
    • On the global error of discretization methods for highly-oscillatory ordinary differential equations
    • A. ISERLES, On the global error of discretization methods for highly-oscillatory ordinary differential equations, BIT, 42 (2002), pp. 561-599.
    • (2002) BIT , vol.42 , pp. 561-599
    • Iserles, A.1
  • 13
    • 85001667552 scopus 로고    scopus 로고
    • Lie-group methods
    • Cambridge University Press, Cambridge, UK
    • A. ISERLES, H. Z. MUNTHE-KAAS, S. P. NØRSETT, AND A. ZANNA, Lie-group methods, in Acta Numer. 9, Cambridge University Press, Cambridge, UK, 2000, pp. 215-365.
    • (2000) Acta Numer. , vol.9 , pp. 215-365
    • Iserles, A.1    Munthe-Kaas, H.Z.2    Nørsett, S.P.3    Zanna, A.4
  • 16
    • 0142086987 scopus 로고    scopus 로고
    • Numerical integrators for quantum dynamics close to the adiabatic limit
    • T. JAHNKE AND CH. LUBICH, Numerical integrators for quantum dynamics close to the adiabatic limit, Numer. Math., 94 (2003), pp. 289-314.
    • (2003) Numer. Math. , vol.94 , pp. 289-314
    • Jahnke, T.1    Lubich, Ch.2
  • 17
    • 84940252991 scopus 로고
    • On the exponential solution of differential equations for a linear operator
    • W. MAGNUS, On the exponential solution of differential equations for a linear operator, Comm. Pure Appl. Math., 7 (1954), pp. 649-673.
    • (1954) Comm. Pure Appl. Math. , vol.7 , pp. 649-673
    • Magnus, W.1
  • 18
    • 0000323669 scopus 로고    scopus 로고
    • Ab initia molecular dynamics: Theory and implementation
    • J. Grotendorst, ed., John von Neumann Institute for Computing, Forschungszentrum Jülich, Jülich
    • D. MARX AND J. HUTTER, Ab initia molecular dynamics: Theory and implementation, in Modern Methods and Algorithms of Quantum Chemistry, J. Grotendorst, ed., John von Neumann Institute for Computing, Forschungszentrum Jülich, Jülich, 2000, pp. 329-477.
    • (2000) Modern Methods and Algorithms of Quantum Chemistry , pp. 329-477
    • Marx, D.1    Hutter, J.2
  • 19
    • 0042889856 scopus 로고    scopus 로고
    • Numerical integrators for quantum-classical molecular dynamics
    • Computational Molecular Dynamics: Challenges, Methods, Ideas, Springer-Verlag, Berlin
    • P. NETTESHEIM AND CH. SCHÜTTE, Numerical integrators for quantum-classical molecular dynamics, in Computational Molecular Dynamics: Challenges, Methods, Ideas, Lecture Notes in Comput. Sci. Engrg. 4, Springer-Verlag, Berlin, 1999, pp. 396-411.
    • (1999) Lecture Notes in Comput. Sci. Engrg. , vol.4 , pp. 396-411
    • Nettesheim, P.1    Schütte, Ch.2
  • 22
    • 0001332554 scopus 로고
    • Nonadiabatic crossing of energy levels
    • C. ZENER, Nonadiabatic crossing of energy levels, Proc. Roy. Soc. London Ser. A, 137 (1932), pp. 696-702.
    • (1932) Proc. Roy. Soc. London Ser. A , vol.137 , pp. 696-702
    • Zener, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.