메뉴 건너뛰기




Volumn 40, Issue 50, 2007, Pages 15001-15017

Sufficient conditions for the convergence of the Magnus expansion

Author keywords

[No Author keywords available]

Indexed keywords


EID: 36749044406     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/40/50/006     Document Type: Article
Times cited : (76)

References (32)
  • 2
    • 0032498043 scopus 로고    scopus 로고
    • Magnus and Fer expansions for matrix differential equations: The convergence problem
    • Blanes S, Casas F, Oteo J A and Ros J 1998 Magnus and Fer expansions for matrix differential equations: the convergence problem J. Phys. A: Math. Gen. 22 259-68
    • (1998) J. Phys. A: Math. Gen. , vol.31 , Issue.1 , pp. 259-268
    • Blanes, S.1    Casas, F.2    Oteo, J.A.3    Ros, J.4
  • 4
    • 0001292617 scopus 로고    scopus 로고
    • Improved high order integrators based on the Magnus expansion
    • Blanes S, Casas F and Ros J 2000 Improved high order integrators based on the Magnus expansion BIT 40 434-50
    • (2000) BIT , vol.40 , Issue.3 , pp. 434-450
    • Blanes, S.1    Casas, F.2    Ros, J.3
  • 5
    • 0013364797 scopus 로고    scopus 로고
    • High order optimized geometric integrators for linear differential equations
    • Blanes S, Casas F and Ros J 2002 High order optimized geometric integrators for linear differential equations BIT 42 262-84
    • (2002) BIT , vol.42 , Issue.2 , pp. 262-284
    • Blanes, S.1    Casas, F.2    Ros, J.3
  • 6
    • 0000819022 scopus 로고
    • Recursion formulas for the Lie integral
    • Chacon R V and Fomenko A T 1991 Recursion formulas for the Lie integral Adv. Math. 88 200-57
    • (1991) Adv. Math. , vol.88 , Issue.2 , pp. 200-257
    • Chacon, R.V.1    Fomenko, A.T.2
  • 8
    • 0000352005 scopus 로고
    • L'application exponentielle dans les groupes de Lie résolubles
    • Dixmier J 1957 L'application exponentielle dans les groupes de Lie résolubles Bull. Soc. Math. France 85 113-21
    • (1957) Bull. Soc. Math. France , vol.85 , pp. 113-121
    • Dixmier, J.1
  • 10
    • 0039300310 scopus 로고
    • On the convergence of the Magnus expansion for spin systems in periodic magnetic fields
    • Fel'dman E B 1984 On the convergence of the Magnus expansion for spin systems in periodic magnetic fields Phys. Lett. A 104 479-81
    • (1984) Phys. Lett. , vol.104 , Issue.9 , pp. 479-481
    • Fel'Dman, E.B.1
  • 12
    • 0001249155 scopus 로고
    • Note on the derivatives with respect to a parameter of the solutions of a system of differential equation
    • Gronwall T H 1919 Note on the derivatives with respect to a parameter of the solutions of a system of differential equation Ann. Math. 20 292-6
    • (1919) Ann. Math. , vol.20 , Issue.4 , pp. 292-296
    • Gronwall, T.H.1
  • 16
    • 0346968523 scopus 로고    scopus 로고
    • On the solution of linear differential equations in Lie groups
    • Iserles A and Nørsett S P 1999 On the solution of linear differential equations in Lie groups Phil. Trans. R. Soc. A 357 983-1019
    • (1999) Phil. Trans. R. Soc. , vol.357 , Issue.1754 , pp. 983-1019
    • Iserles, A.1    Nørsett, S.P.2
  • 17
    • 0346516514 scopus 로고
    • Infinite products and T products of exponentials
    • Karasev M V and Mosolova M V 1977 Infinite products and T products of exponentials J. Theor. Math. Phys. 28 721-30
    • (1977) J. Theor. Math. Phys. , vol.28 , Issue.2 , pp. 721-730
    • Karasev, M.V.1    Mosolova, M.V.2
  • 18
    • 38249026175 scopus 로고
    • Analytic properties of the Magnus operator for two solvable Hamiltonians
    • Klarsfeld S and Oteo J A 1989 Analytic properties of the Magnus operator for two solvable Hamiltonians Phys. Lett. A 142 393-7
    • (1989) Phys. Lett. , vol.142 , Issue.6-7 , pp. 393-397
    • Klarsfeld, S.1    Oteo, J.A.2
  • 19
    • 0001291205 scopus 로고
    • Recursive generation of higher-order terms in the Magnus expansion
    • Klarsfeld S and Oteo J A 1989 Recursive generation of higher-order terms in the Magnus expansion Phys. Rev. A 39 3270-3273
    • (1989) Phys. Rev. , vol.39 , Issue.7 , pp. 3270-3273
    • Klarsfeld, S.1    Oteo, J.A.2
  • 21
    • 84940252991 scopus 로고
    • On the exponential solution of differential equations for a linear operator
    • Magnus W 1954 On the exponential solution of differential equations for a linear operator Commun. Pure Appl. Math. VII 649-73
    • (1954) Commun. Pure Appl. Math. , vol.7 , Issue.4 , pp. 649-673
    • Magnus, W.1
  • 22
    • 36549092408 scopus 로고
    • Convergence of Magnus expansion for time-dependent two-level systems
    • Maricq M M 1987 Convergence of Magnus expansion for time-dependent two-level systems J. Chem. Phys. 86 5647-51
    • (1987) J. Chem. Phys. , vol.86 , Issue.10 , pp. 5647-5651
    • Maricq, M.M.1
  • 24
    • 36749056642 scopus 로고    scopus 로고
    • Moan P C 1998 Efficient approximation of Sturm-Liouville problems using Lie-group methods Technical Report 1998/NA11 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England
    • (1998) Technical Report 1998/NA11
    • Moan, P.C.1
  • 25
    • 0039657206 scopus 로고    scopus 로고
    • On the existence of the exponential solution of linear differential systems
    • Moan P C, Oteo J A and Ros J 1999 On the existence of the exponential solution of linear differential systems J. Phys. A: Math. Gen. 32 5133-9
    • (1999) J. Phys. A: Math. Gen. , vol.32 , Issue.27 , pp. 5133-5139
    • Moan, P.C.1    Oteo, J.A.2    Ros, J.3
  • 26
    • 33646376070 scopus 로고    scopus 로고
    • Moan P C 2002 On backward error analysis and Nekhoroshev stability in the numerical analysis of conservative systems of ODEs PhD Thesis University of Cambridge
    • (2002) PhD Thesis
    • Moan, P.C.1
  • 28
    • 36849102615 scopus 로고
    • On the exponential form of time-displacement operators in quantum mechanics
    • Pechukas P and Light J C 1966 On the exponential form of time-displacement operators in quantum mechanics J. Chem. Phys. 44 3897-912
    • (1966) J. Chem. Phys. , vol.44 , Issue.10 , pp. 3897-3912
    • Pechukas, P.1    Light, J.C.2
  • 30
    • 0009689191 scopus 로고
    • Convergence of Magnus and Magnus-like expansions in the Schrödinger representation
    • Salzman W R 1986 Convergence of Magnus and Magnus-like expansions in the Schrödinger representation J. Chem. Phys. 85 4605-13
    • (1986) J. Chem. Phys. , vol.85 , Issue.8 , pp. 4605-4613
    • Salzman, W.R.1
  • 31
    • 36849123046 scopus 로고
    • Note on global validity of the Baker-Hausdorff and Magnus theorems
    • Wei J 1963 Note on global validity of the Baker-Hausdorff and Magnus theorems J. Math. Phys. 4 1337-41
    • (1963) J. Math. Phys. , vol.4 , Issue.10 , pp. 1337-1341
    • Wei, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.