Magnus and Fer expansions for matrix differential equations: The convergence problem

Journal of Physics A: Mathematical and General

Volumn 31, Issue 1, 1998, Pages 259-268

  Blanes, S ^a   Casas, F ^b   Oteo, J A ^a   Ros, J ^a  

^a UNIVERSITY OF VALENCIA   (Spain)

^b UNIVERSITAT JAUME I   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032498043     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/31/1/023     Document Type: Article

References (39)

1. Pechukas P and Light J C 1966 On the exponential form of time-displacement operators in quantum mechanics J. Chem. Phys. 44 3897-912
2. Magnus W 1954 On the exponential solution of differential equations for a linear operator Commun. Pure Appl. Math. 7 649-73
3. Fer F 1958 Résolution de l'equation matricielle U̇ = pU par produit infini d'exponentielles matricielles Bull. Classe Sci. Acad Roy. Bel. 44 818-29
4. Klarsfeld S and Oteo J A 1989 Recursive generation of higher-order terms in the Magnus expansion Phys. Rev. A 39 3270-3
5. Milfeld K F and Wyatt R E 1983 Study, extension and application of Floquet theory for quantum molecular systems in an oscillating field Phys. Rev. A 27 72-94
6. Prato D and Lamberti P W 1997 A note on Magnus formula J. Chem. Phys. 106 4640-3
7. Iserles A and Nørsett S P 1997 On the solution of linear differential equations in Lie groups DAMTP tech. report 1997/NA3, University of Cambridge Iserles A and Nørsett S P 1997 Linear ODEs in Lie groups DAMTP tech report 1997/NA9, University of Cambridge
8. Iserles A and Nørsett S P 1997 On the solution of linear differential equations in Lie groups DAMTP tech. report 1997/NA3, University of Cambridge Iserles A and Nørsett S P 1997 Linear ODEs in Lie groups DAMTP tech report 1997/NA9, University of Cambridge
9. Burum D P 1981 Magnus expansion generator Phys. Rev. B 24 3684-92
10. Klarsfeld S and Oteo J A 1989 Exponential infinite-product representations of the time displacement operator J. Phys. A: Math. Gen. 22 2687-94
11. Robinson D W 1963 Multiple Coulomb excitations of deformed nuclei Helv. Phys. Acta 36 140-54
12. Baye D and Heenen P H 1973 A theoretical study of fast proton-atomic hydrogen scattering J. Phys. B: At. Mol. Phys. 6 105-13
13. Schek I, Jortner J and Sage M L 1981 Application of the Magnus expansion for high-order multiphoton excitation Chem. Phys. 59 11-27
14. Evans WAB 1968 On some application of Magnus expansion in nuclear magnetic resonance Ann. Phys. 48 72-93
15. Waugh J S 1982 Theory of broadband spin decoupling J. Magn. Reson. 50 30-49
16. Cady W A 1974 Rotational spectral line broadening of OCS by noble gases J. Chem. Phys. 60 3318-23
17. Dahmen H D, Scholz B and Steiner F 1982 Infrared dynamics of QED and the asymptotic behavior of the electron form factor Nucl. Phys. B 202 365-81
18. D'Olivo J C and Oteo J A 1990 Magnus expansion and the two-neutrino oscillations in matter Phys. Rev. D 42 256-9 D'Olivo J C and Oteo J A 1996 Nonadiabatic three-neutrino oscillations in matter Phys. Rev. D 54 1187-93
19. D'Olivo J C and Oteo J A 1990 Magnus expansion and the two-neutrino oscillations in matter Phys. Rev. D 42 256-9 D'Olivo J C and Oteo J A 1996 Nonadiabatic three-neutrino oscillations in matter Phys. Rev. D 54 1187-93
20. Ernst R R, Bodenhausen G and Wokaun A 1986 Principles of NMR in One and Two Dimensions (Oxford: Clarendon)
21. Oteo J A and Ros J 1991 The Magnus expansion for classical Hamiltonian systems J. Phys. A: Math. Gen. 24 5751-62
22. Wilcox R M 1967 Exponential operators and parameter differentiation in quantum physics J. Math. Phys. 8 962-82
23. Wei J and Norman E 1963 Lie algebraic solution of linear differential equations J. Math. Phys. 4 575-81
24. Casas F, Oteo J A and Ros J 1991 Lie algebraic approach to Fer's expansion for classical Hamiltonian systems J. Phys. A: Math. Gen. 24 4037-46
25. Dragt A J and Finn J M 1976 Lie series and invariant functions for analytic symplectic maps J. Math. Phys. 17 2215-27
26. Casas F 1996 Fer's factorization as a symplectic integrator Num. Math. 74 283-303
27. Casas F 1996 Solution of linear partial differential equations by Lie algebraic methods J. Comp. Appl. Math. 76 159-70
28. Iserles A 1984 Solving linear ordinary differential equations by exponentials of iterated commutators Num. Math. 45 183-99
29. Zanna A 1996 The method of iterated commutators for ordinary differential equations on Lie groups DAMTP tech. report 1996/NA12, University of Cambridge
30. Wei J 1963 Note on global validity of the Baker-Hausdorff and Magnus theorems J. Math. Phys. 4 1337-41
31. Klarsfeld S and Oteo J A 1989 The Baker-Campbell-Hausdorff formula and the convergence of Magnus expansion J. Phys. A: Math. Gen. 22 4565-72
32. Klarsfeld S and Oteo J A 1989 Analytic properties for the Magnus operator for two solvable hamiltonians Phys. Lett. 142A 393-7
33. Fel'dman E B 1984 On the convergence of the Magnus expansion for spin systems in periodic magnetic fields Phys. Lett. 104A 479-81
34. Salzman W R 1987 New criterion for convergence of exponential perturbation theory in the Schrödinger representation Phys. Rev. A 36 5074-6
35. Maricq M M 1987 Convergence of Magnus expansion for time-dependent two-level systems J. Chem. Phys. 86 5647-51
36. Fernández F M 1990 Convergence of the Magnus expansion Phys. Rev. A 41 2311-14
37. Blanes S 1994 Evolución de sistemas dinámicos: desarrollos de Magnus y Fer Master Thesis University of Valencia
38. Abramowitz M A and Stegun I A 1965 Handbook of Mathematical Functions (New York: Dover)
39. Casas F, Oteo J A and Ros J 1994 Linear time-dependent Hamiltonian systems beyond the adiabatic limit J. Phys. A: Math. Gen. 27 4325-39