A Chebychev propagator with iterative time ordering for explicitly time-dependent Hamiltonians

Journal of Chemical Physics

Volumn 132, Issue 6, 2010, Pages

  Ndong, Mamadou ^a   Tal Ezer, Hillel ^b   Kosloff, Ronnie ^c   Koch, Christiane P ^a  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

^b ACADEMIC COLLEGE OF TEL AVIV YAFFO   (Israel)

^c HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

DINGER EQUATION; PROPAGATION METHOD; TIME DEPENDENCE; TIME ORDERING; TIME-DEPENDENT; TIME-DEPENDENT HAMILTONIANS;

HAMILTONIANS;

EID: 76749090197     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3312531     Document Type: Article

References (35)

1. M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L'Huillier, and P. B. Corkum, Phys. Rev. A 1050-2947 49, 2117 (1994). 10.1103/PhysRevA.49.2117
2. J. Itatani, D. Zeidler, J. Levesque, M. Spanner, D. M. Villeneuve, and P. B. Corkum, Phys. Rev. Lett. 0031-9007 94, 123902 (2005). 10.1103/PhysRevLett. 94.123902
3. H. Dietz and V. Engel, J. Phys. Chem. A 1089-5639 102, 7406 (1998). 10.1021/jp981890w
4. R. Kosloff, S. A. Rice, P. Gaspard, S. Tersigni, and D. Tannor, Chem. Phys. 0301-0104 139, 201 (1989). 10.1016/0301-0104(89)90012-8
5. W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 0021-9606 108, 1953 (1998). 10.1063/1.475576
6. S. Blanes, F. Casas, J. A. Oteo, and J. Ros, Phys. Rep. 0370-1573 470, 151 (2009). 10.1016/j.physrep.2008.11.001
7. W. Magnus, Commun. Pure Appl. Math. 0010-3640 7, 649 (1954). 10.1002/cpa.3160070404
8. H. Tal-Ezer, R. Kosloff, and C. Cerjan, J. Comput. Phys. 0021-9991 100, 179 (1992). 10.1016/0021-9991(92)90318-S
9. C. Cerjan and R. Kosloff, Phys. Rev. A 1050-2947 47, 1852 (1993). 10.1103/PhysRevA.47.1852
10. M. Klaiber, D. Dimitrovski, and J. S. Briggs, Phys. Rev. A 1050-2947 79, 043402 (2009). 10.1103/PhysRevA.79.043402
11. U. Peskin, R. Kosloff, and N. Moiseyev, J. Phys. Chem. 0022-3654 100, 8849 (1994). 10.1063/1.466739
12. R. Kosloff, J. Phys. Chem. 0022-3654 92, 2087 (1988). 10.1021/j100319a003
13. A. Bandrauk and H. Shen, Chem. Phys. Lett. 0009-2614 176, 428 (1991). 10.1016/0009-2614(91)90232-X
14. R. Fischer, A. Staudt, and C. Keitel, Comput. Phys. Commun. 0010-4655 157, 139 (2004). 10.1016/S0010-4655(03)00517-4
15. A. Bandrauk, E. Dehghanian, and H. Lu, Chem. Phys. Lett. 0009-2614 419, 346 (2006). 10.1016/j.cplett.2005.12.006 (Pubitemid 43220491)
16. Y. Ohtsuki, H. Kono, and Y. Fujimura, J. Chem. Phys. 0021-9606 109, 9318 (1998). 10.1063/1.477593 (Pubitemid 128672515)
17. Y. Ohtsuki and K. Nakagami, Phys. Rev. A 1050-2947 77, 033414 (2008). 10.1103/PhysRevA.77.033414
18. M. Hsieh and H. Rabitz, Phys. Rev. E 1063-651X 77, 037701 (2008). 10.1103/PhysRevE.77.037701
19. C. Gollub and R. de Vivie-Riedle, Phys. Rev. A 1050-2947 78, 033424 (2008). 10.1103/PhysRevA.78.033424
20. A. S. Leathers, D. A. Micha, and D. S. Kilin, J. Chem. Phys. 0021-9606 131, 144106 (2009). 10.1063/1.3246168
21. J. C. Tremblay and J. Tucker Carrington, J. Chem. Phys. 0021-9606 121, 11535 (2004). 10.1063/1.1814103 (Pubitemid 40044257)
22. C. P. Koch, J. P. Palao, R. Kosloff, and F. Masnou-Seeuws, Phys. Rev. A 1050-2947 70, 013402 (2004). 10.1103/PhysRevA.70.013402
23. M. D. Feit, J. A. Fleck, and A. Steiger, J. Comput. Phys. 0021-9991 47, 412 (1982). 10.1016/0021-9991(82)90091-2
24. K. Kormann, S. Holmgren, and H. O. Karlsson, J. Chem. Phys. 0021-9606 128, 184101 (2008). 10.1063/1.2916581 (Pubitemid 351707223)
25. C. Leforestier, R. Bisseling, C. Cerjan, M. Feit, R. Friesner, A. Guldberg, A. Dell Hammerich, G. Julicard, W. Karrlein, H. Dieter Meyer, N. Lipkin, O. Roncero, and R. Kosloff, J. Comput. Phys. 0021-9991 94, 59 (1991). 10.1016/0021-9991(91)90137-A
26. M. Ndong, H. Tal-Ezer, R. Kosloff, and C. P. Koch, J. Chem. Phys. 0021-9606 130, 124108 (2009). 10.1063/1.3098940
27. R. Baer, Phys. Rev. A 1050-2947 62, 063810 (2000). 10.1103/PhysRevA.62. 063810 (Pubitemid 32076715)
28. x are given in terms of Bessel functions. Here, our accuracy is limited to the relative error specified by Eq. because the expansion coefficients can only be obtained numerically by fast cosine transformation.
29. L. C. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, New York, 1988).
30. Y. I. Salamin, J. Phys. A 0305-4470 28, 1129 (1995). 10.1088/0305-4470/ 28/4/032
31. R. Kosloff, Annu. Rev. Phys. Chem. 0066-426X 45, 145 (1994). 10.1146/annurev.pc.45.100194.001045
32. I. Kondov, U. Kleinekathöfer, and M. Schreiber, J. Chem. Phys. 0021-9606 114, 1497 (2001). 10.1063/1.1335656 (Pubitemid 32168711)
33. N. F. Scherer, R. J. Carlson, A. Matro, M. Du, A. J. Ruggiero, V. Romero-Rochin, J. A. Cina, G. R. Fleming, and S. A. Rice, J. Chem. Phys. 0021-9606 95, 1487 (1991). 10.1063/1.461064
34. D. J. Tannor, Introduction to Quantum Mechanics. A Time-Dependent Perspective (University Science Books, Sausalito, 2007).
35. K. Ohmori, H. Katsuki, H. Chiba, M. Honda, Y. Hagihara, K. Fujiwara, Y. Sato, and K. Ueda, Phys. Rev. Lett. 0031-9007 96, 093002 (2006). 10.1103/PhysRevLett.96.093002 (Pubitemid 43344774)