Nonperturbative time-convolutionless quantum master equation from the path integral approach

Journal of Chemical Physics

Volumn 130, Issue 13, 2009, Pages

  Nan, Guangjun ^a   Shi, Qiang ^a   Shuai, Zhigang ^a,b  

^a INSTITUTE OF CHEMISTRY   (China)

^b TSINGHUA UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

NONPERTURBATIVE; PATH INTEGRAL APPROACHES; PERTURBATIVE CALCULATIONS; QUANTUM MASTER EQUATIONS; QUANTUM SYSTEMS; REDUCED DYNAMICS; SYSTEM-BATH COUPLINGS; TWO-LEVEL SYSTEMS;

QUANTUM ELECTRONICS; QUANTUM OPTICS; TENSORS;

SYSTEMS ANALYSIS;

EID: 64549145803     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3108521     Document Type: Article

References (48)

1. Classical and Quantum Dynamics in Condensed Phase Simulations, edited by, B. J. Berne, G. Ciccotti, and, D. F. Coker, (World Scientific, New Jersey, 1998).
2. V. May and O. Kühn, Charge and Energy Transfer Dynamics in Molecular Systems, 2nd ed. (Wiley-VCH, Weinheim, 2004).
3. K. Blum, Density Matrix Theory and Applications (Plenum, New York, 1996).
4. W. T. Pollard, A. K. Felts, and R. A. Friesner, Adv. Chem. Phys. 0065-2385 10.1002/9780470141526.ch3 93, 77 (1996).
5. Y. J. Yan and R. X. Xu, Annu. Rev. Phys. Chem. 0066-426X 10.1146/annurev.physchem.55.091602.094425 56, 187 (2005).
6. S. Nakajima, Prog. Theor. Phys. 0033-068X 10.1143/PTP.20.948 20, 948 (1958).
7. R. Zwanzig, Lect. Theor. Phys. 3, 106 (1960).
8. R. Zwanzig, Physica 30, 1109 (1964). 0031-8914
9. N. Hashitsumae, F. Shibata, and M. Shing, J. Stat. Phys. 0022-4715 10.1007/BF01040099 17, 155 (1977).
10. F. Shibata, Y. Takahashi, and N. Hashitsume, J. Stat. Phys. 0022-4715 10.1007/BF01040100 17, 171 (1977).
11. S. Jang, J. Cao, and R. J. Silbey, J. Chem. Phys. 0021-9606 10.1063/1.1445105 116, 2705 (2002).
12. B. B. Laird, J. Budimir, and J. L. Skinner, J. Chem. Phys. 0021-9606 10.1063/1.460626 94, 4391 (1991).
13. B. B. Laird and J. L. Skinner, J. Chem. Phys. 0021-9606 10.1063/1.460627 94, 4405 (1991).
14. D. R. Reichman and R. J. Silbey, J. Chem. Phys. 0021-9606 10.1063/1.470916 104, 1506 (1996).
15. M. Schröder, M. Schreiber, and U. Kleinekathöfer, J. Chem. Phys. 0021-9606 10.1063/1.2538754 126, 114102 (2007).
16. M. Sparpaglione and S. Mukamel, J. Chem. Phys. 0021-9606 10.1063/1.453922 88, 3263 (1988).
17. A. A. Golosov and D. R. Reichman, J. Chem. Phys. 0021-9606 10.1063/1.1412611 115, 9848 (2001).
18. A. A. Golosov and D. R. Reichman, J. Chem. Phys. 0021-9606 10.1063/1.1412612 115, 9862 (2001).
19. A. Pomyalov and D. J. Tannor, J. Chem. Phys. 0021-9606 10.1063/1.2121649 123, 204111 (2005).
20. A. A. Golosov, R. A. Friesner, and P. Pechukas, J. Chem. Phys. 0021-9606 10.1063/1.478130 110, 138 (1999).
21. A. A. Golosov, R. A. Friesner, and P. Pechukas, J. Chem. Phys. 0021-9606 10.1063/1.480888 112, 2095 (2000).
22. Q. Shi and E. Geva, J. Chem. Phys. 0021-9606 10.1063/1.1624830 119, 12063 (2003).
23. Q. Shi and E. Geva, J. Chem. Phys. 0021-9606 10.1063/1.1738109 120, 10647 (2004).
24. M. -L. Zhang, B. J. Ka, and E. Geva, J. Chem. Phys. 0021-9606 10.1063/1.2218342 125, 044106 (2006).
25. D. Egorova, M. Thoss, W. Domcke, and H. Wang, J. Chem. Phys. 0021-9606 10.1063/1.1587121 119, 2761 (2003).
26. M. Schröder, U. Kleinekathöfer, and M. Schreiber, J. Chem. Phys. 0021-9606 10.1063/1.2171188 124, 084903 (2006).
27. H. Grabert, P. Schramm, and G. L. Ingold, Phys. Rep. 0370-1573 10.1016/0370-1573(88)90023-3 168, 115 (1988).
28. U. Weiss, Quantum Dissipative Systems, 2nd ed. (World Scientific, London, 1999).
29. S. Mukamel, Principles of Nonlinear Optical Spectroscopy (Oxford, New York, 1995).
30. A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. Fisher, A. Garg, and W. Zwerger, Rev. Mod. Phys. 0034-6861 10.1103/RevModPhys.59.1 59, 1 (1987).
31. C. H. Mak and D. Chandler, Phys. Rev. A 1050-2947 10.1103/PhysRevA.41. 5709 41, 5709 (1990).
32. C. Mak and R. Egger, Adv. Chem. Phys. 93, 39 (1996). 0065-2385
33. M. Topaler and N. Makri, J. Chem. Phys. 0021-9606 10.1063/1.468244 101, 7500 (1994).
34. N. Makri and D. Makarov, J. Chem. Phys. 0021-9606 10.1063/1.469508 102, 4600 (1995).
35. N. Makri and D. Makarov, J. Chem. Phys. 0021-9606 10.1063/1.469509 102, 4611 (1995).
36. N. Makri, J. Math. Phys. 0022-2488 10.1063/1.531046 36, 2430 (1995).
37. Y. Tanimura, J. Phys. Soc. Jpn. 0031-9015 10.1143/JPSJ.75.082001 75, 082001 (2006).
38. Y. Tanimura and R. K. Kubo, J. Phys. Soc. Jpn. 0031-9015 10.1143/JPSJ.58.101 58, 101 (1989).
39. Y. Tanimura, Phys. Rev. A 1050-2947 10.1103/PhysRevA.41.6676 41, 6676 (1990).
40. Y. Tanimura and P. J. Wolynes, Phys. Rev. A 1050-2947 10.1103/PhysRevA.43.4131 43, 4131 (1991).
41. R. X. Xu, P. Cui, X. Q. Li, Y. Mo, and Y. J. Yan, J. Chem. Phys. 0021-9606 10.1063/1.1850899 122, 041103 (2005).
42. A. Ishizaki and Y. Tanimura, J. Phys. Soc. Jpn. 0031-9015 10.1143/JPSJ.74.3131 74, 3131 (2005).
43. J. S. Jin, X. Zheng, and Y. J. Yan, J. Chem. Phys. 0021-9606 10.1063/1.2938087 128, 234703 (2008).
44. A. Ishizaki and Y. Tanimura, Chem. Phys. 0301-0104 10.1016/j.chemphys. 2007.10.037 347, 185 (2008).
45. As shown in this study, when taking the time derivative of the path integral expression [Eq.], the contributions from the system action and influence functional can not be separated in general cases [see the second term on the right hand side of Eq.]. The authors in Ref. tried to find a way to separate them using equations in the interaction picture. However, there is an error in the derivation from Eqs. (2.12) and (2.13) to (2.14) in Ref.: the time ordering in Eq. (2.12) should be kept in Eq. (2.14), so the equation is again not separable, since (I) (tj) at different time does not commute. The only case Eq. (2.14) holds is when (I) (tj) at different time commutes, i.e., when commutes with H S. This is just the case of pure dephasing.
46. F. Haake, Quantum Statistics in Optics and Solid State Physics (Springer-Verlag, Berlin, 1973).
47. R. P. Feynman and F. L. Vernon, Jr., Ann. Phys. 0003-3804 10.1016/0003-4916(63)90068-X 24, 118 (1963).
48. A. O. Caldeira and A. J. Leggett, Ann. Phys. 0003-3804 10.1016/0003-4916(83)90202-6 149, 374 (1983).