On the relaxation of a two-level system: Beyond the weak-coupling approximation

Journal of Chemical Physics

Volumn 104, Issue 4, 1996, Pages 1506-1518

  Reichman, David R ^a   Silbey, Robert J ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008600720     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.470916     Document Type: Article

References (52)

1. C. P. Schlicter, Principles of Magnetic Resonance, 3rd ed. (Springer, Berlin, 1990);
2. A. Abragam, The Principles of Nuclear Magnetism (Oxford University, London, 1961).
3. W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, New York, 1973).
4. K. Blum, Density Matrix Theory and Applications (Plenum, New York, 1981).
5. A. G. Redfield, Adv. Mag. Reson. 1, 1 (1965).
6. F. Bloch, Phys. Rev. 70, 460 (1946);
7. R. K. Wangsness and F. Bloch, ibid. 89, 728 (1953);
8. A. G. Redfield, IBM J. 19, 1 (1957).
9. R. Silbey, in Relaxation Processes in Molecular Excited States, edited by J. Funschilling (Kluwer Academic, Dordrecht, 1989).
10. I. Oppenheim, K. E. Shuler, and G. H. Weiss, Stochastic Processes in Chemical Physics: The Master Equation (MIT, Cambridge, 1977).
11. D. M. Burland and A. H. Zewail, Adv. Chem. Phys. 40, 1 (1979).
12. J. Budimir and J. L. Skinner, J. Stat. Phys. 49, 1029 (1987).
13. H. M. Sevian and J. L. Skinner, J. Chem. Phys. 91, 1775 (1989).
14. P. Reineker, B. Kaiser, and A. M. Jayannayar, Phys. Rev. A 39, 1469 (1989).
15. B. B. Laird, J. Budimir, and J. L. Skinner, J. Chem. Phys. 94, 4391 (1991).
16. B. B. Laird and J. L. Skinner, J. Chem. Phys. 94, 4405 (1991).
17. T.-M. Chang and J. L. Skinner, Physica A 193, 483 (1993).
18. B. B. Laird, T.-M. Chang, and J. L. Skinner, J. Chem. Phys. 101, 852 (1994).
19. A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987).
20. B. Carmeli and D. Chandler, J. Chem. Phys. 82, 3400 (1985).
21. A. Suarez and R. Silbey, J. Chem. Phys. 94, 4809 (1991).
22. C. Aslangul, N. Pettier, and D. Saint-James, J. Phys. (Paris) 46, 2031 (1985);
23. 47, 1657 (1986).
24. R. Silbey and R. Harris, J. Chem. Phys. 80, 2615 (1984);
25. J. Phys. Chem. 93, 7062 (1989).
26. U. Weiss, Quantum Dissipative Dynamics (World Scientific, Singapore, 1993).
27. H. Spohn and R. Dümcke, J. Stat. Phys. 41, 389 (1985);
28. H. Spohn, Commun. Math. Phys. 123, 305 (1989).
29. D. Vitali and P. Grigolini, Phys. Rev. A 43, 7091 (1990);
30. T. Tsuzuki, Prog. Theor. Phys. 81, 770 (1989).
31. C. Mak and D. Chandler, Phys. Rev. A 44, 2352 (1991);
32. W. T. Pollard and R. Friesner, J. Chem. Phys. 100, 5054 (1994);
33. M. Topaler and N. Makri, ibid. 101, 7500 (1994).
34. K. Lindenberg and B. West, Phys. Rev. A 30, 568 (1984).
35. K. Kassner, Phys. Rev. A 36, 5381 (1987).
36. S. H. Lin, J. Chem. Phys. 61, 3810 (1974).
37. R. I. Cukier and J. M. Deutch, J. Chem. Phys. 50, 36 (1969).
38. A. Suarez and R. Silbey, J. Chem. Phys. 95, 9115 (1991).
39. R. Zwanzig, Lect. Theor. Phys. (Boulder) 3, 106 (1960).
40. G. Baym, Lectures On Quantum Mechanics (Addison-Wesley, Reading, MA 1990).
41. M. Wagner, Unitary Transformations in Solid State Physics (North-Holland, Amsterdam, 1986).
42. A. Suarez and R. Silbey, J. Chem. Phys. 97, 5101 (1992).
43. S. Rackovsky and R. Silbey, Mol. Phys. 25, 61 (1973).
44. B. West and K. Lindenberg, J. Chem. Phys. 83, 4118 (1985).
45. G. W. Ford, M. Kac, and P. Mazur, J. Math. Phys. 6, 504 (1965).
46. P. E. Parris and R. Silbey, J. Chem. Phys. 86, 6381 (1987).
47. R. Englman, The Dynamical John-Teller Effect (Wiley, New York, 1972).
48. J. Alper and R. Silbey, J. Chem. Phys. 52, 569 (1970).
49. See, for instance, A. Zawadowski and G. T. Zimanyi, Phys. Rev. A 32, 1373 (1985).
50. R. Wertheimer and R. Silbey, Chem. Phys. Lett. 75, 243 (1980).
51. Such a restriction is, in fact, a reflection of proper normalization. Goldstone's theorem [J. Goldstone, Proc. R. Soc. London 239A, 267 (1957)]
52. shows that when the normalization is properly included, such divergent, "disconnected" pieces cancel, and the remaining sum is taken over the "connected" states that differ from the physical states involved in the transition. The fact that the Redfied method avoids this problem is a reflection of the fact that the density matrix in this approach is properly normalized to all orders. See also, A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971).