Semigroup representations, site couplings, and relaxation in quantum systems

Journal of Physical Chemistry A

Volumn 102, Issue 47, 1998, Pages 9360-9366

  Davis, William B ^a   Wasielewski, Michael R ^a,b   Kosloff, Ronnie ^c   Ratner, Mark A ^a  

^a NORTHWESTERN UNIVERSITY   (United States)

^b ARGONNE NATIONAL LABORATORY   (United States)

^c HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011741432     PISSN: 10895639     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp9813544     Document Type: Article

References (64)

1. Levine, R. D. Quantum Mechanics of Molecular Rate Processes; Clarendon: Oxford, 1969.
2. Remade, F.; Levine, R. D. Mol. Phys. 1996, 87, 899.
3. Remade, F.; Levine, R. D.; Ratner, M. A. Chem. Phys. Lett., in press.
4. Wangsness, R. K.; Bloch, F. Phys. Rev. 1953, 89, 728.
5. Fano, U. Rev. Mod. Phys. 1957, 29, 74.
6. Redfield, A. G. IBM J. Res. Dev. 1957, 1, 19.
7. Redfield, A. G. Adv. Magn. Reson. 1965, 1. 1.
8. Makarov, D. E.; Makri, N. Chem. Phys. Lett. 1994, 221, 482.
9. Makri, N.; Makarov, D. E. J. Chem. Phys. 1995, 102, 4600.
10. Mukamel, S. Annu. Rev. Phys. Chem. 1990, 41, 647.
11. Fried, L. E.; Mukamel, S. Adv. Chem. Phys. 1993, 84, 435.
12. Coalson, R. D.; Evans, D. G.; Nitzan, A. J. Chem. Phys. 1994, 101, 486.
13. Evans, D. G.; Coalson, R. D. J. Chem. Phys. 1995, 102, 5658.
14. Kubo, R.; Toda, M.; Hashitsume, N. Statistical Physics II; Springer-Verlag: New York, 1985.
15. Jean, J. M.; Friesner, R. A.; Fleming, G. R. J. Chem. Phys. 1992, 96, 5827.
16. Jean, J. M. J. Chem. Phys. 1995, 101, 10464; 1996, 104, 5638.
17. Jean, J. M. J. Chem. Phys. 1995, 101, 10464; 1996, 104, 5638.
18. Pollard, W. T.; Friesner, R. A. J. Chem. Phys. 1994, 100, 5054.
19. Felts, A. K.; Pollard, W. T.; Friesner, R. A. J. Phys. Chem. 1995, 99, 2929. Pollard, W. T.; Felts, A. K.; Friesner, R. A. Adv. Chem. Phys. 1996, 93, 77.
20. Felts, A. K.; Pollard, W. T.; Friesner, R. A. J. Phys. Chem. 1995, 99, 2929. Pollard, W. T.; Felts, A. K.; Friesner, R. A. Adv. Chem. Phys. 1996, 93, 77.
21. van Kampen, N. G. J. Stat. Phys. 1995, 78, 299.
22. Kosloff, R.; Rice, S. A. J. Chem. Phys. 1980, 72, 4591.
23. Kosloff, R.; Ratner, M. A. J. Chem. Phys. 1982, 77, 2841; 1984, 80, 2352. Kosloff, R. J. Chem. Phys. 1984, 80, 1625.
24. Kosloff, R.; Ratner, M. A. J. Chem. Phys. 1982, 77, 2841; 1984, 80, 2352. Kosloff, R. J. Chem. Phys. 1984, 80, 1625.
25. Kosloff, R.; Ratner, M. A. J. Chem. Phys. 1982, 77, 2841; 1984, 80, 2352. Kosloff, R. J. Chem. Phys. 1984, 80, 1625.
26. Geva, E.; Kosloff, R. Phys. Rev. E 1994, 49, 3903. Saalfrank, P.; Baer, R.; Kosloff, R. Chem. Phys. Lett. 1994, 230, 463. Kosloff, R.; Davis, W. B.; Ratner, M. A. J. Chem. Phys. 1997, 106, 7036. Baer, R.; Kosloff, R. J. Chem. Phys. 1997, 106, 8862.
27. Geva, E.; Kosloff, R. Phys. Rev. E 1994, 49, 3903. Saalfrank, P.; Baer, R.; Kosloff, R. Chem. Phys. Lett. 1994, 230, 463. Kosloff, R.; Davis, W. B.; Ratner, M. A. J. Chem. Phys. 1997, 106, 7036. Baer, R.; Kosloff, R. J. Chem. Phys. 1997, 106, 8862.
28. Geva, E.; Kosloff, R. Phys. Rev. E 1994, 49, 3903. Saalfrank, P.; Baer, R.; Kosloff, R. Chem. Phys. Lett. 1994, 230, 463. Kosloff, R.; Davis, W. B.; Ratner, M. A. J. Chem. Phys. 1997, 106, 7036. Baer, R.; Kosloff, R. J. Chem. Phys. 1997, 106, 8862.
29. Geva, E.; Kosloff, R. Phys. Rev. E 1994, 49, 3903. Saalfrank, P.; Baer, R.; Kosloff, R. Chem. Phys. Lett. 1994, 230, 463. Kosloff, R.; Davis, W. B.; Ratner, M. A. J. Chem. Phys. 1997, 106, 7036. Baer, R.; Kosloff, R. J. Chem. Phys. 1997, 106, 8862.
30. Lindblad, G. Commun. Math. Phys. 1976, 48, 119.
31. Gorini, V.; Kossokowski, A.; Sundarshan, E. C. G. J. Math. Phys. 1976, 17, 821.
32. Alicki, R.; Lendi, K. Quantum Dyanmical Semigroups and Applications; Springer-Verlag; New York, 1987.
33. As the referee noted, Pechukas (Pechukas, P. Phys. Rev. Lett. 1994, 73, 1060) pointed out that when the overall initial density matrix cannot be factored into a product of system and bath density matrixes, the totality of system states may not be positive. However, Lindblad (Lindblad, G. J. Phys. A 1996, 29, 4197) responded to Pechukas' comments by showing that one cannot avoid complete positivity. In our model we effectively use product initial conditions which makes none of these concerns relevant.
34. As the referee noted, Pechukas (Pechukas, P. Phys. Rev. Lett. 1994, 73, 1060) pointed out that when the overall initial density matrix cannot be factored into a product of system and bath density matrixes, the totality of system states may not be positive. However, Lindblad (Lindblad, G. J. Phys. A 1996, 29, 4197) responded to Pechukas' comments by showing that one cannot avoid complete positivity. In our model we effectively use product initial conditions which makes none of these concerns relevant.
35. For overviews, see for example: Fleming, G. R.; Cho, M. Annu. Rev. Phys. Chem. 1996, 47, 109. Ultrafast Process in Chemistry and Photobiology; El-Sayed, M. A.; Tanaka, I.; Molin, Y., Eds.; Blackwell: Oxford, 1995. Theoretical interpretations are advanced by Mukamel: Mukamel, S. In Principles of Nonlinear Optical Spectroscopy; Oxford: Oxford, 1995.
36. For overviews, see for example: Fleming, G. R.; Cho, M. Annu. Rev. Phys. Chem. 1996, 47, 109. Ultrafast Process in Chemistry and Photobiology; El-Sayed, M. A.; Tanaka, I.; Molin, Y., Eds.; Blackwell: Oxford, 1995. Theoretical interpretations are advanced by Mukamel: Mukamel, S. In Principles of Nonlinear Optical Spectroscopy; Oxford: Oxford, 1995.
37. For overviews, see for example: Fleming, G. R.; Cho, M. Annu. Rev. Phys. Chem. 1996, 47, 109. Ultrafast Process in Chemistry and Photobiology; El-Sayed, M. A.; Tanaka, I.; Molin, Y., Eds.; Blackwell: Oxford, 1995. Theoretical interpretations are advanced by Mukamel: Mukamel, S. In Principles of Nonlinear Optical Spectroscopy; Oxford: Oxford, 1995.
38. See Kohen et al. (Kohen, D.; Marston, C. C.; Tannor, D. J. J. Chem. Phys. 1997, 107, 5236) for a comparison of six approaches to quantum dissipation in the context of the harmonic oscillator, and point out their advantages, difficulties, and differences. Other important theoretical studies include, in addition to the work already cited here, Agarwal, G. S. Phys. Rev. A 1971, 4, 739. Sargent, M., III; Scully, M. O.; Lamb, W. E., Jr. Laser Physics; Addison-Wesley: Redwood City, CA, 1974. Louisell, W. H. Quantum Coherence Properties of Radiation; Wiley: New York, 1973. Gardiner, C. W. Quantum Noise; Springer-Verlag: New York, 1991. Caldeira, A. O.; Leggett, A. J. Physica 1983, 121A, 587. Oppenheim, I.; Romero-Rochin, V. Physica 1987, 147A, 184. Suarez, A.; Silbey, R.; Oppenheim, I. J. Chem. Phys. 1992, 97, 5101. Yan, Y. J.; Mukamel, S. J. Chem. Phys. 1988, 88, 5160; 1988, 88, 5735. Schwartz, B. J.; Rossky, P. J. J. Chem. Phys. 1996, 105, 6997. Sevian, H. M.; Skinner, J. J. Chem. Phys. 1992, 91, 1775. Pechukas, P. Phys. Rev. Lett. 1994, 73, 1060. Egoron, S. A.; Rabani, E.; Berne, B. J. J. Chem. Phys. 1998, 108, 1407.
39. See Kohen et al. (Kohen, D.; Marston, C. C.; Tannor, D. J. J. Chem. Phys. 1997, 107, 5236) for a comparison of six approaches to quantum dissipation in the context of the harmonic oscillator, and point out their advantages, difficulties, and differences. Other important theoretical studies include, in addition to the work already cited here, Agarwal, G. S. Phys. Rev. A 1971, 4, 739. Sargent, M., III; Scully, M. O.; Lamb, W. E., Jr. Laser Physics; Addison-Wesley: Redwood City, CA, 1974. Louisell, W. H. Quantum Coherence Properties of Radiation; Wiley: New York, 1973. Gardiner, C. W. Quantum Noise; Springer-Verlag: New York, 1991. Caldeira, A. O.; Leggett, A. J. Physica 1983, 121A, 587. Oppenheim, I.; Romero-Rochin, V. Physica 1987, 147A, 184. Suarez, A.; Silbey, R.; Oppenheim, I. J. Chem. Phys. 1992, 97, 5101. Yan, Y. J.; Mukamel, S. J. Chem. Phys. 1988, 88, 5160; 1988, 88, 5735. Schwartz, B. J.; Rossky, P. J. J. Chem. Phys. 1996, 105, 6997. Sevian, H. M.; Skinner, J. J. Chem. Phys. 1992, 91, 1775. Pechukas, P. Phys. Rev. Lett. 1994, 73, 1060. Egoron, S. A.; Rabani, E.; Berne, B. J. J. Chem. Phys. 1998, 108, 1407.
40. See Kohen et al. (Kohen, D.; Marston, C. C.; Tannor, D. J. J. Chem. Phys. 1997, 107, 5236) for a comparison of six approaches to quantum dissipation in the context of the harmonic oscillator, and point out their advantages, difficulties, and differences. Other important theoretical studies include, in addition to the work already cited here, Agarwal, G. S. Phys. Rev. A 1971, 4, 739. Sargent, M., III; Scully, M. O.; Lamb, W. E., Jr. Laser Physics; Addison-Wesley: Redwood City, CA, 1974. Louisell, W. H. Quantum Coherence Properties of Radiation; Wiley: New York, 1973. Gardiner, C. W. Quantum Noise; Springer-Verlag: New York, 1991. Caldeira, A. O.; Leggett, A. J. Physica 1983, 121A, 587. Oppenheim, I.; Romero-Rochin, V. Physica 1987, 147A, 184. Suarez, A.; Silbey, R.; Oppenheim, I. J. Chem. Phys. 1992, 97, 5101. Yan, Y. J.; Mukamel, S. J. Chem. Phys. 1988, 88, 5160; 1988, 88, 5735. Schwartz, B. J.; Rossky, P. J. J. Chem. Phys. 1996, 105, 6997. Sevian, H. M.; Skinner, J. J. Chem. Phys. 1992, 91, 1775. Pechukas, P. Phys. Rev. Lett. 1994, 73, 1060. Egoron, S. A.; Rabani, E.; Berne, B. J. J. Chem. Phys. 1998, 108, 1407.
41. See Kohen et al. (Kohen, D.; Marston, C. C.; Tannor, D. J. J. Chem. Phys. 1997, 107, 5236) for a comparison of six approaches to quantum dissipation in the context of the harmonic oscillator, and point out their advantages, difficulties, and differences. Other important theoretical studies include, in addition to the work already cited here, Agarwal, G. S. Phys. Rev. A 1971, 4, 739. Sargent, M., III; Scully, M. O.; Lamb, W. E., Jr. Laser Physics; Addison-Wesley: Redwood City, CA, 1974. Louisell, W. H. Quantum Coherence Properties of Radiation; Wiley: New York, 1973. Gardiner, C. W. Quantum Noise; Springer-Verlag: New York, 1991. Caldeira, A. O.; Leggett, A. J. Physica 1983, 121A, 587. Oppenheim, I.; Romero-Rochin, V. Physica 1987, 147A, 184. Suarez, A.; Silbey, R.; Oppenheim, I. J. Chem. Phys. 1992, 97, 5101. Yan, Y. J.; Mukamel, S. J. Chem. Phys. 1988, 88, 5160; 1988, 88, 5735. Schwartz, B. J.; Rossky, P. J. J. Chem. Phys. 1996, 105, 6997. Sevian, H. M.; Skinner, J. J. Chem. Phys. 1992, 91, 1775. Pechukas, P. Phys. Rev. Lett. 1994, 73, 1060. Egoron, S. A.; Rabani, E.; Berne, B. J. J. Chem. Phys. 1998, 108, 1407.
42. See Kohen et al. (Kohen, D.; Marston, C. C.; Tannor, D. J. J. Chem. Phys. 1997, 107, 5236) for a comparison of six approaches to quantum dissipation in the context of the harmonic oscillator, and point out their advantages, difficulties, and differences. Other important theoretical studies include, in addition to the work already cited here, Agarwal, G. S. Phys. Rev. A 1971, 4, 739. Sargent, M., III; Scully, M. O.; Lamb, W. E., Jr. Laser Physics; Addison-Wesley: Redwood City, CA, 1974. Louisell, W. H. Quantum Coherence Properties of Radiation; Wiley: New York, 1973. Gardiner, C. W. Quantum Noise; Springer-Verlag: New York, 1991. Caldeira, A. O.; Leggett, A. J. Physica 1983, 121A, 587. Oppenheim, I.; Romero-Rochin, V. Physica 1987, 147A, 184. Suarez, A.; Silbey, R.; Oppenheim, I. J. Chem. Phys. 1992, 97, 5101. Yan, Y. J.; Mukamel, S. J. Chem. Phys. 1988, 88, 5160; 1988, 88, 5735. Schwartz, B. J.; Rossky, P. J. J. Chem. Phys. 1996, 105, 6997. Sevian, H. M.; Skinner, J. J. Chem. Phys. 1992, 91, 1775. Pechukas, P. Phys. Rev. Lett. 1994, 73, 1060. Egoron, S. A.; Rabani, E.; Berne, B. J. J. Chem. Phys. 1998, 108, 1407.
43. See Kohen et al. (Kohen, D.; Marston, C. C.; Tannor, D. J. J. Chem. Phys. 1997, 107, 5236) for a comparison of six approaches to quantum dissipation in the context of the harmonic oscillator, and point out their advantages, difficulties, and differences. Other important theoretical studies include, in addition to the work already cited here, Agarwal, G. S. Phys. Rev. A 1971, 4, 739. Sargent, M., III; Scully, M. O.; Lamb, W. E., Jr. Laser Physics; Addison-Wesley: Redwood City, CA, 1974. Louisell, W. H. Quantum Coherence Properties of Radiation; Wiley: New York, 1973. Gardiner, C. W. Quantum Noise; Springer-Verlag: New York, 1991. Caldeira, A. O.; Leggett, A. J. Physica 1983, 121A, 587. Oppenheim, I.; Romero-Rochin, V. Physica 1987, 147A, 184. Suarez, A.; Silbey, R.; Oppenheim, I. J. Chem. Phys. 1992, 97, 5101. Yan, Y. J.; Mukamel, S. J. Chem. Phys. 1988, 88, 5160; 1988, 88, 5735. Schwartz, B. J.; Rossky, P. J. J. Chem. Phys. 1996, 105, 6997. Sevian, H. M.; Skinner, J. J. Chem. Phys. 1992, 91, 1775. Pechukas, P. Phys. Rev. Lett. 1994, 73, 1060. Egoron, S. A.; Rabani, E.; Berne, B. J. J. Chem. Phys. 1998, 108, 1407.
44. See Kohen et al. (Kohen, D.; Marston, C. C.; Tannor, D. J. J. Chem. Phys. 1997, 107, 5236) for a comparison of six approaches to quantum dissipation in the context of the harmonic oscillator, and point out their advantages, difficulties, and differences. Other important theoretical studies include, in addition to the work already cited here, Agarwal, G. S. Phys. Rev. A 1971, 4, 739. Sargent, M., III; Scully, M. O.; Lamb, W. E., Jr. Laser Physics; Addison-Wesley: Redwood City, CA, 1974. Louisell, W. H. Quantum Coherence Properties of Radiation; Wiley: New York, 1973. Gardiner, C. W. Quantum Noise; Springer-Verlag: New York, 1991. Caldeira, A. O.; Leggett, A. J. Physica 1983, 121A, 587. Oppenheim, I.; Romero-Rochin, V. Physica 1987, 147A, 184. Suarez, A.; Silbey, R.; Oppenheim, I. J. Chem. Phys. 1992, 97, 5101. Yan, Y. J.; Mukamel, S. J. Chem. Phys. 1988, 88, 5160; 1988, 88, 5735. Schwartz, B. J.; Rossky, P. J. J. Chem. Phys. 1996, 105, 6997. Sevian, H. M.; Skinner, J. J. Chem. Phys. 1992, 91, 1775. Pechukas, P. Phys. Rev. Lett. 1994, 73, 1060. Egoron, S. A.; Rabani, E.; Berne, B. J. J. Chem. Phys. 1998, 108, 1407.
45. See Kohen et al. (Kohen, D.; Marston, C. C.; Tannor, D. J. J. Chem. Phys. 1997, 107, 5236) for a comparison of six approaches to quantum dissipation in the context of the harmonic oscillator, and point out their advantages, difficulties, and differences. Other important theoretical studies include, in addition to the work already cited here, Agarwal, G. S. Phys. Rev. A 1971, 4, 739. Sargent, M., III; Scully, M. O.; Lamb, W. E., Jr. Laser Physics; Addison-Wesley: Redwood City, CA, 1974. Louisell, W. H. Quantum Coherence Properties of Radiation; Wiley: New York, 1973. Gardiner, C. W. Quantum Noise; Springer-Verlag: New York, 1991. Caldeira, A. O.; Leggett, A. J. Physica 1983, 121A, 587. Oppenheim, I.; Romero-Rochin, V. Physica 1987, 147A, 184. Suarez, A.; Silbey, R.; Oppenheim, I. J. Chem. Phys. 1992, 97, 5101. Yan, Y. J.; Mukamel, S. J. Chem. Phys. 1988, 88, 5160; 1988, 88, 5735. Schwartz, B. J.; Rossky, P. J. J. Chem. Phys. 1996, 105, 6997. Sevian, H. M.; Skinner, J. J. Chem. Phys. 1992, 91, 1775. Pechukas, P. Phys. Rev. Lett. 1994, 73, 1060. Egoron, S. A.; Rabani, E.; Berne, B. J. J. Chem. Phys. 1998, 108, 1407.
46. See Kohen et al. (Kohen, D.; Marston, C. C.; Tannor, D. J. J. Chem. Phys. 1997, 107, 5236) for a comparison of six approaches to quantum dissipation in the context of the harmonic oscillator, and point out their advantages, difficulties, and differences. Other important theoretical studies include, in addition to the work already cited here, Agarwal, G. S. Phys. Rev. A 1971, 4, 739. Sargent, M., III; Scully, M. O.; Lamb, W. E., Jr. Laser Physics; Addison-Wesley: Redwood City, CA, 1974. Louisell, W. H. Quantum Coherence Properties of Radiation; Wiley: New York, 1973. Gardiner, C. W. Quantum Noise; Springer-Verlag: New York, 1991. Caldeira, A. O.; Leggett, A. J. Physica 1983, 121A, 587. Oppenheim, I.; Romero-Rochin, V. Physica 1987, 147A, 184. Suarez, A.; Silbey, R.; Oppenheim, I. J. Chem. Phys. 1992, 97, 5101. Yan, Y. J.; Mukamel, S. J. Chem. Phys. 1988, 88, 5160; 1988, 88, 5735. Schwartz, B. J.; Rossky, P. J. J. Chem. Phys. 1996, 105, 6997. Sevian, H. M.; Skinner, J. J. Chem. Phys. 1992, 91, 1775. Pechukas, P. Phys. Rev. Lett. 1994, 73, 1060. Egoron, S. A.; Rabani, E.; Berne, B. J. J. Chem. Phys. 1998, 108, 1407.
47. See Kohen et al. (Kohen, D.; Marston, C. C.; Tannor, D. J. J. Chem. Phys. 1997, 107, 5236) for a comparison of six approaches to quantum dissipation in the context of the harmonic oscillator, and point out their advantages, difficulties, and differences. Other important theoretical studies include, in addition to the work already cited here, Agarwal, G. S. Phys. Rev. A 1971, 4, 739. Sargent, M., III; Scully, M. O.; Lamb, W. E., Jr. Laser Physics; Addison-Wesley: Redwood City, CA, 1974. Louisell, W. H. Quantum Coherence Properties of Radiation; Wiley: New York, 1973. Gardiner, C. W. Quantum Noise; Springer-Verlag: New York, 1991. Caldeira, A. O.; Leggett, A. J. Physica 1983, 121A, 587. Oppenheim, I.; Romero-Rochin, V. Physica 1987, 147A, 184. Suarez, A.; Silbey, R.; Oppenheim, I. J. Chem. Phys. 1992, 97, 5101. Yan, Y. J.; Mukamel, S. J. Chem. Phys. 1988, 88, 5160; 1988, 88, 5735. Schwartz, B. J.; Rossky, P. J. J. Chem. Phys. 1996, 105, 6997. Sevian, H. M.; Skinner, J. J. Chem. Phys. 1992, 91, 1775. Pechukas, P. Phys. Rev. Lett. 1994, 73, 1060. Egoron, S. A.; Rabani, E.; Berne, B. J. J. Chem. Phys. 1998, 108, 1407.
48. See Kohen et al. (Kohen, D.; Marston, C. C.; Tannor, D. J. J. Chem. Phys. 1997, 107, 5236) for a comparison of six approaches to quantum dissipation in the context of the harmonic oscillator, and point out their advantages, difficulties, and differences. Other important theoretical studies include, in addition to the work already cited here, Agarwal, G. S. Phys. Rev. A 1971, 4, 739. Sargent, M., III; Scully, M. O.; Lamb, W. E., Jr. Laser Physics; Addison-Wesley: Redwood City, CA, 1974. Louisell, W. H. Quantum Coherence Properties of Radiation; Wiley: New York, 1973. Gardiner, C. W. Quantum Noise; Springer-Verlag: New York, 1991. Caldeira, A. O.; Leggett, A. J. Physica 1983, 121A, 587. Oppenheim, I.; Romero-Rochin, V. Physica 1987, 147A, 184. Suarez, A.; Silbey, R.; Oppenheim, I. J. Chem. Phys. 1992, 97, 5101. Yan, Y. J.; Mukamel, S. J. Chem. Phys. 1988, 88, 5160; 1988, 88, 5735. Schwartz, B. J.; Rossky, P. J. J. Chem. Phys. 1996, 105, 6997. Sevian, H. M.; Skinner, J. J. Chem. Phys. 1992, 91, 1775. Pechukas, P. Phys. Rev. Lett. 1994, 73, 1060. Egoron, S. A.; Rabani, E.; Berne, B. J. J. Chem. Phys. 1998, 108, 1407.
49. See Kohen et al. (Kohen, D.; Marston, C. C.; Tannor, D. J. J. Chem. Phys. 1997, 107, 5236) for a comparison of six approaches to quantum dissipation in the context of the harmonic oscillator, and point out their advantages, difficulties, and differences. Other important theoretical studies include, in addition to the work already cited here, Agarwal, G. S. Phys. Rev. A 1971, 4, 739. Sargent, M., III; Scully, M. O.; Lamb, W. E., Jr. Laser Physics; Addison-Wesley: Redwood City, CA, 1974. Louisell, W. H. Quantum Coherence Properties of Radiation; Wiley: New York, 1973. Gardiner, C. W. Quantum Noise; Springer-Verlag: New York, 1991. Caldeira, A. O.; Leggett, A. J. Physica 1983, 121A, 587. Oppenheim, I.; Romero-Rochin, V. Physica 1987, 147A, 184. Suarez, A.; Silbey, R.; Oppenheim, I. J. Chem. Phys. 1992, 97, 5101. Yan, Y. J.; Mukamel, S. J. Chem. Phys. 1988, 88, 5160; 1988, 88, 5735. Schwartz, B. J.; Rossky, P. J. J. Chem. Phys. 1996, 105, 6997. Sevian, H. M.; Skinner, J. J. Chem. Phys. 1992, 91, 1775. Pechukas, P. Phys. Rev. Lett. 1994, 73, 1060. Egoron, S. A.; Rabani, E.; Berne, B. J. J. Chem. Phys. 1998, 108, 1407.
50. See Kohen et al. (Kohen, D.; Marston, C. C.; Tannor, D. J. J. Chem. Phys. 1997, 107, 5236) for a comparison of six approaches to quantum dissipation in the context of the harmonic oscillator, and point out their advantages, difficulties, and differences. Other important theoretical studies include, in addition to the work already cited here, Agarwal, G. S. Phys. Rev. A 1971, 4, 739. Sargent, M., III; Scully, M. O.; Lamb, W. E., Jr. Laser Physics; Addison-Wesley: Redwood City, CA, 1974. Louisell, W. H. Quantum Coherence Properties of Radiation; Wiley: New York, 1973. Gardiner, C. W. Quantum Noise; Springer-Verlag: New York, 1991. Caldeira, A. O.; Leggett, A. J. Physica 1983, 121A, 587. Oppenheim, I.; Romero-Rochin, V. Physica 1987, 147A, 184. Suarez, A.; Silbey, R.; Oppenheim, I. J. Chem. Phys. 1992, 97, 5101. Yan, Y. J.; Mukamel, S. J. Chem. Phys. 1988, 88, 5160; 1988, 88, 5735. Schwartz, B. J.; Rossky, P. J. J. Chem. Phys. 1996, 105, 6997. Sevian, H. M.; Skinner, J. J. Chem. Phys. 1992, 91, 1775. Pechukas, P. Phys. Rev. Lett. 1994, 73, 1060. Egoron, S. A.; Rabani, E.; Berne, B. J. J. Chem. Phys. 1998, 108, 1407.
51. See Kohen et al. (Kohen, D.; Marston, C. C.; Tannor, D. J. J. Chem. Phys. 1997, 107, 5236) for a comparison of six approaches to quantum dissipation in the context of the harmonic oscillator, and point out their advantages, difficulties, and differences. Other important theoretical studies include, in addition to the work already cited here, Agarwal, G. S. Phys. Rev. A 1971, 4, 739. Sargent, M., III; Scully, M. O.; Lamb, W. E., Jr. Laser Physics; Addison-Wesley: Redwood City, CA, 1974. Louisell, W. H. Quantum Coherence Properties of Radiation; Wiley: New York, 1973. Gardiner, C. W. Quantum Noise; Springer-Verlag: New York, 1991. Caldeira, A. O.; Leggett, A. J. Physica 1983, 121A, 587. Oppenheim, I.; Romero-Rochin, V. Physica 1987, 147A, 184. Suarez, A.; Silbey, R.; Oppenheim, I. J. Chem. Phys. 1992, 97, 5101. Yan, Y. J.; Mukamel, S. J. Chem. Phys. 1988, 88, 5160; 1988, 88, 5735. Schwartz, B. J.; Rossky, P. J. J. Chem. Phys. 1996, 105, 6997. Sevian, H. M.; Skinner, J. J. Chem. Phys. 1992, 91, 1775. Pechukas, P. Phys. Rev. Lett. 1994, 73, 1060. Egoron, S. A.; Rabani, E.; Berne, B. J. J. Chem. Phys. 1998, 108, 1407.
52. Lindblad, G. Rep. Math. Phys. 1976, 10, 393.
53. A simple physical argument for this statement involves equilibration: for the correct equilibrium to be achieved at long times, the appropriate (Bose, Fermi, Boltzmann) statistics must hold for system eigenstates, not for local states. In the simple two-site model studied here, it is the molecular orbitals, not the atomic orbitals, whose populations must obey Fermi statistics at equilibrium.
54. Schatz, G. C.; Ratner, M. A. Quantum Mechanics in Chemistry; Prentice Hall: Englewood Cliffs, NJ, 1994; Chapter 10.
55. Leggett, A. J.; Chakravarty, S.; Dorsey, A. T.; Fisher, M. P. A.; Garg, A.; Zerger, W. Rev. Mod. Phys. 1987, 59, 1.
56. Schatz, G. C.; Ratner, M. A. Quantum Mechanics in Chemistry; Prentice Hall: Englewood Cliffs, NJ, 1994; Chapter 11. Blum, K. Density Matrix Theory and Applications; Plenum: New York, 1981. Laird, B. B.; Budimir, J.; Skinner, J. L. J. Chem. Phys. 1991, 94, 4391.
57. Schatz, G. C.; Ratner, M. A. Quantum Mechanics in Chemistry; Prentice Hall: Englewood Cliffs, NJ, 1994; Chapter 11. Blum, K. Density Matrix Theory and Applications; Plenum: New York, 1981. Laird, B. B.; Budimir, J.; Skinner, J. L. J. Chem. Phys. 1991, 94, 4391.
58. Schatz, G. C.; Ratner, M. A. Quantum Mechanics in Chemistry; Prentice Hall: Englewood Cliffs, NJ, 1994; Chapter 11. Blum, K. Density Matrix Theory and Applications; Plenum: New York, 1981. Laird, B. B.; Budimir, J.; Skinner, J. L. J. Chem. Phys. 1991, 94, 4391.
59. Farrar, T. C.; Harriman, J. E. Density Matrix Theory and its Applications to NMR Spectroscopy; Farragut: Madison, 1992.
60. Davies, E. B. Commun. Math. Phys. 1974, 39, 91.
61. Oxtoby, D. W. Annu. Rev. Phys. Chem. 1981, 32, 77.
62. Geva, E.; Kosloff, R.; Skinner, J. L. J. Chem. Phys. 1995, 102, 8541.
63. MathCad is a registered product of MathSoft, Inc., 101 Main St., Cambridge, MA 02142.
64. Kosloff, R. J. Phys. Chem. 1988, 92, 2087.