Quantum dissipation in open harmonic systems - Operator solution and application to decay process

Progress of Theoretical Physics

Volumn 98, Issue 1, 1997, Pages 9-28

  Joichi, Izumi ^a   Matsumoto, Shigeki ^a   Yoshimura, Motohiko ^a  

^a TOHOKU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031493921     PISSN: 0033068X     EISSN: None     Source Type: Journal    
DOI: 10.1143/PTP.98.9     Document Type: Article

References (27)

1. I. R. Senitzky, Phys. Rev. 119 (1960), 670 and references therein. A. O. Caldeira and A. J. Leggett, Physica 121A (1983), 587 and references therein.
2. I. R. Senitzky, Phys. Rev. 119 (1960), 670 and references therein. A. O. Caldeira and A. J. Leggett, Physica 121A (1983), 587 and references therein.
3. We give only an incomplete list of papers that have greatly influenced our thinking on this problem. Quantum Langevin equation: P. Ullersma, Physica 32 (1966), 27 and references therein. K. Lindenberg and B. J. West, Phys. Rev. A30 (1984), 568. G. W. Ford, J. T. Lewis and R. F. O'Connell, Phys. Rev. A37 (1988), 4419. Path integral approach: R. P. Feynman and F. L. Vernon, Ann. of Phys. 24 (1963), 118. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integral (McGraw Hill, New York, 1965). A. O. Caldeira and A. J. Leggett, Physica 121A (1983), 587; Ann. of Phys. 149 (1983), 374. H. Grabert, P. Schramm and G.-L. Ingold, Phys. Rep. 168 (1988), 115 and references therein. W. G. Unruh and W. H. Zurek, Phys. Rev. D40 (1989), 1071. B. L. Hu, J. P. Paz and Y. Zhang, Phys. Rev. D45 (1992), 2843.
4. We give only an incomplete list of papers that have greatly influenced our thinking on this problem. Quantum Langevin equation: P. Ullersma, Physica 32 (1966), 27 and references therein. K. Lindenberg and B. J. West, Phys. Rev. A30 (1984), 568. G. W. Ford, J. T. Lewis and R. F. O'Connell, Phys. Rev. A37 (1988), 4419. Path integral approach: R. P. Feynman and F. L. Vernon, Ann. of Phys. 24 (1963), 118. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integral (McGraw Hill, New York, 1965). A. O. Caldeira and A. J. Leggett, Physica 121A (1983), 587; Ann. of Phys. 149 (1983), 374. H. Grabert, P. Schramm and G.-L. Ingold, Phys. Rep. 168 (1988), 115 and references therein. W. G. Unruh and W. H. Zurek, Phys. Rev. D40 (1989), 1071. B. L. Hu, J. P. Paz and Y. Zhang, Phys. Rev. D45 (1992), 2843.
5. We give only an incomplete list of papers that have greatly influenced our thinking on this problem. Quantum Langevin equation: P. Ullersma, Physica 32 (1966), 27 and references therein. K. Lindenberg and B. J. West, Phys. Rev. A30 (1984), 568. G. W. Ford, J. T. Lewis and R. F. O'Connell, Phys. Rev. A37 (1988), 4419. Path integral approach: R. P. Feynman and F. L. Vernon, Ann. of Phys. 24 (1963), 118. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integral (McGraw Hill, New York, 1965). A. O. Caldeira and A. J. Leggett, Physica 121A (1983), 587; Ann. of Phys. 149 (1983), 374. H. Grabert, P. Schramm and G.-L. Ingold, Phys. Rep. 168 (1988), 115 and references therein. W. G. Unruh and W. H. Zurek, Phys. Rev. D40 (1989), 1071. B. L. Hu, J. P. Paz and Y. Zhang, Phys. Rev. D45 (1992), 2843.
6. We give only an incomplete list of papers that have greatly influenced our thinking on this problem. Quantum Langevin equation: P. Ullersma, Physica 32 (1966), 27 and references therein. K. Lindenberg and B. J. West, Phys. Rev. A30 (1984), 568. G. W. Ford, J. T. Lewis and R. F. O'Connell, Phys. Rev. A37 (1988), 4419. Path integral approach: R. P. Feynman and F. L. Vernon, Ann. of Phys. 24 (1963), 118. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integral (McGraw Hill, New York, 1965). A. O. Caldeira and A. J. Leggett, Physica 121A (1983), 587; Ann. of Phys. 149 (1983), 374. H. Grabert, P. Schramm and G.-L. Ingold, Phys. Rep. 168 (1988), 115 and references therein. W. G. Unruh and W. H. Zurek, Phys. Rev. D40 (1989), 1071. B. L. Hu, J. P. Paz and Y. Zhang, Phys. Rev. D45 (1992), 2843.
7. We give only an incomplete list of papers that have greatly influenced our thinking on this problem. Quantum Langevin equation: P. Ullersma, Physica 32 (1966), 27 and references therein. K. Lindenberg and B. J. West, Phys. Rev. A30 (1984), 568. G. W. Ford, J. T. Lewis and R. F. O'Connell, Phys. Rev. A37 (1988), 4419. Path integral approach: R. P. Feynman and F. L. Vernon, Ann. of Phys. 24 (1963), 118. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integral (McGraw Hill, New York, 1965). A. O. Caldeira and A. J. Leggett, Physica 121A (1983), 587; Ann. of Phys. 149 (1983), 374. H. Grabert, P. Schramm and G.-L. Ingold, Phys. Rep. 168 (1988), 115 and references therein. W. G. Unruh and W. H. Zurek, Phys. Rev. D40 (1989), 1071. B. L. Hu, J. P. Paz and Y. Zhang, Phys. Rev. D45 (1992), 2843.
8. We give only an incomplete list of papers that have greatly influenced our thinking on this problem. Quantum Langevin equation: P. Ullersma, Physica 32 (1966), 27 and references therein. K. Lindenberg and B. J. West, Phys. Rev. A30 (1984), 568. G. W. Ford, J. T. Lewis and R. F. O'Connell, Phys. Rev. A37 (1988), 4419. Path integral approach: R. P. Feynman and F. L. Vernon, Ann. of Phys. 24 (1963), 118. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integral (McGraw Hill, New York, 1965). A. O. Caldeira and A. J. Leggett, Physica 121A (1983), 587; Ann. of Phys. 149 (1983), 374. H. Grabert, P. Schramm and G.-L. Ingold, Phys. Rep. 168 (1988), 115 and references therein. W. G. Unruh and W. H. Zurek, Phys. Rev. D40 (1989), 1071. B. L. Hu, J. P. Paz and Y. Zhang, Phys. Rev. D45 (1992), 2843.
9. We give only an incomplete list of papers that have greatly influenced our thinking on this problem. Quantum Langevin equation: P. Ullersma, Physica 32 (1966), 27 and references therein. K. Lindenberg and B. J. West, Phys. Rev. A30 (1984), 568. G. W. Ford, J. T. Lewis and R. F. O'Connell, Phys. Rev. A37 (1988), 4419. Path integral approach: R. P. Feynman and F. L. Vernon, Ann. of Phys. 24 (1963), 118. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integral (McGraw Hill, New York, 1965). A. O. Caldeira and A. J. Leggett, Physica 121A (1983), 587; Ann. of Phys. 149 (1983), 374. H. Grabert, P. Schramm and G.-L. Ingold, Phys. Rep. 168 (1988), 115 and references therein. W. G. Unruh and W. H. Zurek, Phys. Rev. D40 (1989), 1071. B. L. Hu, J. P. Paz and Y. Zhang, Phys. Rev. D45 (1992), 2843.
10. We give only an incomplete list of papers that have greatly influenced our thinking on this problem. Quantum Langevin equation: P. Ullersma, Physica 32 (1966), 27 and references therein. K. Lindenberg and B. J. West, Phys. Rev. A30 (1984), 568. G. W. Ford, J. T. Lewis and R. F. O'Connell, Phys. Rev. A37 (1988), 4419. Path integral approach: R. P. Feynman and F. L. Vernon, Ann. of Phys. 24 (1963), 118. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integral (McGraw Hill, New York, 1965). A. O. Caldeira and A. J. Leggett, Physica 121A (1983), 587; Ann. of Phys. 149 (1983), 374. H. Grabert, P. Schramm and G.-L. Ingold, Phys. Rep. 168 (1988), 115 and references therein. W. G. Unruh and W. H. Zurek, Phys. Rev. D40 (1989), 1071. B. L. Hu, J. P. Paz and Y. Zhang, Phys. Rev. D45 (1992), 2843.
11. We give only an incomplete list of papers that have greatly influenced our thinking on this problem. Quantum Langevin equation: P. Ullersma, Physica 32 (1966), 27 and references therein. K. Lindenberg and B. J. West, Phys. Rev. A30 (1984), 568. G. W. Ford, J. T. Lewis and R. F. O'Connell, Phys. Rev. A37 (1988), 4419. Path integral approach: R. P. Feynman and F. L. Vernon, Ann. of Phys. 24 (1963), 118. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integral (McGraw Hill, New York, 1965). A. O. Caldeira and A. J. Leggett, Physica 121A (1983), 587; Ann. of Phys. 149 (1983), 374. H. Grabert, P. Schramm and G.-L. Ingold, Phys. Rep. 168 (1988), 115 and references therein. W. G. Unruh and W. H. Zurek, Phys. Rev. D40 (1989), 1071. B. L. Hu, J. P. Paz and Y. Zhang, Phys. Rev. D45 (1992), 2843.
12. We give only an incomplete list of papers that have greatly influenced our thinking on this problem. Quantum Langevin equation: P. Ullersma, Physica 32 (1966), 27 and references therein. K. Lindenberg and B. J. West, Phys. Rev. A30 (1984), 568. G. W. Ford, J. T. Lewis and R. F. O'Connell, Phys. Rev. A37 (1988), 4419. Path integral approach: R. P. Feynman and F. L. Vernon, Ann. of Phys. 24 (1963), 118. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integral (McGraw Hill, New York, 1965). A. O. Caldeira and A. J. Leggett, Physica 121A (1983), 587; Ann. of Phys. 149 (1983), 374. H. Grabert, P. Schramm and G.-L. Ingold, Phys. Rep. 168 (1988), 115 and references therein. W. G. Unruh and W. H. Zurek, Phys. Rev. D40 (1989), 1071. B. L. Hu, J. P. Paz and Y. Zhang, Phys. Rev. D45 (1992), 2843.
13. I. Joichi, Sh. Matsumoto and M. Yoshimura, hep-th/9609223.
14. For a recent review from the path integral view point, H. Grabert, P. Schramm and G.-L. Ingold, Phys. Rep. 168 (1988), 115.
15. J. Schwinger, Ann. of Phys. 9 (1960), 169. A. Peres, Ann. of Phys. 129 (1980), 33 and references therein.
16. J. Schwinger, Ann. of Phys. 9 (1960), 169. A. Peres, Ann. of Phys. 129 (1980), 33 and references therein.
17. P. Ullersma, Physica 32 (1966), 27.
18. M. Srednicki, Phys. Rev. Lett. 71 (1993), 666 and references therein.
19. M. Hotta, I. Joichi, Sh. Matsumoto and M. Yoshimura, Phys. Rev. D55 (1997), 4614.
20. G. V. Efimov and W. von Waldenfels, Ann. of Phys. 233 (1994), 182.
21. R. P. Feynman and F. L. Vernon, Ann. of Phys. 24 (1963), 118. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integral (McGraw Hill, New York, 1965).
22. R. P. Feynman and F. L. Vernon, Ann. of Phys. 24 (1963), 118. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integral (McGraw Hill, New York, 1965).
23. The contour deformation used here is the one in M. L. Goldberger and K. M. Watson, Collision Theory (John Wiley and Sons, New York, 1964), Chap. 8, in which detailed account of the decay of prepared states in quantum mechanics is given.
24. H. Grabert, U. Weiss and P. Talkner, Z. Phys. B55 (1984), 87.
25. F. Haake and R. Reibold, Phys. Rev. A32 (1985), 2462.
26. H. A. Weldon, Phys. Rev. D28 (1983), 2007.
27. For a recent review, M. Yoshimura, hep-th/9605246, and Journal of the Korean Physical Society 29 (1996), S236.