Free initial wave packets and the long-time behavior of the survival and nonescape probabilities

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 68, Issue 2, 2003, Pages 5-

  Miyamoto, Manabu ^a  

^a WASEDA UNIVERSITY   (Japan)

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Indexed keywords

EID: 84868327235     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.68.022702     Document Type: Article

References (25)

1. K. Unnikrishnan, Am. J. Phys. 65, 526 (1997)
2. Am. J. Phys.K. Unnikrishnan66, 632 (1998).
3. F. Lillo and R.N. Mantegna, Phys. Rev. Lett. 84, 1061 (2000)
4. Phys. Rev. Lett.F. LilloR.N. Mantegna84, 4516 (2000).
5. R.S. Mendes and C. Anteneodo, e-print cond-mat/0003366.
6. J.A. Damborenea, I.L. Egusquiza, and J.G. Muga, Am. J. Phys. 70, 738 (2002).
7. L. Fonda, G.C. Ghirardi, and A. Rimini, Rep. Prog. Phys. 41, 587 (1977).
8. H. Nakazato, M. Namiki, and S. Pascazio, Int. J. Mod. Phys. B 10, 247 (1996).
9. G. García-Calderón, J.L. Mateos, and M. Moshinsky, Phys. Rev. Lett. 74, 337 (1995).
10. W. van Dijk and Y. Nogami, Phys. Rev. C 65, 024608 (2002)
11. W. van DijkY. NogamiPhys. Rev. Lett. 83, 2867 (1999).
12. H.M. Nussenzveig, Causality and Dispersion Relations (Academic, New York, 1972), p. 183.
13. J.G. Muga, V. Delgado, and R.F. Snider, Phys. Rev. B 52, 16 381 (1995).
14. M. Miyamoto, J. Phys. A 35, 7159 (2002).
15. One may feel that the terms, “survival” and “nonescape,” are not appropriate for a free system. However, as is seen in Eqs. (1) and (2), the definitions of (Formula presented) and (Formula presented) are mathematically natural extensions of them for the potential systems, and their physical meanings are obvious.
16. R.M. Cavalcanti, Phys. Rev. Lett. 80, 4353 (1998)
17. Phys. Rev. Lett.G. García-Calderón, J.L. Mateos, and M. Moshinsky, 80, 4354 (1998)
18. Phys. Rev. Lett.W. van Dijk and Y. Nogami, 90, 028901 (2003)
19. Phys. Rev. Lett.G. García-Calderón, J.L. Mateos, and M. Moshinsky, 90, 028902 (2003).
20. F.W.J. Olver, Asymptotics and Special Functions (Academic Press, New York, 1974).
21. E.T. Copson, Asymptotic Expansions (Cambridge University Press, Cambridge, 1965), Chap. 3, Secs. 10 and 11.
22. Actually, (Formula presented) is the expansion coefficient of the free resolvent (Formula presented) at small z 11.
23. J. Rauch, Commun. Math. Phys. 61, 149 (1978)
24. A. Jensen and T. Kato, Duke Math. J. 46, 583 (1979)
25. M. Murata, J. Funct. Anal. 49, 10 (1982).