Initial state maximizing the nonexponentially decaying survival probability for unstable multilevel systems

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 70, Issue 3, 2004, Pages

  Miyamoto, Manabu ^a  

^a WASEDA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; EIGENVALUES AND EIGENFUNCTIONS; ELECTROMAGNETIC FIELD EFFECTS; HAMILTONIANS; NEUTRON EMISSION; PROBABILITY; QUANTUM THEORY; WAVE EFFECTS;

MULTILEVEL SYSTEMS; POWER-DECAY LAW; SPONTANEOUS-EMISSIONS; SURVIVAL PROBABILITY;

NUCLEAR PHYSICS;

EID: 19644400594     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.70.032108     Document Type: Article

References (34)

1. For a review, see, for example, H. Nakazato, M. Namiki, and S. Pascazio, Int. J. Mod. Phys. B 10, 247 (1996).
2. L. A. Khalfin, Zh. Eksp. Teor. Fiz. 33, 1371 (1957) [Sov. Phys. JETP 6, 1053 (1958)].
3. L. A. Khalfin, Zh. Eksp. Teor. Fiz. 33, 1371 (1957) [Sov. Phys. JETP 6, 1053 (1958)].
4. P. T. Greenland, Nature (London) 335, 298 (1988).
5. S. R. Wilkinson et al., Nature (London) 387, 575 (1997).
6. K. O. Friedrichs, Commun. Pure Appl. Math. 1, 361 (1948).
7. P. Exner, Open Quantum Systems and Feynman Integrals (Reidel, Dordrecht, 1985).
8. P. Facchi and S. Pascazio, Phys. Lett. A 241, 139 (1998).
9. I. Antoniou, E. Karpov, G. Pronko, and E. Yarevsky, Phys. Rev. A 63, 062110 (2001).
10. K. Rza̧żewski, M. Lewenstein, and J. H. Eberly, J. Phys. B 15, L661 (1982).
11. S. L. Haan and J. Cooper, J. Phys. B 17, 3481 (1984).
12. H. Nakazato, in Fundamental Aspects of Quantum Physics, edited by L. Accardi and S. Tasaki (World Scientific, Teaneck, NJ, 2003).
13. E. Frishman and M. Shapiro, Phys. Rev. Lett. 87, 253001 (2001); Phys. Rev. A 68, 032717 (2003).
14. E. Frishman and M. Shapiro, Phys. Rev. Lett. 87, 253001 (2001); Phys. Rev. A 68, 032717 (2003).
15. I. Antoniou, E. Karpov, G. Pronko, and E. Yarevsky, Int. J. Theor. Phys. 42, 2403 (2003).
16. I. Antoniou, E. Karpov, G. Pronko, and E. Yarevsky, e-print quant-ph/0402210.
17. M. Miyamoto, in Proceedings of the Workshop on Quantum Mechanics and Chaos: From Fundamental Problems through Nanosciences 2003 [Bussei Kenkyu 82, 743 (2004)] (in Japanese).
18. M. Miyamoto, in Proceedings of the Workshop on Quantum Mechanics and Chaos: From Fundamental Problems through Nanosciences 2003 [Bussei Kenkyu 82, 743 (2004)] (in Japanese).
19. E. B. Davies, J. Math. Phys. 15, 2036 (1974).
20. E. P. Wigner, Phys. Rev. 73, 1002 (1948).
21. This is the case for the strong-coupling interactions (see, e.g., [11]), and for the degenerated multilevel systems [14].
22. E. T. Copson, Asymptotic Expansions (Cambridge University Press, Cambridge, 1965), Chap. 3.
23. 2) for our interaction Hamiltonian λV. This does not contradict the behavior of A(t) at long times [13].
24. J. Seke, Physica A 203, 269 (1994).
25. H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One-and Two-Electron Atoms (Springer-Verlag, Berlin, 1957), Sec. 63.
26. -55 for N=1, an extremely small value.
27. K. Unnikrishnan, Am. J. Phys. 65, 526 (1997); 66, 632 (1998); F. Lillo and R. N. Mantegna, Phys. Rev. Lett. 84, 1061 (2000); 84, 4516 (2000); J. A. Damborenea, I. L. Egusquiza, and J. G. Muga, Am. J. Phys. 70, 738 (2002); M. Miyamoto, J. Phys. A 35, 7159 (2002); Phys. Rev. A 68, 022702 (2003).
28. K. Unnikrishnan, Am. J. Phys. 65, 526 (1997); 66, 632 (1998); F. Lillo and R. N. Mantegna, Phys. Rev. Lett. 84, 1061 (2000); 84, 4516 (2000); J. A. Damborenea, I. L. Egusquiza, and J. G. Muga, Am. J. Phys. 70, 738 (2002); M. Miyamoto, J. Phys. A 35, 7159 (2002); Phys. Rev. A 68, 022702 (2003).
29. K. Unnikrishnan, Am. J. Phys. 65, 526 (1997); 66, 632 (1998); F. Lillo and R. N. Mantegna, Phys. Rev. Lett. 84, 1061 (2000); 84, 4516 (2000); J. A. Damborenea, I. L. Egusquiza, and J. G. Muga, Am. J. Phys. 70, 738 (2002); M. Miyamoto, J. Phys. A 35, 7159 (2002); Phys. Rev. A 68, 022702 (2003).
30. K. Unnikrishnan, Am. J. Phys. 65, 526 (1997); 66, 632 (1998); F. Lillo and R. N. Mantegna, Phys. Rev. Lett. 84, 1061 (2000); 84, 4516 (2000); J. A. Damborenea, I. L. Egusquiza, and J. G. Muga, Am. J. Phys. 70, 738 (2002); M. Miyamoto, J. Phys. A 35, 7159 (2002); Phys. Rev. A 68, 022702 (2003).
31. K. Unnikrishnan, Am. J. Phys. 65, 526 (1997); 66, 632 (1998); F. Lillo and R. N. Mantegna, Phys. Rev. Lett. 84, 1061 (2000); 84, 4516 (2000); J. A. Damborenea, I. L. Egusquiza, and J. G. Muga, Am. J. Phys. 70, 738 (2002); M. Miyamoto, J. Phys. A 35, 7159 (2002); Phys. Rev. A 68, 022702 (2003).
32. K. Unnikrishnan, Am. J. Phys. 65, 526 (1997); 66, 632 (1998); F. Lillo and R. N. Mantegna, Phys. Rev. Lett. 84, 1061 (2000); 84, 4516 (2000); J. A. Damborenea, I. L. Egusquiza, and J. G. Muga, Am. J. Phys. 70, 738 (2002); M. Miyamoto, J. Phys. A 35, 7159 (2002); Phys. Rev. A 68, 022702 (2003).
33. K. Unnikrishnan, Am. J. Phys. 65, 526 (1997); 66, 632 (1998); F. Lillo and R. N. Mantegna, Phys. Rev. Lett. 84, 1061 (2000); 84, 4516 (2000); J. A. Damborenea, I. L. Egusquiza, and J. G. Muga, Am. J. Phys. 70, 738 (2002); M. Miyamoto, J. Phys. A 35, 7159 (2002); Phys. Rev. A 68, 022702 (2003).
34. M. Miyamoto, Phys. Rev. A 69, 042704 (2004).