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Journal
2009 | 7 | 4 | 696-703
Article title

Long time properties of the evolution of an unstable state

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EN
Abstracts
EN
An effect generated by the nonexponential behavior of the survival amplitude of an unstable state in the long time region is considered. In 1957 Khalfin proved that this amplitude tends to zero as t → ∞ more slowly than any exponential function of t. This can be described in terms of the time-dependent decay rate γ(t) which, when considered with the Khalfin result, means that this γ(t) is not a constant for large t but that it tends to zero as t → ∞. We find that a similar conclusion can be drawn for a large class of models of unstable states for a quantity, which can be interpreted as the “instantaneous energy” of the unstable state. This energy should be much smaller for suitably larger values of t than when t is of the order of the lifetime of the considered state. Within a given model we show that the energy corrections in the long (t → ∞) and relatively short (lifetime of the state) time regions, are different. This is a purely quantum mechanical effect. It is hypothesized that there is a possibility to detect this effect by analyzing the spectra of distant astrophysical objects. The above property of unstable states may influence the measured values of astrophysical and cosmological parameters.
Publisher
Journal
Year
Volume
7
Issue
4
Pages
696-703
Physical description
Dates
published
1 - 12 - 2009
online
21 - 7 - 2009
References
  • [1] L. P. Horwitz, J. P. Marchand, Rocky Mt. J. Math. 1, 225 (1971) http://dx.doi.org/10.1216/RMJ-1971-1-1-225[Crossref]
  • [2] W. Królikowski, J. Rzewuski, Nuovo Cimento B 25, 739 (1975) http://dx.doi.org/10.1007/BF02724749[Crossref]
  • [3] R. Zwanzig, Physica 30, 1109 (1964) http://dx.doi.org/10.1016/0031-8914(64)90102-8[Crossref]
  • [4] A. Agodi, M. Baldo, E. Recami, Ann. Phys. 77, 157 (1973) http://dx.doi.org/10.1016/0003-4916(73)90413-2[Crossref]
  • [5] F. Haake, Staistical Treatment of Open Systems by Generalized master Equations, Springer Tracts in Modern Physics Vo. 66 (Springer, Berlin, 1973)
  • [6] K. Urbanowski, Phys. Rev. A 50, 2847 (1994) http://dx.doi.org/10.1103/PhysRevA.50.2847[Crossref]
  • [7] Y. Aharonov and D. Rohrlich, Quantum Paradoxes (Wiley- VCH, Weinheim, 2005) http://dx.doi.org/10.1002/9783527619115[Crossref]
  • [8] Y. Aharonov, L. Vaidman, J. Phys. A-Math. Gen. 24, 2315 (1991) http://dx.doi.org/10.1088/0305-4470/24/10/018[Crossref]
  • [9] Y. Aharonov, L. Vaidman, Phys. Rev. A 41, 11 (1990) http://dx.doi.org/10.1103/PhysRevA.41.11[Crossref]
  • [10] Y. Aharonav, D. Albert and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988) http://dx.doi.org/10.1103/PhysRevLett.60.1351[Crossref]
  • [11] P. C. W. Davies, arXiv:0807.1357 [WoS]
  • [12] V. F. Weisskopf, E. T. Wigner, Z. Phys. 63, 54 (1930) http://dx.doi.org/10.1007/BF01336768[Crossref]
  • [13] V. F. Weisskopf, E. T. Wigner, Z. Phys. 65, 18 (1930) http://dx.doi.org/10.1007/BF01397406[Crossref]
  • [14] M. L. Goldberger, K. M. Watson, Collision Theory (Willey, New York, 1964)
  • [15] S. Krylov, V. A. Fock, Zh. Eksp. Teor. Fiz.+ 17, 93 (1947)
  • [16] L. A. Khalfin, Zh. Eksp. Teor. Fiz.+ 33, 1371 (1957)
  • [17] L. A. Khalfin, Sov. Phys. JETP-USSR 6, 1053 (1958)
  • [18] R. E. A. C. Paley, N. Wiener, Fourier transforms in the comlex domain (American Mathematical Society, New York, 1934)
  • [19] R. G. Newton, Scattering Theory of Waves and Particles, 2nd edtition (Springer, New York, 1982)
  • [20] L. Fonda, G. C. Ghirardii, A. Rimini, Rep. Prog. Phys. 41, 587 (1978) http://dx.doi.org/10.1088/0034-4885/41/4/003[Crossref]
  • [21] A. Peres, Ann. Phys. 129, 33 (1980) http://dx.doi.org/10.1016/0003-4916(80)90288-2[Crossref]
  • [22] P. T. Greenland, Nature 335, 298 (1988) http://dx.doi.org/10.1038/335298a0[Crossref]
  • [23] D. G. Arbo, M. A. Castagnino, F. H. Gaioli, S. Iguri, Physica A 227, 469 (2000) http://dx.doi.org/10.1016/S0378-4371(99)00480-X[Crossref]
  • [24] J. M. Wessner, D. K. Andreson, R. T. Robiscoe, Phys. Rev. Lett. 29, 1126 (1972) http://dx.doi.org/10.1103/PhysRevLett.29.1126[Crossref]
  • [25] E. B. Norman, S. B. Gazes, S. C. Crane, D. A. Bennet, Phys. Rev. Lett. 60, 2246 (1988) http://dx.doi.org/10.1103/PhysRevLett.60.2246[Crossref]
  • [26] E. B. Norman, B. Sur, K. T. Lesko, R.-M. Larimer, Phys. Lett. B 357, 521 (1995) http://dx.doi.org/10.1016/0370-2693(95)00818-6[Crossref]
  • [27] J. Seke, W. N. Herfort, Phys. Rev. A 38, 833 (1988) http://dx.doi.org/10.1103/PhysRevA.38.833[Crossref]
  • [28] R. E. Parrot, J. Lawrence, Europhys. Lett. 57, 632 (2002) http://dx.doi.org/10.1209/epl/i2002-00509-0[Crossref]
  • [29] J. Lawrence, Journ. Opt. B: Quant. Semiclass. Opt. 4, S446 (2002) http://dx.doi.org/10.1088/1464-4266/4/4/337[Crossref]
  • [30] I. Joichi, Sh. Matsumoto, M. Yoshimura, Phys. Rev. D 58, 045004 (1998) http://dx.doi.org/10.1103/PhysRevD.58.045004[Crossref]
  • [31] N. G. Kelkar, M. Nowakowski, K. P. Khemchandani, Phys. Rev. C 70, 024601 (2004) http://dx.doi.org/10.1103/PhysRevC.70.024601[Crossref]
  • [32] M. Nowakowski, N. G. Kelkar, AIP Conf. Proc. 1030, 250 (2008) http://dx.doi.org/10.1063/1.2973508[Crossref]
  • [33] T. Jiitoh, S. Matsumoto, J. Sato, Y. Sato, K. Takeda, Phys Rev. A 71, 012109 (2005) http://dx.doi.org/10.1103/PhysRevA.71.012109[Crossref]
  • [34] C. Rothe, S. I. Hintschich, A. P. Monkman, Phys. Rev. Lett. 96, 163601 (2006) http://dx.doi.org/10.1103/PhysRevLett.96.163601[Crossref]
  • [35] K. M. Sluis, E. A. Gislason, Phys. Rev. A 43, 4581 (1991) http://dx.doi.org/10.1103/PhysRevA.43.4581[Crossref]
  • [36] M. Abramowitz, I. A. Stegun (Eds.), Handbook of Mathematical Functions, Natl. Bur. Stand. Appl. Math. Ser. No 55 (U.S. GPO, Washington, D.C., 1964)
  • [37] R. M. Corless, G. H. Gonet, D. E. G. Hare, D. J. Jeffrey, D. E. Khnut, Adv. Comput. Math. 5, 329 (1996) http://dx.doi.org/10.1007/BF02124750[Crossref]
  • [38] F. W. J. Olver, Asymptotics and special functions (Academic Press, New York, 1974)
  • [39] F. M. Dittes, H. L. Harney, A. Müller, Phys. Rev. A 45, 701 (1992) http://dx.doi.org/10.1103/PhysRevA.45.701[Crossref]
  • [40] W. Heitler, The Quantum Theory of Radiation (Oxford University Press, London, 1954; Dover Publications, New York, 1984)
  • [41] E. W. Kolb, M. S. Turner, The Early Universe (Addison-Wesley Publ. Co., 1993)
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-009-0053-5
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