Long Time Deviations from the Exponential Decay Law: Possible Observational Effects
Urbanowski Krzysztof, Piskorski Jarosław
University of Zielona Góra, Institute of Physics,
ul. Prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland
e-mail: {K.Urbanowski/J.Piskorski}@proton.if.uz.zgora.pl
Received:
Received: 23 March 2010; accepted: 5 July 2010; published online: 1 September 2010
DOI: 10.12921/cmst.2010.16.02.201-205
OAI: oai:lib.psnc.pl:732
Abstract:
An effect generated by the nonexponential behavior of the survival amplitude of an unstable state in the long time region is considered. We find that the instantaneous energy of the unstable state for a large class of models of unstable states tends to the minimal energy of the system Emin as t → ∞ which is much smaller than the energy of this state for t of the order of the lifetime of the considered state. Analyzing the transition time region between the exponential and non-exponential form of the survival amplitude, we find that the instantaneous energy of the considered unstable state can take large values, much larger than the energy of this state for t from the exponential time region. Taking into account results obtained for a considered model, it is hypothesized that this purely quantum mechanical effect may be responsible for the properties of broad resonances such as σ meson as well as having astrophysical and cosmological consequences.
Key words:
References:
[1] S. Krylov, V.A. Fock, Zh. Eksp. Teor. Fiz. 17, 93 (1947).
[2] L. Fonda, G.C. Ghirardii, A. Rimini, Rep. on Prog. in Phys. 41, 587 (1978).
[3] L.A. Khalfin, Zh. Eksp. Teor. Fiz. 33, 1371 (1957), [Sov. Phys. – JETP 6, 1053 (1958)].
[4] R.E.A.C. Paley, N. Wiener, Fourier transforms in the complex domain. American Mathematical Society, New York (1934).
[5] C. Rothe, S.I. Hintschich, A.P. Monkman, Phys. Rev. Lett. 96, 163601 (2006).
[6] K. Urbanowski, Phys. Rev. A 50, 2847 (1994).
[7] K. Urbanowski, Cent. Eur. J. Phys. 7 (2009), DOI:10.2478/s11534– 009–0053–5.
[8] K. Urbanowski, Eur. Phys. J. D 54, 25 (2009).
[9] K.M. Sluis, E.A. Gislason, Phys. Rev. A 43, 4581 (1991).
[10] Handbook of Mathematical Functions, Natl. Bur. Stand. Appl. Math. Ser. No 55, eds. M. Abramowitz, I.A. Stegun (U.S. GPO, Washington, D.C., 1964).
[11] N.G. Kelkar, M. Nowakowski, K.P. Khemchadani, Phys. Rev. C 70, 024601 (2004).
[12] C. Amsler at al., Phys. Lett. B 667, 1 (2008).
[13] M. Nowakowski, N.G. Kelkar, Nishiharima 2004, Penataquark – Proceedings of International Workshop on PENATAQUARK 04, Spring – 8, Hyogo, Japan, 23-24 July 2004,
pp. 182-189; arXiv: hep–ph/0411317.
[14] M. Nowakowski, N.G. Kelkar, AIP Conf. Proc. 1030, 250- 255 (2008); ArXiv:0807.5103.
An effect generated by the nonexponential behavior of the survival amplitude of an unstable state in the long time region is considered. We find that the instantaneous energy of the unstable state for a large class of models of unstable states tends to the minimal energy of the system Emin as t → ∞ which is much smaller than the energy of this state for t of the order of the lifetime of the considered state. Analyzing the transition time region between the exponential and non-exponential form of the survival amplitude, we find that the instantaneous energy of the considered unstable state can take large values, much larger than the energy of this state for t from the exponential time region. Taking into account results obtained for a considered model, it is hypothesized that this purely quantum mechanical effect may be responsible for the properties of broad resonances such as σ meson as well as having astrophysical and cosmological consequences.
Key words:
References:
[1] S. Krylov, V.A. Fock, Zh. Eksp. Teor. Fiz. 17, 93 (1947).
[2] L. Fonda, G.C. Ghirardii, A. Rimini, Rep. on Prog. in Phys. 41, 587 (1978).
[3] L.A. Khalfin, Zh. Eksp. Teor. Fiz. 33, 1371 (1957), [Sov. Phys. – JETP 6, 1053 (1958)].
[4] R.E.A.C. Paley, N. Wiener, Fourier transforms in the complex domain. American Mathematical Society, New York (1934).
[5] C. Rothe, S.I. Hintschich, A.P. Monkman, Phys. Rev. Lett. 96, 163601 (2006).
[6] K. Urbanowski, Phys. Rev. A 50, 2847 (1994).
[7] K. Urbanowski, Cent. Eur. J. Phys. 7 (2009), DOI:10.2478/s11534– 009–0053–5.
[8] K. Urbanowski, Eur. Phys. J. D 54, 25 (2009).
[9] K.M. Sluis, E.A. Gislason, Phys. Rev. A 43, 4581 (1991).
[10] Handbook of Mathematical Functions, Natl. Bur. Stand. Appl. Math. Ser. No 55, eds. M. Abramowitz, I.A. Stegun (U.S. GPO, Washington, D.C., 1964).
[11] N.G. Kelkar, M. Nowakowski, K.P. Khemchadani, Phys. Rev. C 70, 024601 (2004).
[12] C. Amsler at al., Phys. Lett. B 667, 1 (2008).
[13] M. Nowakowski, N.G. Kelkar, Nishiharima 2004, Penataquark – Proceedings of International Workshop on PENATAQUARK 04, Spring – 8, Hyogo, Japan, 23-24 July 2004,
pp. 182-189; arXiv: hep–ph/0411317.
[14] M. Nowakowski, N.G. Kelkar, AIP Conf. Proc. 1030, 250- 255 (2008); ArXiv:0807.5103.
