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- W2894544492 abstract "Methods based on the use of Green's functions or the Jost functions and the Fock-Krylov method are apparently very different approaches to understand the time evolution of unstable states. We show that the two former methods are equivalent up to some constants and as an outcome find an analytic expression for the energy density of states in the Fock-Krylov amplitude in terms of the coefficients introduced in the Green's functions and the Jost functions methods. This model-independent density is further used to obtain an analytical expression for the survival amplitude and study its behaviour at large times. Using these expressions, we investigate the origin of the oscillatory behaviour of the decay law in the region of the transition from the exponential to the non-exponential at large times. With the objective to understand the failure of nuclear and particle physics experiments in observing the non-exponential decay law predicted by quantum mechanics for large times, we derive analytical formulae for the critical transition time, $t_c$, from the exponential to the inverse power law behaviour at large times. Evaluating $tau_c = Gamma t_c$ for some particle resonances and narrow nuclear states which have been tested experimentally to verify the exponential decay law, we conclude that the large time power law in particle and nuclear decay is hard to find experimentally." @default.
- W2894544492 created "2018-10-05" @default.
- W2894544492 creator A5006250156 @default.
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- W2894544492 date "2019-01-08" @default.
- W2894544492 modified "2023-09-27" @default.
- W2894544492 title "Quantum decay law: critical times and the equivalence of approaches" @default.
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- W2894544492 doi "https://doi.org/10.1088/1751-8121/aaf9f3" @default.
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