By employing the time-dependent approach, we investigate a quantum tunneling decay of many-particle systems. We apply it to a schematic one-dimensional three-body model with a heavy-core nucleus and two valence protons. We calculate the decay width for two-proton emission from the survival probability, which well obeys the exponential decay law after a sufficient time. The effect of the correlation between the two emitted protons is also studied by observing the time evolution of the two-particle density distribution. It is shown that the pairing correlation significantly enhances the probability for the simultaneous diproton decay.By employing the time-dependent approach, we investigate a quantum tunneling decay of many-particle systems. We apply it to a schematic one-dimensional three-body model with a heavy-core nucleus and two valence protons. We calculate the decay width for two-proton emission from the survival probability, which well obeys the exponential decay law after a sufficient time. The effect of the correlation between the two emitted protons is also studied by observing the time evolution of the two-particle density distribution. It is shown that the pairing correlation significantly enhances the probability for the simultaneous diproton decay.

arXiv:1207.1540Physical Review COct 1, 201228 citations

Non-Markovian Quantum Decay in Complex Environments: A Hyperstatistical Approach

Nicola Fabiano

The exponential decay of an unstable quantum state, as described by standard Markovian theories such as Fermi's Golden Rule, assumes a simple, structureless environment. However, in complex environments characterized by disorder, long-range interactions, or strong fluctuations, local decay rates fluctuate, leading to non-Markovian dynamics and power-law ``long-time tails.'' In this paper, we apply the recently proposed \textit{hyperstatistics} framework to the problem of quantum decay in such complex environments. By considering a $γ$ -distribution of local decay rates across mesoscopic domains, we derive a macroscopic survival probability governed by a $q$ -exponential function. We then use the $q$ -generalized Gamma function, defined via the Mellin transform of the $q$ -exponential, to calculate the moments of the decay-time distribution. We show that the mean quantum lifetime is $\langle t\rangle = \int_0^\infty P(t)\,dt= [\langleΓ\rangle(2-q)]^{-1},$ and is therefore finite for $q<2$ . The convergence of the second moment, and hence of the lifetime variance, instead requires the stricter condition $q<3/2$ . These results provide a refined physical interpretation: for $1<q<3/2$ both the mean lifetime and its variance are finite; for $3/2\le q<2$ the mean lifetime remains finite but lifetime fluctuations become infinitely broad; and for $q\ge2$ the mean lifetime itself diverges, corresponding to a truly trapped, localized, or Griffiths-like regime.The exponential decay of an unstable quantum state, as described by standard Markovian theories such as Fermi's Golden Rule, assumes a simple, structureless environment. However, in complex environments characterized by disorder, long-range interactions, or strong fluctuations, local decay rates fluctuate, leading to non-Markovian dynamics and power-law ``long-time tails.'' In this paper, we apply the recently proposed \textit{hyperstatistics} framework to the problem of quantum decay in such complex environments. By considering a $γ$-distribution of local decay rates across mesoscopic domains, we derive a macroscopic survival probability governed by a $q$-exponential function. We then use the $q$-generalized Gamma function, defined via the Mellin transform of the $q$-exponential, to calculate the moments of the decay-time distribution. We show that the mean quantum lifetime is $\langle t\rangle = \int_0^\infty P(t)\,dt= [\langleΓ\rangle(2-q)]^{-1},$ and is therefore finite for $q<2$. The convergence of the second moment, and hence of the lifetime variance, instead requires the stricter condition $q<3/2$. These results provide a refined physical interpretation: for $1<q<3/2$ both the mean lifetime and its variance are finite; for $3/2\le q<2$ the mean lifetime remains finite but lifetime fluctuations become infinitely broad; and for $q\ge2$ the mean lifetime itself diverges, corresponding to a truly trapped, localized, or Griffiths-like regime.

quant-pharXiv:2609.22190Sep 1, 20260 citations

Long Time Deviations from the Exponential Decay Law: Possible Observational Effects

K. Urbanowski, Jarosław Piskorski

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 E min 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: decay law, non exponential decayAn 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 E min 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: decay law, non exponential decay

Computational Methods in Science and TechnologyJan 1, 20101 citation

γ

-distribution of local decay rates across mesoscopic domains, we derive a macroscopic survival probability governed by a

q

-exponential function. We then use the

q

-generalized Gamma function, defined via the Mellin transform of the

q

-exponential, to calculate the moments of the decay-time distribution. We show that the mean quantum lifetime is

\langle t\rangle = \int_0^\infty P(t)\,dt= [\langleΓ\rangle(2-q)]^{-1},

and is therefore finite for

q<2

. The convergence of the second moment, and hence of the lifetime variance, instead requires the stricter condition

q<3/2

. These results provide a refined physical interpretation: for

1<q<3/2

both the mean lifetime and its variance are finite; for

3/2\le q<2

the mean lifetime remains finite but lifetime fluctuations become infinitely broad; and for

q\ge2

the mean lifetime itself diverges, corresponding to a truly trapped, localized, or Griffiths-like regime.