Abstract
The Krylov-Fock expression of non-decay (or survival) probability, which allows to evaluate the deviations from the exponential decay law (nowadays well established experimentally), is more informative as it readily provides the distribution function for the lifetime as a random quantity. Guided by the well established formalism for describing nuclear alpha decay, we use this distribution function to figure out the mean value of lifetime and its fluctuation rate. This theoretical framework is of considerable interest inasmuch as it allows an experimental verification. Next, we apply the Krylov-Fock approach to the decay of a metastable state at a finite temperature in the framework of thermo-field dynamics. In contrast to the existing formalism, this approach shows the interference effect between the tunnelings from different metastable states as well as between the tunneling and the barrier hopping. This effect looks quite natural in the framework of consistent quantum mechanical description as a manifestation of the "double-slit experiment". In the end we discuss the field theory applications of the results obtained.
Highlights
The phenomenon of false vacuum decay plays an important role in evolution of the universe from its early beginnings to the present state [1,2]
We know that the temporal development of the decay of a metastable state manifests the presence of three regimes: initially decay is slower than exponential; comes the exponential decay, which for the long times is followed by the inverse power law [5,6,7,8]
After discussing the mean lifetime and its fluctuation rate, we address the decay of an unstable system at a finite temperature
Summary
The phenomenon of false vacuum decay plays an important role in evolution of the universe from its early beginnings to the present state [1,2]. We know that the temporal development of the decay of a metastable state manifests the presence of three regimes: initially decay is slower than exponential; comes the exponential decay, which for the long times is followed by the inverse power law [5,6,7,8] The existence of these three regimes appears to be a universal feature of the decay process.. The attempt to use ωðtÞ for a better estimate of the mean lifetime of a false vacuum was made a few years ago in [10,11] Their approach does not address the questions posed above but rather is aimed to extract the Γ factor that governs the decay at intermediate timescales.
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