Mean lifetime of a false vacuum in terms of the Krylov-Fock non-escape probability

TL;DR

This paper uses the Krylov-Fock formalism to analyze the lifetime distribution of false vacuum decay, including temperature effects and interference phenomena, with potential for experimental verification and applications in field theory.

Contribution

It introduces a novel application of the Krylov-Fock approach to false vacuum decay, incorporating temperature effects and interference, extending existing formalism.

Findings

Derived the mean lifetime and fluctuation rate of false vacuum decay.

Identified interference effects between tunneling pathways.

Discussed implications for quantum field theory applications.

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.