  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.
