  Boltzmann equation plays important roles in particle cosmology in studying
the evolution of distribution functions (also called as occupation numbers) of
various particles. For the case of the decay of a scalar condensation $\phi$
into a pair of scalar particles (called $\chi$), we point out that the system
may not be well described by the Boltzmann equation when the occupation number
of $\chi$ becomes large even in the so-called narrow resonance regime. We study
the particle production including the possible enhancement due to a large
occupation number of the final state particle, known as the stimulated emission
or the parametric resonance. Based on the quantum field theory (QFT), we derive
a set of equations which directly govern the evolution of the distribution
function of $\chi$. Comparing the results of the QFT calculation and those from
the Boltzmann equation, we find non-agreements in some cases. In particular, in
the expanding Universe, the occupation number of $\chi$ based on the QFT may
differ by many orders of magnitude from that from the Boltzmann equation. We
also discuss a possible relation between the evolution equations based on the
QFT and the Boltzmann equation.
