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Boltzmann equation plays important roles in particle cosmology in studyingthe evolution of distribution functions (also called as occupation numbers) ofvarious 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 systemmay not be well described by the Boltzmann equation when the occupation numberof $\chi$ becomes large even in the so-called narrow resonance regime. We studythe particle production including the possible enhancement due to a largeoccupation number of the final state particle, known as the stimulated emissionor the parametric resonance. Based on the quantum field theory (QFT), we derivea set of equations which directly govern the evolution of the distributionfunction of $\chi$. Comparing the results of the QFT calculation and those fromthe Boltzmann equation, we find non-agreements in some cases. In particular, inthe expanding Universe, the occupation number of $\chi$ based on the QFT maydiffer by many orders of magnitude from that from the Boltzmann equation. Wealso discuss a possible relation between the evolution equations based on theQFT and the Boltzmann equation.

Particle Production from Oscillating Scalar Field and Consistency of Boltzmann Equation