Non-perturbative Corrections to Particle Production from Coherent
  Oscillation
  We investigate particle production from coherent oscillation by using the
method based on the Bogolyubov transformation. Especially, we study the case
when the amplitude of the oscillation and also the coupling constants with the
oscillating field are small in order to avoid the non-perturbative corrections
from the broad parametric resonance. We derive the expressions for the
distribution functions and the number densities of produced particles at the
leading order of coupling constant. It is, however, found that these results
fail to describe the exact particle production eventually due to the
non-perturbative effects even if the coupling constants are small. We then
introduce a simple method to handle with such corrections, i.e., the time
averaging method. It is shown that this method successfully provides the
evolution of the occupation numbers of the growing mode. Further, we point out
that the approximate results by this method satisfy the exact scaling
properties coming from the periodicity of the coherent oscillation.
