Nonperturbative Corrections to Particle Production from Coherent Oscillation

We investigate particle production from coherent oscillation using the method based on the Bogolyubov transformation. In particular, we study the case when the amplitude of the oscillation and also the coupling constants with the oscillating field are small to avoid the nonperturbative 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 nonperturbative effects even if the coupling constants are small. We then introduce a simple method of handling such corrections, i.e., the time averaging method. It is shown that this method can successfully provide the evolution of the occupation numbers of the growing mode. Furthermore, we point out that the approximate results obtained by this method satisfy the exact scaling properties coming from the periodicity of the coherent oscillation.