  We consider the particle creation process associated with a quantum field
\chi in a time-dependent, homogeneous and isotropic, classical background. It
is shown that the field square \chi^2, the energy density and the pressure of
the created particles have large fluctuations comparable to their vacuum
expectation values. Possible effects of these fluctuations on the reheating
process after inflation are discussed. After determining the correlation length
of the fluctuations in two different models, corresponding to the decay in the
parametric resonance regime and in the perturbation theory, it is found that
these fluctuations should be taken into account in the final thermalization
process, in the back-reaction effects and when the formation of primordial
black holes is considered. In both models, by comparing quantum and thermal
fluctuations with each other it is observed that very quick thermalization
after the complete inflaton decay is not always possible even when the
interaction rates are large. On the other hand, when the back-reaction effects
are included during the preheating stage, the coherence of the inflaton
oscillations is shown to be lost because of the fluctuations in \chi^2.
Finally, we note that a large fluctuation in the energy density may cause a
black hole to form and we determine the fraction of total energy density that
goes into such primordial black holes in the model of preheating we consider.
