  Taking into account the effect of self-interaction, the dynamics of the
quantum fluctuations of the inflaton field with $\lambda\phi^4$ potential is
studied in detail. We find that the self interaction efficiently drives the
initial pure state into a mixed one, which can be understood as a statistical
ensemble. Further, the expectation value of the squared field operator is found
to be converted into the variance of this statistical ensemble without giving
any significant change in its amplitude. These results verify the ansatz of the
quantum-to-classical transition that has been assumed in the standard
evaluation of the amplitude of the primordial fluctuations of the universe.
