  Quantum fluctuations are believed to play an important role in the
thermalization of classical fields in inflationary cosmology but their
relevance for isotropization/thermalization of the classical fields produced in
heavy ion collisions is not completely understood. We consider a scalar
$\phi^4$ toy model coupled to a strong external source, like in the Color Glass
Condensate description of the early time dynamics of ultrarelativistic heavy
ion collisions. The leading order classical evolution of the scalar fields is
significantly modified by the rapid growth of time-dependent quantum
fluctuations, necessitating an all order resummation of such "secular" terms.
We show that the resummed expressions cause the system to evolve in accordance
with ideal hydrodynamics. We comment briefly on the thermalization of our
quantum system and the extension of our results to a gauge theory.
