Role of quantum fluctuations in a system with strong fields: Onset of hydrodynamical flow

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 Φ4 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 the quantum system and the extension of our results to a gauge theory.