Quantum rolling down out of equilibrium.

In a scalar field theory, when the tree level potential admits broken symmetry ground states, the quantum corrections to the static effective potential are complex. (The imaginary part is a consequence of an instability towards phase separation and the static effective potential is not a relevant quantity for understanding the dynamics). Instead, we study here the equations of motion obtained from the one loop effective action for slow rollover out of equilibrium. We considering the case in which a scalar field theory undergoes a rapid phase transition from Ti > Tc to Tf < Tc. We find that, for slow rollover initial conditions (the field near the maximum of the tree level potential), the process of phase separation controlled by unstable longwavelength fluctuations introduces dramatic corrections to the dynamical evolution of the field. We find that these effects slow the rollover even further thus delaying the phase transition, and increasing the time that the field spends near the ”false vacuum”. Moreover, when the initial value of the field is very close to zero, the dynamics becomes non-perturbative.