  Various aspects of time-dependent processes are studied within the large N
approximation of O(N) vector models in three dimensions. These include the
rolling of fields, the tunneling and decay of vacua. We present an exact
solution for the quantum conformal case and find a solution for more general
potentials when the total change of the value of the field is small.
Characteristic times are found to be shorter when the time dependence of the
field is taken into account in constructing the exact large N effective
potentials. We show that the different approximations yield the same answers in
the regions of the overlap of the validity. A numerical solution of this
potential reveals a tunneling in which the bubble that separates the true
vacuum from the false one is thick.
