  The quantum dynamics of the symmetry broken \lambda (\Phi^2)^2 scalar field
theory in the presence of an homogeneous external field is investigated in the
large N limit. We consider an initial thermal state of temperature T for a
constant external field J. A subsequent sign flip of the external field, J to
-J, gives rise to an out of equilibrium nonperturbative quantum field dynamics.
We review here the dynamics for the symmetry broken lambda(\Phi^2)^2 scalar N
component field theory in the large N limit, with particular stress in the
comparison between the results when the initial temperature is zero and when it
is finite. The presence of a finite temperature modifies the dynamical
effective potential for the expectation value, and also makes that the
transition between the two regimes of the early dynamics occurs for lower
values of the external field. The two regimes are characterized by the presence
or absence of a temporal trapping close to the metastable equilibrium position
of the potential. In the cases when the trapping occurs it is shorter for
larger initial temperatures.
