  We study non-equilibrium order parameter dynamics of the non-linear sigma
model in the large $N$ limit, using Keldysh formalism. We provide a scheme for
obtaining stable numerical solutions of the Keldysh saddle point equations, and
use them to study the order parameter dynamics of the model either following a
ramp, or in the presence of a periodic drive. We find that the transient
dynamics of the order parameter in the presence of a periodic drive is
controlled by the drive frequency displaying the phenomenon of synchronization.
We also study the approach of the order parameter to its steady state value
following a ramp and find out the effective temperature of the steady state. We
chart out the steady state temperature of the ordered phase as a function of
ramp time and amplitude, and discuss the relation of our results to
experimentally realizable spin models.
