  We use the semi-classical approach to study the non-equilibrium dynamics of
the O(3) non-linear sigma model. For a class of quenches defined in the text,
we obtain the order parameter dynamical correlator in the thermodynamic limit.
In particular we predict quench-dependent relaxation times and correlation
lengths. The approach developed for the O(3) non-linear sigma model can also be
applied to the transverse field Ising chain, where the semi-classical results
can be directly compared to both the exact and the numerical ones, revealing
the limits of the method.
