  We investigate the non-equilibrium dynamics of a class of isolated
one-dimensional systems possessing two degenerate ground states, initialized in
a low-energy symmetric phase. We report the emergence of a time-scale
separation between fast (radiation) and slow (kink or domain wall) degrees of
freedom. We find a universal long-time dynamics, largely independent of the
microscopic details of the system, in which the kinks control the relaxation of
relevant observables and correlations. The resulting late-time dynamics can be
described by a set of phenomenological equations, which yield results in
excellent agreement with the numerical tests.
