  In ultrafast experiments, an optical pump pulse often generates transient
domain walls of the order parameter in materials with spontaneous symmetry
breaking, due to either a finite penetration depth of the light on a
three-dimensional (3D) material, or a finite spot size on a two-dimensional
(2D) material. We clarify the decaying process of such a domain wall that is
caused by fluctuations of the order parameters. We study a generic system with
$U(1)$-symmetric order, and those with an additional weak $Z_2$
($U(1)$-symmetry-breaking) term, representing the charge-density-wave (CDW)
orders in recent experiments. The decay process comprises two non-trivial
stages. During the first stage, exponentially growing thermal fluctuations
convert the domain wall into an interface with randomly distributed topological
defects. In the second stage, the topological defects undergo a coarsening
dynamics within the interface. For a 2D interface in the 3D system, the
coarsening dynamics leads to a diffusive growth of the correlation length. For
a one-dimensional (1D) interface in the 2D system with the weak $Z_2$ term, the
correlation-length growth shows a crossover from diffusive to sub-diffusive
behavior. Our theory provides a fundamental physical picture for the dynamics
of pump-induced domain walls in ultrafast experiments.
