  We study the non-equilibrium condensation process in a holographic
superconductor with nonlinear corrections to the U(1) gauge field. We start
with an asymptotic Anti-de-Sitter(AdS) black hole against a complex scalar
perturbation at the initial time, and solve the dynamics of the gravitational
systems in the bulk. When the black hole temperature T is smaller than a
critical value Tc, the scalar perturbation grows exponentially till saturation,
the final state of spacetime approaches to a hairy black hole. In the bulk
theory, we find the clue of the influence of nonlinear corrections in the gauge
field on the process of the scalar field condensation. We show that the bulk
dynamics in the non-equilibrium process is completely consistent with the
observations on the boundary order parameter. Furthermore we examine the time
evolution of horizons in the bulk non-equilibrium transformation process from
the bald AdS black hole to the AdS hairy hole. Both the evolution of apparent
and event horizons show that the original AdS black hole configuration requires
more time to finish the transformation to become a hairy black hole if there is
nonlinear correction to the electromagnetic field. We generalize our
non-equilibrium discussions to the holographic entanglement entropy and find
that the holographic entanglement entropy can give us further understanding of
the influence of the nonlinearity in the gauge field on the scalar
condensation. In our analysis, we also compare the effect of different models
on the corrections to the gauge field on the formation of holographic
superconductor.
