  We present a detailed numerical study of the equilibrium and non-equilibrium
dynamics of the phase transition in the finite-temperature Abelian Higgs model.
Our simulations use classical equations of motion both with and without
hard-thermal-loop corrections, which take into account the leading quantum
effects. From the equilibrium real-time correlators, we determine the Landau
damping rate, the plasmon frequency and the plasmon damping rate. We also find
that, close to the phase transition, the static magnetic field correlator shows
power-law magnetic screening at long distances. The information about the
damping rates allows us to derive a quantitative prediction for the number
density of topological defects formed in a phase transition. We test this
prediction in a non-equilibrium simulation and show that the relevant time
scale for defect formation is given by the Landau damping rate.
