Abstract
We study the nonequilibrium condensation process of a holographic $p$-wave superconductor model, which is described by Einstein-Maxwell theory coupled with the charged complex vector field in asymptotic anti-de Sitter (AdS) spacetime. By solving the gravitational dynamics in the asymptotic AdS spacetime numerically, we obtain the full time dependent solution of the system, and observe a dynamical process from the perturbed Reissner-Nordstr\om-AdS black hole to the anisotropic black hole with vector hair when the initial black hole temperature is smaller than the critical temperature ${T}_{c}$. By holography, this nonlinear dynamical process is then dual to the phase transition process from a normal state to a $p$-wave superconducting state on the boundary theory. We also investigate the time evolution of the superconducting condensate operator and horizon area.
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