Nonequilibrium condensation process of a holographic superconductor in de Rham-Gabadadze-Tolley massive gravity

Abstract

We study the nonequilibrium condensation process of a holographic s-wave superconductor constructed in the background of de Rham-Gabadadze-Tolley massive gravity theory. When the temperature is lower than a critical value, this model has an asymptotic anti–de Sitter (AdS) bald black hole solution and a black hole solution with nontrivial scalar hair, which can be identified as the normal phase and the superconducting phase in boundary theory, respectively. We consider Gaussian-type perturbation of a scalar field on the background of bald AdS black hole spacetime, and we numerically solve the full nonlinear dynamics of the gravitational system in the bulk. With the full time-dependent solution of the gravitational system, we observe a dynamical process from the perturbed bald AdS black hole to the black hole with scalar hair. According to holographic duality, this process can be regarded as the dynamical phase transition process from normal state to s-wave superconducting state in boundary theory. We also investigate the time evolution of the superconducting condensate operator and clarify how the condensation process from the far-from-equilibrium state proceeds in boundary theory. By fitting the evolution data of the superconducting order parameter at early time, we show that the initial nonequilibrium condensation process can be predicted by linear quasinormal modes of scalar field perturbation on the background of the bald AdS black hole. Finally, we study the time evolution of the event and apparent horizons.

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