Non-equilibrium condensation process in a holographic superconductor

Abstract

We study the non-equilibrium condensation process in a holographic superconductor. When the temperature T is smaller than a critical temperature T c , there are two black hole solutions, the Reissner-Nordström-AdS black hole and a black hole with a scalar hair. In the boundary theory, they can be regarded as the supercooled normal phase and the superconducting phase, respectively. We consider perturbations on supercooled Reissner-Nordström-AdS black holes and study their non-linear time evolution to know about physical phenomena associated with rapidly-cooled superconductors. We find that, for T < T c , the initial perturbations grow exponentially and, eventually, spacetimes approach the hairy black holes. We also clarify how the relaxation process from a far-from-equilibrium state proceeds in the boundary theory by observing the time dependence of the superconducting order parameter. Finally, we study the time evolution of event and apparent horizons and discuss their correspondence with the entropy of the boundary theory. Our result gives a first step toward the holographic understanding of the non-equilibrium process in superconductors.

Non-equilibrium condensation process in holographic superconductor with nonlinear electrodynamics

“…To answer these questions, we cannot just look at the dual operator on the AdS boundary in an equilibrium system, we need to concentrate on the non-equilibrium dynamics in the bulk gravitational configurations to disclose the process of addressing the scalar hair onto the bald AdS black hole. In [34], the non-equilibrium process in the bulk Einstein-Maxwell-scalar background has been studied. It was observed that during the time evolution, the initial scalar perturbation in the bulk spacetime first moves towards the AdS boundary, it is then bounced back by the AdS wall, grows and moves towards the bald black hole.…”

“…Subsequently this perturbation falls onto the bald hole and accumulates there and finally makes the bald black hole become hairy. The time evolutions of the event and apparent horizons of the bulk black hole in the AdS bulk were disclosed in [34]. Employing the AdS/CFT duality, the authors related the observed properties in the AdS bulk to the boundary CFT, and further they displayed the time dependence of the superconducting order parameter in the holographic superconductor.…”

“…As b → 0, both kinds of the nonlinear electromagnetic fields reduce to the Maxwell field, L(F ) → −F 2 /4, and the model action (2.1) reduces to that in [34].…”

“…In the limit b → 0, F 2 → 1, the system and the equations of motion go back to those described in [34]. In our numerical computation, we will mainly consider the first four equations, eqs.…”

“…With this method, we can reproduce the phase transition temperature in [34]. The critical temperatures of black holes with nonlinear electromagnetic field in the forms BINE and LNE are listed in table 1.…”