Non-equilibrium Condensation Process in a Holographic Superconductor

TL;DR

This paper investigates the non-equilibrium dynamics of holographic superconductors by analyzing black hole solutions and their evolution, revealing how superconducting states emerge from perturbations and relate to entropy changes.

Contribution

It provides a detailed study of the time evolution of non-equilibrium processes in holographic superconductors, linking gravitational dynamics to boundary theory phenomena.

Findings

Perturbations grow exponentially below T_c

Spacetimes evolve towards hairy black holes

Horizon dynamics relate to entropy changes

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-Nordstrom-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-Nordstrom-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.