Dynamical Condensation in a Holographic Superconductor Model with Anisotropy

TL;DR

This paper investigates the dynamical process of condensation in an anisotropic holographic superconductor model, revealing how anisotropy affects black hole evolution, condensate growth, and boundary pressure through numerical simulations and quasinormal mode analysis.

Contribution

It introduces a novel anisotropic holographic superconductor model with time-dependent analysis, extending isotropic studies to include anisotropic effects on condensation and relaxation dynamics.

Findings

Condensate exhibits exponential growth and saturation in anisotropic backgrounds.

Boundary pressure evolves nontrivially over time due to anisotropy.

Scalar quasinormal modes correlate with condensate relaxation times.

Abstract

We study dynamical condensation process in a holographic superconductor model with anisotropy. The time-dependent numerical solution is constructed for the Einstein-Maxwell-dilaton theory with complex scalar in asymptotic AdS spacetime. The introduction of dilaton field generates the anisotropy in boundary spatial directions. In analogy of isotropic case, we have two black hole solutions below certain critical temperature $T_c$, the anisotropic charged black hole with and without scalar hair, corresponding respectively to the supercooled normal phase and superconducting phase in the boundary theory. We observe a nonlinear evolution from a supercooled anisotropic black hole without scalar hair to a anisotropic hairy black hole. Via AdS/CFT correspondence, we extract time evolution of the condensate operator, which shows an exponential growth and subsequent saturation, similar to the isotropic case. Furthermore, we obtain a nontrivial time evolution of the boundary pressure, while in isotropic case it remains a constant. We also generalize quasinormal modes calculation to anisotropic black holes and shows scalar quasinormal modes match with relaxation time scale of the condensate operator. In addition, we present the final temperature and anisotropic pressure as functions of initial temperature and background anisotropy.