Holographic Equilibration under External Dynamical Electric Field

TL;DR

This paper investigates the equilibration dynamics of a strongly coupled gauge theory under a time-dependent electric field using holography, revealing universal behaviors and time ordering in the relaxation processes.

Contribution

It introduces a detailed analysis of equilibration times under external electric fields in holography, highlighting universal scaling laws and the persistence of static time ordering.

Findings

Universal behavior of re-scaled equilibration times.

Persistence of static time ordering in out-of-equilibrium processes.

Dependence of equilibration times on electric field and temperature ratios.

Abstract

The holographic equilibration of a far-from-equilibrium strongly coupled gauge theory is investigated. The dynamics of a probe D7-brane in an AdS-Vaidya background is studied in the presence of an external time-dependent electric field. Defining the equilibration times $t_{eq}^c$ and $t_{eq}^j$, at which condensation and current relax to their final equilibrated values, receptively, the smallness of transition time $k_M$ or $k_E$ is enough to observe a universal behaviour for re-scaled equilibration times $k_M k_E (t_{eq}^c)^{-2}$ and $k_M k_E (t_{eq}^j)^{-2}$. Moreover, regardless of the values for $k_M$ and $k_E$, $t_{eq}^c/t_{eq}^j$ also behaves universally for large enough value of the ratio of the final electric field to final temperature. Then a simple discussion of the static case reveals that $t_{eq}^c \leq t_{eq}^j$. For an out-of-equilibrium process, our numerical results show that, apart from the cases for which $k_E$ is small, the static time ordering persists.