Holographic Equilibration under External Dynamical Electric Field

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.