\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
The dependence of the rescaled equilibration time on different parameters for field theories with a holographic dual has been investigated in this paper. We consider field theories with nonzero chemical potential at finite temperature which are dual to asymptotically AdS charged black hole. We consider a dynamical probe scalar operator where its dynamics is due to a time-dependent source (quantum quench) or out-of-equilibrium initial condition in field theory with fixed or varying temperature and chemical potential. We observe that the behavior of the scalar operator equilibration time with respect to temperature or chemical potential can not be predicted by merely field theory parameters and depends on how fast the energy is injected into the system. We also observe that the rescaled equilibration time as one approaches the critical point enhances and acquires an infinite slope though its value remains finite. We show that for fast quenches the dynamical critical exponent is the same as the one reported for quasi-normal modes in the same background. However for slow quenches the dynamical critical exponent picks up a different value.
\end{document}