Dynamically probing strongly-coupled field theories with critical point

TL;DR

This paper investigates how the equilibration time of strongly-coupled field theories with holographic duals depends on parameters like temperature and chemical potential, especially near critical points, revealing critical behavior and quench-dependent dynamics.

Contribution

It provides new insights into the dependence of equilibration times on energy injection rates and critical points in holographic field theories with chemical potential.

Findings

Rescaled equilibration time shorter in thermodynamically stable systems.

Equilibration time diverges with infinite slope near the critical point.

Dynamical critical exponent matches quasi-normal mode results for fast quenches.

Abstract

The dependence of the rescaled equilibration time on different parameters of the 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 holes. We examine 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 merely by field theory parameters and depends on how fast the energy is injected into the system. It is shown that in field theories with critical point the rescaled equilibration time is shorter for thermodynamically stable systems. 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, even though the system is far from equilibrium, 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.