Meson excitation time as a probe of holographic critical point

We study the time evolution of expectation value of Wilson loop as a non-local observable in a strongly coupled field theory with a critical point at finite temperature and nonzero chemical potential, which is dual to an asymptotically AdS charged black hole via gauge/gravity duality. Due to inject of energy into the plasma, the temperature and a chemical potential increase to finite values and the plasma experiences an out-of-equilibrium process. By defining meson excitation time t${}_{ex}$ as a time at which the meson falls into the final excited state, we investigate the behavior of t${}_{ex}$ near the critical point as the system evolves towards the critical point. We observe that by increasing the interquark distance the dynamical critical exponent increases smoothly. Also, we obtain for slow quenches different values of the dynamical critical exponent, although for fast quenches our result for the dynamical critical exponent is in agreement with the one that is reported for studying the quasi-normal modes. Consequently, this indicates that in this model for fast quenches and small values of interquark distances the gauge invariant Wilson loop is a good non-local observable to probe the critical point.