Meson excitation time as a probe of holographic critical point

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