Evolution of critical correlations at the QCD phase transition

We investigate the evolution of the density-density correlations in the isoscalar critical condensate formed at the QCD critical point. The initial equilibrium state of the system is characterized by a fractal measure determining the distribution of isoscalar particles (sigmas) in configuration space. Non-equilibrium dynamics is induced through a sudden symmetry breaking leading gradually to the deformation of the initial fractal geometry. After constructing an ensemble of configurations describing the initial state of the isoscalar field we solve the equations of motion and show that remnants of the critical state and the associated fractal geometry survive for time scales larger than the time needed for the mass of the isoscalar particles to reach the two-pion threshold. This result is more transparent in an event-by-event analysis of the phenomenon. Thus, we conclude that the initial fractal properties can eventually be transferred to the observable pion-sector through the decay of the sigmas even in the case of a quench