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In this proceeding, we investigate the dynamical evolution of the σ field with a trajectory across the 1st order phase transition boundary, using the Langevin equation from the linear sigma model. We find the high order cumulants of the σ field are largely enhanced during the dynamical evolution, compared with the equilibrium values, due to the supercooling effect of the first order phase transition.
In this proceeding, we study the dynamical evolution of the sigma field within the framework of Langevin dynamics. We find that, as the system evolves in the critical regime, the magnitudes and signs of the cumulants of sigma field, C3 and C4, can be dramatically different from the equilibrated ones due to the memory effects near Tc. For the dynamical evolution across the 1st order phase transition boundary, the supercooling effect leads the sigma field to be widely distributed in the thermodynamical potential, which largely enhances the cumulants C3, C4, correspondingly.