Linear Langevin Equation of Critical Fluctuation in Chiral Phase Transition

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We derive the linear Langevin equation that describes the behavior of critical fluctuation above the critical temperature of the chiral phase transition in the Nambu-Jona-Lasinio model. The Langevin equation relaxes exhibiting oscillation and shows thermalization. The relaxation becomes slower as the system approaches the critical point(the critical slowing down). The time correlation function also calculated using the Langevin equation shows that there exists the same soft mode as the previous calculation in the linear response theory.