Dissipation and Fluctuation at the Chiral Phase Transition

Utilizing the Langevin equation for the linear model we investigate the interplay of friction and white noise on the evolution and stability of collective pionic fields in energetic heavy ion collisions. We find that the smaller the volume, the more stable transverse (pionic) fluctuations become on a homogeneous disoriented chiral field background (the average transverse mass 〈mₓ^2〉 increases). On the other hand the variance of mₓ^2 increases even more, so for a system thermalized in an initial volume of 10fm^3 about 96% and even in 1000fm^3 about 60% of the individual trajectories enter into unstable regions (mₓ^2<0) for a while during a rapid one-dimensional expansion (₀0ex{0ex}=0ex{0ex}10ex{0ex}fm/c). In contrast the ensemble averaged solution in this case remains stable. This result supports the idea of looking for disoriented chiral condensate (DCC) formation in individual events.