Spinodal Decomposition and the Deconfining Phase Transition

Lattice gauge theory investigations of the deconfining phase transitions have mainly been limited to equilibrium studies (an exception is the work by Miller and Ogilvie [1]). The equilibrium transition with two massless quarks is likely second order and it becomes a crossover with two light quarks (and the heavier strange quark) [2]. In nature the finite temperature phase transition is governed by temperature driven dynamics. Early universe: We have a slow cooling process (10−5−10−6 >> 10−23 s). Most likely, the effects of the dynamics are negligible and no signals of the transition are observable nowadays. Heavy ion collisions – Bjorken’s [3] standard scenario: In the center of mass frame the incident nuclei are Lorentz contracted into pancake shapes. They pass through each other and leave behind a region of hot vacuum. The heating is presumably not slow on the relaxation time scale, but usually considered as a quench, i.e., an instantaneous process. Subsequently, the cooling is not much slower than the scale of 10−23 s. Quenching is a process in which the temperature in the symmetric phase below Tc is raised instantaneously to a temperature in the broken phase above Tc. Quenching has been much stud∗This work was in part supported by the US Department of Energy under contract DE-FG02-97ER41022. ied in condensed matter physics. One finds that the dynamics of long-wave modes groups theories into dynamical universality classes described by the same equations of motion. Correlated domains emerge and grow with time in such a way that the correlation function of a generic field φ has the simple scaling form g(~r, ~r ′, t) = 〈φ(~r, t)φ(~r ′, t)〉 (1) = f(|~r − ~r ′|/L(t)), L(t) ∼ t