Spinodal instabilities of baryon-rich quark matter in heavy ion collisions

Using the test-particle method to solve the transport equation derived from the Nambu-Jona-Lasino (NJL) model, we study how phase separation occurs in an expanding quark matter like that in a heavy ion collision. To test our method, we first investigate the growth rates of unstable modes of quark matter in a static cubic box and find them to agree with the analytical results that were previously obtained using the linear response theory. In this case, we also find the higher-order scaled density moments to increase with time and saturate at values significantly larger than one, which corresponds to a uniform density distribution, after the phase separation. The skewness of the quark number event-by-event distribution in a small sub-volume of the system is also found to increase, but this feature disappears if the sub-volume is large. For the expanding quark matter, two cases are considered with one using a blast-wave model for the initial conditions and the other using initial conditions from a mulple-phase transport (AMPT) model. In both cases, we find the expansion of the quark matter is slowed down by the presence of a first-order phase transition. Also, density clumps appear in the system and the momentum distribution of partons becomes anisotropic , which can be characterized by large scaled density moments and non-vanishing anisotropic elliptic and quadrupolar flows, respectively. The large density fluctuations further lead to an enhancement in the dilepton yield. In the case with the AMPT initial conditions, the presence of a first-order phase transition also results in a narrower rapidity distribution of partons after their freeze out. These effects of density fluctuations can be regarded as possible signals for a first-order phase transition that occurs in the baryon-rich quark matter formed in relativistic heavy ion collisions.