Hydrodynamical-model analysis of the (3+1)-dimensional cylindrically symmetric baryon-rich quark-gluon plasma with phase transition

We analyze numerically the space-time evolution of a baryon-rich quark-gluon plasma fluid by means of a hydrodynamical model which takes account of a net baryon-number conservation law. We first introduce a simple effective equation of state that gives QCD phase-transition-like behavior of thermodynamical quantities on the T-μ plane (here T is temperature and μ is the chemical potential for the net baryon number.) This equation of state is based on a semiphenomenological quantum Langevin equation. Numerically solving the hydrodynamical equation coupled with the net baryon-number current density conservation law using the model equation of state, we discuss in detail the space-time evolution of the thermodynamical quantities and the local four-velocity of a baryon-rich quark-gluon plasma fluid. Finally we apply our hydrodynamical model to the recent experimental results from the CERN NA35 S+S 200 GeV/A collisions and discuss the possible occurrence of a quark-gluon plasma phase.