Dynamical scheme for hadronization with first-order phase transition

We present a dynamical scheme for hadronization with first-order confinement phase transition. The thermodynamical conditions of phase equilibrium, the fluid velocity profile, and the dissipative effect determine the macroscopic changes of the parton volume and the corresponding hadron volume during the phase transition. The macroscopic volume changes are the basis for building up a dynamical scheme by considering microscopic transition processes from partons to hadrons and backwards. The established scheme is proved by comparing the numerical results with the analytical solutions in the case of a one-dimensional expansion of a dissipative fluid with Bjorken boost invariance. The comparisons show almost perfect agreements, which demonstrate the applicability of the introduced scheme.

Figure 1

The time evolution of the number and kinetic energy density and the temperature of gluons from ${\tau }_0=0.5\text{fm}/\mathrm{c}$ to the time shortly after ${\tau }_c=1.4386\text{fm}/\mathrm{c}$. The numerical results are depicted by solid curves (in black), while the analytical solutions are shown by the dashed curves (in red). The dotted curves (in blue) correspond to the shift of the analytical curves down to meet the values of $e_g$ and $T_g$ at ${\tau }_c$.

Figure 2

The time evolution of the gluon fraction. The solid curve (in black) depicts the numerical result, while the dashed curve (in red) depicts the expected function.

Figure 3

The time evolution of the mean transition cross sections and the factor $x$.

Figure 4

The time evolution of the number and the kinetic energy density. The black (red) curves are for gluons (pions). The dashed lines depict the values at ${\tau }_c$. From ${\tau }_e=8.055\text{fm}/\mathrm{c}$, the densities of gluons are zero (not plotted).

Figure 5

Same as Fig. 4. From top to bottom: The time evolution of the pressure, the temperature, the chemical potential to the temperature ratio, and the entropy density.

Figure 6

The time evolution of the total number, energy, and entropy density. The solid curves (in black) depict the numerical densities, while the dashed curves (in red) depict the analytical solutions.

Figure 7

Same as Fig. 6, but for the total entropy per space-time rapidity per transverse area.