Non-equilibrium phase transition in relativistic nuclear collisions: Importance of the equation of state

Within the context of relativistic nuclear collisions aimed at exploring hot and baryon-dense matter, we investigate how the general features of the expansion dynamics, as well as a number of specific observables, depend on the equation of state used in dynamical simulations of the non-equilibrium confinement phase transition.

Figure 1

Illustration of the equation of state of the HQ model: The pressure $p$ as a function of the net baryon density $\rho$ at the fixed temperature $T=100$ MeV (solid curve) and the corresponding Maxwell construction (dashed line). The middle (red [gray]) shaded area shows the mechanically unstable density region while the adjacent (blue [gray]) shaded areas show the metastable regions (in which matter is mechanically stable but thermodynamically unstable).

Figure 2

Illustration of the equation of state of the PQM model: The pressure $p$ as a function of the net baryon density $\rho$ at the fixed temperature $T=100$ MeV (solid curve) and the corresponding Maxwell construction (dashed line). The middle (red [gray]) shaded area shows the mechanically unstable density region while the adjacent (blue [gray]) shaded areas show the metastable regions (in which matter is mechanically stable but thermodynamically unstable).

Figure 3

The PQM equation of state $p(T,\rho )$: The pressure a function of both temperature and net baryon density. The phase-coexistence boundary is delineated (dashed path) and the plane of zero pressure is shown (red [gray]), making it easier to see where the pressure is negative.

Figure 4

The pseudocritical pressure as a function of the temperature, $p_{\mathrm{pc}}\left(T\right)$, for both the HQ (blue [gray] dashed curve with squares) and the PQM model (black curves) models. The black dashed line with open circles shows the result of the PQM model with finite quark vector coupling. On a scale magnified by a factor of 50, the PQM results (gray) are compared with the nuclear liquid-gas transition (which displays the familiar liquid-gas phase transition).

Figure 5

(a) Initial net baryon density distribution in the $x$$y$ plane. The initial state is constructed to lie just above the unstable region of the PQM equation of state. (b) Net baryon density distribution in the $x$$y$ plane after $160\mathrm{fm}/c$ evolution with the PQM equation of state that has an unstable region. The clusters of high baryon density are clearly visible.

Figure 6

The net baryon density in the $xy$ plane, $\rho (x,y,0,t)$, after $t=2\mathrm{fm}/c$ (a) and $t=10\mathrm{fm}/c$ (b), as obtained with the unstable HQ EoS: Clumps of dense quark matter are formed at early times (a) but they disappear after further evolution (b).

Figure 7

The fifth density moment [see Eq. (21)], normalized to its initial value, as a function of time for the HQ (solid) and the PQM (dashed) EoS. In each case, the upper curve (red [gray]) depicts results obtained with the unstable EoS, while the lower curve (black) has been obtained with the corresponding Maxwell partner EoS.

Figure 8

The ratios of the $A=5$ and $A=8$ nuclei over the deuteron yield as functions of time. For simplicity, the degeneracy factors for $A=8$, $A=5$, and $A=2$ have been set to equal values. Shown are results for the HQ equation of state with an unstable region (solid lines) and with a Maxwell construction (dashed lines).

Figure 9

The position-space two-baryon angular correlation strength $V_n^{\mathrm{pos}}$ for various values of $n$ as obtained with the HQ (circles) and PQM (squares) EoS. The results obtained with an unstable EoS (solid) are contrasted with those employing the Maxwell partner (open).

Figure 10

The momentum-space two-baryon angular correlation strength $V_n^{\mathrm{mom}}$ for various values of $n$ as obtained with the HQ (circles) and PQM (squares) EoS. The results obtained with an unstable EoS (solid) are contrasted with those employing the Maxwell partner (open).