Thermodynamic properties and bulk viscosity near phase transition in the Z(2) and O(4) models

We investigate the thermodynamic properties including equation of state, the trace anomaly, the sound velocity and the specific heat, as well as transport properties like bulk viscosity in the Z(2) and O(4) models in the Hartree approximation of Cornwall-Jackiw-Tomboulis (CJT) formalism. We study these properties in different cases, e.g. first order phase transition, second order phase transition, crossover and the case without phase transition, and discuss the correlation between the bulk viscosity and the thermodynamic properties of the system. We find that the bulk viscosity over entropy density ratio exhibits an upward cusp at the second order phase transition, and a sharp peak at the 1st order phase transition. However, this peak becomes smooth or disappears in the case of crossover. This indicates that at RHIC, where there is no real phase transition and the system experiences a crossover, the bulk viscosity over entropy density might be small, and it will not affect too much on hadronization. We also suggest that the bulk viscosity over entropy density ratio is a better quantity than the shear viscosity over entropy density ratio to locate the critical endpoint.Comment: 19 pages, 30 figures, 1 tabl

On Particle Production in Lead-Gold Collision and Azimuthal Anisotropy at Top SPS Energy

In a multisource thermal model, we analyze the dependence of elliptic flow v2 on the transverse momentum PT. The model results are compared with the data of π-, KS0, p, and Λ measured in Pb + Au collisions at top SPS energy, 17.3 GeV. It is found that the azimuthal anisotropy in the evolution process of high-energy collisions is correlated highly to the number of participant nucleons

Higher-order effects on the incompressibility of isospin asymmetric nuclear matter

Analytical expressions for the saturation density as well as the binding energy and incompressibility at the saturation density of asymmetric nuclear matter are given exactly up to 4th-order in the isospin asymmetry delta =(rho_n - rho_p)/rho using 11 characteristic parameters defined at the normal nuclear density rho_0. Using an isospin- and momentum-dependent modified Gogny (MDI) interaction and the SHF approach with 63 popular Skyrme interactions, we have systematically studied the isospin dependence of the saturation properties of asymmetric nuclear matter, particularly the incompressibility $K_{sat}(\delta )=K_{0}+K_{sat,2}\delta ^{2}+K_{sat,4}\delta ^{4}+O(\delta ^{6})$ at the saturation density. Our results show that the magnitude of the high-order $K_{sat,4}$ parameter is generally small compared to that of the K_{\sat,2} parameter. The latter essentially characterizes the isospin dependence of the incompressibility at the saturation density and can be expressed as $K_{sat,2}=K_{sym}-6L-\frac{J_{0}}{K_{0}}L$, Furthermore, we have constructed a phenomenological modified Skyrme-like (MSL) model which can reasonably describe the general properties of symmetric nuclear matter and the symmetry energy predicted by both the MDI model and the SHF approach. The results indicate that the high-order $J_{0}$ contribution to $K_{sat,2}$ generally cannot be neglected. In addition, it is found that there exists a nicely linear correlation between $K_{sym}$ and $L$ as well as between $J_{0}/K_{0}$ and $K_{0}$. These correlations together with the empirical constraints on $K_{0}$, $L$, $E_{sym}(\rho_{0})$ and the nucleon effective mass lead to an estimate of $K_{sat,2}=-370\pm 120$ MeV.Comment: 61 pages, 12 figures, 6 Tables. Title changed a little and results of several Skyrme interactions updated. Accepted version to appear in PR