Shear viscosity in microscopic calculations of A+A collisions at energies available at the Nuclotron-based Ion Collider fAcility (NICA)

Abstract

Time evolution of shear viscosity $\eta$, entropy density $s$, and their ratio $\eta / s$ in the central area of central gold-gold collisions at NICA energy range is studied within the UrQMD transport model. The extracted values of energy density, net baryon density and net strangeness density are used as input to (i) statistical model of ideal hadron gas to define temperature, baryo-chemical potential and strangeness chemical potential, and to (ii) UrQMD box with periodic boundary conditions to study the relaxation process of highly excited matter. During the relaxation stage, the shear viscosity is determined in the framework of Green-Kubo approach. The procedure is performed for each of 20 time slices, corresponding to conditions in the central area of the fireball at times from 1~fm/$c$ to 20~fm/$c$. For all tested energies the ratio $\eta / s$ reaches minimum, $\left( \eta/s \right)_{min} \approx 0.3$ at $t \approx 5$~fm/$c$. Then it increases up to the late stages of the system evolution. This rise is accompanied by the drop of both, temperature and strangeness chemical potential, and increase of baryo-chemical potential.