Shear Viscosities from the Chapman-Enskog and the Relaxation Time Approaches

TL;DR

This paper compares shear viscosity calculations from Chapman-Enskog and relaxation time methods across various gas models, highlighting the importance of cross section energy dependence and advocating for quantum molecular dynamics validation.

Contribution

It provides a detailed quantitative comparison of shear viscosity results from two methods for different gas models, emphasizing the impact of differential cross section energy dependence.

Findings

Agreement depends on the energy dependence of cross sections.

Quantum molecular dynamics simulations are needed for validation.

Cross section choice critically affects shear viscosity calculations.

Abstract

The interpretation of the measured elliptic and higher order collective flows in heavy-ion collisions in terms of viscous hydrodynamics depends sensitively on the ratio of shear viscosity to entropy density. Here we perform a quantitative comparison between the results of shear viscosities from the Chapman-Enskog and relaxation time methods for selected test cases with specified elastic differential cross sections: (i) The non-relativistic, relativistic and ultra-relativistic hard sphere gas with angle and energy independent differential cross section (ii) The Maxwell gas, (iii) chiral pions and (iv) massive pions for which the differential elastic cross section is taken from experiments. Our quantitative results reveal that (i) the extent of agreement (or disagreement) depends sensitively on the energy dependence of the differential cross sections employed, and (ii) stress the need to perform quantum molecular dynamical (URQMD) simulations that employ Green-Kubo techniques with similar cross sections to validate the codes employed and to test the accuracy of other methods.