Transport coefficients of causal dissipative relativistic hydrodynamics in quenched lattice simulations

TL;DR

This paper investigates the transport coefficients of causal dissipative relativistic hydrodynamics using quenched lattice simulations, focusing on the shear viscosity and relaxation time ratio in SU(3) gauge theory across a range of temperatures.

Contribution

It introduces a lattice-based method to compute the ratio of shear viscosity to relaxation time using static correlation functions in CDR.

Findings

The ratio of shear viscosity to relaxation time is obtained from lattice simulations.

Simulations cover temperatures from half to 1.8 times the critical temperature.

The method connects transport coefficients to static correlation functions in lattice QCD.

Abstract

Transport coefficients of causal dissipative relativistic fluid dynamics (CDR) are studied in quenched lattice simulations. CDR describes the behavior of relativistic non-Newtonian fluids in which the relaxation time appears as a new transport coefficient besides the shear and bulk viscosities. It was recently shown that these coefficients can be given by the temporal-correlation functions of the energy-momentum tensors as in the case of the Green-Kubo-Nakano formula. By using the new formula in CDR, we study the transport coefficients with lattice simulations in pure SU(3) gauge theory. After defining the energy-momentum tensor on the lattice, we extract a ratio of the shear viscosity to the relaxation time which is given only in terms of the static correlation functions. The simulations are performed on $24^3 \times 4$--16 lattices with $\beta_{_{\rm LAT}} = 6.0$, which corresponds to the temperature range of $0.5 \simle T/T_c \simle 1.8$, where $T_c$ is the critical temperature.