Evaluation of Israel-Stewart parameters in lattice gauge theory

TL;DR

This paper evaluates the ratios of viscosities to relaxation times in the Israel-Stewart hydrodynamic theory using lattice gauge theory, addressing causality issues in relativistic fluid dynamics.

Contribution

It provides a lattice gauge theory calculation of Israel-Stewart parameters, linking entropy constraints to viscosity and relaxation time ratios in quark-gluon plasma.

Findings

Ratios of viscosities to relaxation times are obtained from lattice simulations.

Results support the theoretical relations derived from entropy considerations.

Findings contribute to more accurate modeling of relativistic fluids in high-energy physics.

Abstract

Navier-Stokes equations are known as hydrodynamic equations which take account of effects of dissipations. There are, however, problems in the relativistic Navier-Stokes equations, i.e. the equations violate causality. Israel-Stewart equations, which evade the problems of Navier-Stokes equations by introducing new parameters, such as the relaxation times, have recently been used in describing the space-time evolution of the quark-gluon plasma produced in high energy heavy ion collisions. The viscosities and the relaxation times are related to each other by imposing entropy constraints on the system. According to Boltzmann-Einstein principle, the probability distribution of the fluctuation in the energy-momentum tensor is related to the entropy of the system. Applying this principle to the entropy in Israel-Stewart theory, one can obtain the ratios of the viscosities to the relaxation times. We evaluate the ratios of the viscosities to the relaxation times in SU(3) lattice gauge theory.