Systematic errors in transport calculations of shear viscosity using the Green-Kubo formalism

TL;DR

This paper examines the use of the Green-Kubo formalism for calculating shear viscosity, identifying systematic errors and proposing an optimal fitting method for auto-correlation functions, applied to a hadron gas.

Contribution

It provides a reproducible framework and improved fitting procedure for shear viscosity calculations using the Green-Kubo formalism, addressing limitations in existing methods.

Findings

Fitting the auto-correlation function with fixed intercept improves accuracy.

The method is applicable to systems with constant and energy-dependent cross-sections.

Applied to a hadron gas, the formalism yields the shear viscosity to entropy ratio.

Abstract

The purpose of this study is to provide a reproducible framework in the use of the Green-Kubo formalism to extract transport coefficients. More specifically, in the case of shear viscosity, we investigate the limitations and technical details of fitting the auto-correlation function to a decaying exponential. This fitting procedure is found to be applicable for systems interacting both through constant and energy-dependent cross-sections, although this is only true for sufficiently dilute systems in the latter case. We find that the optimal fit technique consists in simultaneously fixing the intercept of the correlation function and use a fitting interval constrained by the relative error on the correlation function. The formalism is then applied to the full hadron gas, for which we obtain the shear viscosity to entropy ratio.