Green-Kubo formula for Boltzmann and Fermi-Dirac statistics

TL;DR

This paper introduces a new form of the Green-Kubo formula for calculating shear viscosity in nuclear matter, comparing it with traditional methods and the SLLOD algorithm across classical and non-classical regimes.

Contribution

The work presents a novel Green-Kubo formula form and compares its results with existing methods using quantum molecular dynamics and Boltzmann equations.

Findings

Traditional Green-Kubo overestimates shear viscosity in non-classical regimes.

New Green-Kubo form aligns with SLLOD results in classical limits.

Boltzmann-type equation yields lower shear viscosity than Green-Kubo methods.

Abstract

Shear viscosity of nuclear matter is extracted via the Green-Kubo formula and the Gaussian thermostated SLLOD algorithm (the shear rate method) in a periodic box by using an improved quantum molecular dynamic (ImQMD) model without mean field, also it is calculated by a Boltzmann-type equation. Here a new form of the Green-Kubo formula is put forward in the present work. For classical limit at nuclear matter densities of $0.4\rho_{0}$ and $1.0\rho_{0}$, shear viscosity by the traditional and new form of the Green-Kubo formula as well as the SLLOD algorithm are coincident with each other. However, for non-classical limit, shear viscosity by the traditional form of the Green-Kubo formula is higher than those obtained by the new form of the Green-Kubo formula as well as the SLLOD algorithm especially in low temperature region. In addition, shear viscosity from the Boltzmann-type equation is found to be less than that by the Green-Kubo method or the SLLOD algorithm for both classical and non-classical limits.