Classical Strongly Coupled QGP: VII. Shear Viscosity and Self Diffusion

TL;DR

This paper develops a theoretical framework for the classical colored Coulomb plasma, deriving hydrodynamical properties like shear viscosity and self-diffusion, and compares results with simulations, with implications for understanding the strongly coupled quark-gluon plasma.

Contribution

It introduces a Liouville operator approach for the classical colored Coulomb plasma and derives hydrodynamical equations and transport coefficients at strong coupling.

Findings

Shear viscosity exhibits a minimum at Gamma  8 near the liquid point.

Self-diffusion constant decreases as 1/Gamma^{3/2} regardless of regime.

Results align with molecular dynamics simulations of SU(2) colored Coulomb plasma.

Abstract

We construct the Liouville operator for the SU(2) classical colored Coulomb plasma (cQGP) for arbitrary values of the Coulomb coupling $\Gamma=V/K$, the ratio of the mean Coulomb to kinetic energy. We show that its resolvent in the classical colored phase space obeys a hierarchy of equations. We use a free streaming approximation to close the hierarchy and derive an integral equation for the time-dependent structure factor. Its reduction by projection yields hydrodynamical equations in the long-wavelength limit. We discuss the character of the hydrodynamical modes at strong coupling. The shear viscosity is shown to exhibit a minimum at $\Gamma\approx 8$ near the liquid point. This minimum follows from the cross-over between the single particle collisional regime which drops as $1/\Gamma^{5/2}$ and the hydrodynamical collisional regime which rises as $\Gamma^{1/2}$. The self-diffusion constant drops as $1/\Gamma^{3/2}$ irrespective of the regime. We compare our results to molecular dynamics simulations of the SU(2) colored Coulomb plasma. We also discuss the relevance of our results for the quantum and strongly coupled quark gluon plasma (sQGP)