On the critical exponent of \eta/s and a new exponent-less measure of fluidity

TL;DR

This paper investigates the critical behavior of the shear viscosity to entropy density ratio in fluids, introduces a universal, exponent-less fluidity measure based on mode-mode coupling theory, and applies it to quark-gluon plasma to constrain its transport coefficients.

Contribution

It proposes a new universal fluidity measure independent of fluid dynamics type, applicable to both hydrodynamic and nonhydrodynamic regimes, and explores its implications for quark-gluon plasma.

Findings

The new fluidity measure exhibits universality across different fluid types.

It constrains the thermal conductivity of quark-gluon plasma based on elliptic flow data.

The critical exponent of η/s is discussed in relation to fluid phase transitions.

Abstract

We discuss on the critical exponent of $\eta/s$ for a fluid, and propose a new exponent-less measure of fluidity based on a mode-mode coupling theory. This exhibits a remarkable universality for fluids obeying a liquid-gas phase transition both in hydrodynamic as well as in nonhydrodynamic region. We show that this result is independent of the choice of the fluid dynamics, {\em viz.}, relativistic or nonrelativistic. Quark-Gluon Plasma, being a hot relativistic and a nearly perfect fluid produced in relativistic heavy-ion collisions, is expected to obey the same universality constrained by both the viscous and the thermal flow modes in it. We also show that if the elliptic flow data in RHIC puts a constraint on $\eta/s$ then the new fluidity measure for Quark-Gluon Plasma in turn also restricts the other transport coefficient, {\it viz.}, the thermal conductivity.