Viscosity, entropy and the viscosity to entropy density ratio; how perfect is a nucleonic fluid?

TL;DR

This paper investigates the viscosity, entropy, and eta/s ratio of hadronic matter, especially neutron gases, using classical and quantum models, comparing results to the theoretical minimum and exploring conditions near phase transitions.

Contribution

It provides a detailed analysis of the viscosity and entropy density in nucleonic fluids, including quantum and classical limits, and compares eta/s ratios to the AdS/CFT bound.

Findings

Eta/s approaches the string theory minimum in the unitary limit.

Viscosity and entropy scaling laws resemble Fraunhofer diffraction.

Minimum eta/s occurs near phase transition regions.

Abstract

The viscosity of hadronic matter is studied using a classical evaluation of the scattering angle and a quantum mechanical discussion based on phase shifts from a potential. Semi classical limits of the quantum theory are presented. A hard sphere and an attractive square well potential step are each considered as well as the combined effects of both. The lowest classical value of the viscosity for an attractive potential is shown to be a hard sphere limit. The high wave number-short wavelength limits of the quantum result have scaling laws associated with it for both the viscosity and entropy. These scaling laws are similar to the Fraunhoher diffraction increase for the hard sphere geometric cross section. Specific examples for nuclear collisions are given. The importance of the nuclear tensor force and hard core is mentioned. The viscosity (eta), entropy density (s) and eta/s ratio are calculated for a gas of dilute neutrons in the unitary limit of large scattering length. Away from the unitary limit, the ratio of the interaction radius or the scattering length to the interparticle spacing introduces a variable y besides the fugacity z. The isothermal compressibility is shown to impose important constraints. The results for eta/s are compared to the AdS/CFT string theory minimum of (1/4Pi)hbar/kb to see how close a nucleonic gas is to being a perfect fluid. The eta/s ~1hbar/kb for a neutron gas in its unitary limit. The eta/s 3hbar/kb treating the nuclear scattering as billiard ball collisions. The minimum eta/s for a neutron gas occurs in regions of negative isothermal compressibility and high fugacity where higher virial terms are important. In a neutron-proton system higher virial terms are associated with a liquid-gas phase transition and critical opalescent phenomena.The type of flow-laminar,vortex, turbulent- is investigated.