Transport coefficients of dense nucleon matter at low temperature

TL;DR

This paper investigates the bulk and shear viscosities of cold, dense nucleon matter at low temperatures, deriving relations with thermodynamic properties and applying them within the Walecka model to understand stability and fluid behavior.

Contribution

It provides a leading-order calculation of viscosities in dense nucleon matter at low temperature using the relaxation time approximation, linking transport coefficients to thermodynamics.

Findings

Hydrodynamic stability requires positive bulk viscosity.

Derived relations between viscosities and thermodynamic potential.

Applied results to the Walecka model to analyze fluid properties.

Abstract

The transport property of cold and dense nucleon matter is important for nuclear physics but is relatively less studied than that at finite temperatures. In this paper, we present a primary study of bulk and shear viscosities in the limit $T/\mu_B \ll 1$, where $T$ and $\mu_B$ are the temperature and the baryon chemical potential. The analysis is performed for a generic system where nucleons are dressed by the condensation of both scalar and vector interactions. Under the relaxation time approximation of the Boltzmann equation, we compute the viscosities of the system to leading power in $T/\mu_B$ expansion and establish a relation between the thermodynamic potential and transport coefficients, including bulk viscosity ($\zeta$) and shear viscosity ($\eta$). It is found that hydrodynamic stability ($\zeta>0$) imposes additional constraints on the thermodynamic potential. As an example, these relations are applied to the Walecka model. The fluid properties of the cold and dense nucleon matter are characterized by the dimensionless combination of viscosities times the quasi-Fermi momentum over the enthalpy. Furthermore, we discuss the implication of the stability condition on the range of applicability of the model.