Fermi-liquid view of viscosity in cold and dense nucleon matter

TL;DR

The paper develops a mean-field, Fermi-liquid kinetic framework to compute transport in cold, dense relativistic nucleon matter by linearizing the relativistic Boltzmann equation for quasiparticles with medium-dependent dispersion. Employing Landau matching within a relaxation-time approximation, it fixes zero-mode ambiguities and proves the bulk viscosity $\zeta$ is nonnegative; a low-temperature expansion yields $\eta \sim p_F^{*5}\tau_{rel}/\mu^*$ and $\zeta/\eta \propto (T/\mu^*)^4$, with $\zeta$ vanishing as $T\to 0$. Applying the framework to a Walecka mean-field equation of state, the authors compute $\eta$ and $\zeta$ for cold, dense nucleon matter and find bulk dissipation is parametrically subleading to shear in the degenerate regime. The results provide a thermodynamically consistent link between microscopic nucleon interactions and macroscopic transport, with implications for intermediate-energy nuclear experiments and neutron-star phenomenology, and point to future work incorporating microscopic collisions, fluctuations, and more realistic equations of state.

Abstract

We develop a framework to calculate transport properties in cold, dense relativistic quasiparticle system within the Fermi-liquid theory at the mean-field level. Building on our previous study [Phys. Rev. C 111, 044904 (2025)], we start from the linearized relativistic Boltzmann equation tailored to quasiparticles with medium-dependent dispersion relation and implement Landau matching conditions, proving that the bulk viscosity is manifestly nonnegative. A low-temperature expansion then yields leading-order ($T/μ^*$) expressions for the shear ($η$) and bulk ($ζ$) viscosities, where the behavior $ζ/η\propto (T/μ^*)^4$ in the degenerate regime is found to be robust against quasiparticle mass correction. We couple the kinetic framework to a Walecka-type mean-field equation of state and compute $η$ and $ζ$ for cold, dense nucleon matter. The transport properties of nucleonic matter in the degenerate regime can be relevant for intermediate beam-energy nuclear experiments.

Figures (3)

• Figure 1: Separation of equilibrium relabeling induced by $\delta\mu$ from the nonequilibrium correction $\delta f$ obtained from the kinetic equation, where $E_{\boldsymbol{p}}^{\prime *}=\sqrt{m^*(\mu+\delta\mu)+\boldsymbol{p}^2}$ and $\mu^{\prime *}=\mu^*(\mu+\delta\mu)$.
• Figure 2: Input from the mean-field solution at $T=8$ MeV. (a) Quasi-nucleon mass $m_\mathrm{N}^*$ and effective baryon chemical potential $\mu_B^*$ from the gap equations Eq. \ref{['eq:gap_equations']}. (b) The response coefficient $\kappa^*$ obtained from Eq. \ref{['eq:Waleck_dmdmuB']}.
• Figure 3: Dimensionless viscosities at $T=8$ MeV. (a) shear viscosity $\eta$ and (b) bulk viscosity $\zeta$, each scaled by the mean-field enthalpy $\bar{h}_{\mathrm W}$ and effective Fermi momentum $p_\mathrm{F}^*$, shown versus $\mu_B^*/m_\mathrm{N}^*$. Solid (blue) lines are for LO result calculated from Eq. \ref{['eq:LO_viscosity']}. Dashed (red) lines are from full calculations using Eqs. \ref{['eq:viscosity1']}.