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

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 J. Li \emph{et al.} [Phys. Rev. C \textbf{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.