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

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 [], 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mo>(</a:mo> <a:mi>T</a:mi> <a:mo>/</a:mo> <a:msup> <a:mi>μ</a:mi> <a:mo>*</a:mo> </a:msup> <a:mo>)</a:mo> </a:mrow> </a:math> expressions for the shear <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mo>(</b:mo> <b:mi>η</b:mi> <b:mo>)</b:mo> </b:math> and bulk <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mo>(</c:mo> <c:mi>ζ</c:mi> <c:mo>)</c:mo> </c:math> viscosities, where the behavior <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi>ζ</d:mi> <d:mo>/</d:mo> <d:mi>η</d:mi> <d:mo>∝</d:mo> <d:msup> <d:mrow> <d:mo>(</d:mo> <d:mi>T</d:mi> <d:mo>/</d:mo> <d:msup> <d:mi>μ</d:mi> <d:mo>*</d:mo> </d:msup> <d:mo>)</d:mo> </d:mrow> <d:mn>4</d:mn> </d:msup> </d:mrow> </d:math> 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:mi>η</e:mi> </e:math> and <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mi>ζ</f:mi> </f:math> for cold, dense nucleon matter. The transport properties of nucleonic matter in the degenerate regime can be relevant for intermediate beam-energy nuclear experiments.