The relativistic entrainment matrix of a superfluid nucleon-hyperon mixture. II. Effect of finite temperatures

We calculate the important quantity of superfluid hydrodynamics, the relativistic entrainment matrix for a nucleon-hyperon mixture at arbitrary temperature. In the nonrelativistic limit this matrix is also termed the Andreev-Bashkin or mass-density matrix. Our results can be useful for modeling the pulsations of massive neutron stars with superfluid nucleon-hyperon cores and for studies of the kinetic properties of superfluid baryon matter.

💡 Research Summary

The paper presents a comprehensive calculation of the relativistic entrainment matrix (also known in the non‑relativistic limit as the Andreev‑Bashkin or mass‑density matrix) for a superfluid mixture of nucleons and hyperons (neutrons, protons, Λ and Σ hyperons) at arbitrary temperatures. The entrainment matrix ρᵢⱼ quantifies how the momentum of one superfluid component is carried by the flow of another component; it is a central ingredient in the hydrodynamics of multi‑component superfluids and directly influences the spectrum of stellar oscillations, the damping of r‑ and g‑modes, and transport coefficients such as thermal conductivity and shear viscosity in the dense cores of massive neutron stars.

Theoretical framework
The authors start from relativistic Landau‑Fermi‑liquid theory, extending the formalism to include pairing correlations for each baryon species. Using the Nambu‑Gor’kov Green‑function technique within a mean‑field (RMF) description of the strong interaction, they derive the linear response of the system to a small superfluid velocity perturbation. The resulting expression for the entrainment matrix reads

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