# Nonlinear approach to the entrainment matrix of superfluid nucleon mixture at zero temperature

## TL;DR

This paper derives nonlinear equations for the entrainment matrix in superfluid neutron-proton mixtures, revealing significant velocity-dependent effects that impact neutron star dynamics.

## Contribution

It introduces a nonlinear approach to calculating the entrainment matrix considering velocity-dependent energy gaps, a novel aspect in superfluid hydrodynamics.

## Key findings

- Entrainment matrix components depend nonlinearly on superfluid velocities.
- Velocity dependence of energy gaps significantly affects neutron star models.
- Numerical solutions show strong nonlinear behavior in typical cases.

## Abstract

The superfluid drag effect, in hydrodynamics of pulsating neutron stars, is conventionally described with the aid of the entrainment matrix relating the mass currents with the velocities of superfluid flows in the system. Equations for the entrainment matrix of a superfluid mixture of neutrons and protons are derived with allowance for the strong dependence of the energy gaps on the velocities of superfluid flows. The calculations are carried out in the frame of the Fermi-liquid theory. The equations obtained are highly nonlinear. Numerical solutions to the equations for some typical cases demonstrate that the components of the entrainment matrix possess a highly nonlinear dependence on the velocities of the two superflows simultaneously. This effect, previously ignored, can greatly influence the dynamics of neutron stars.