Non-linear approach to the entrainment matrix of superfluid nucleon mixture at zero temperature

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 non-linear. Numerical solutions to the equations for some typical cases demonstrate that the components of the entrainment matrix possess a highly non-linear dependence on the velocities of the two superflows simultaneously. This effect, previously ignored, can greatly influence the dynamics of neutron stars.