Usually, hydrodynamic equations are restricted by the continuity and Euler equations. However, the account of the higher moments of the distribution function gives better description of the kinetic properties. Therefore, the pressure tensor evolution equation (PTEE) is derived for spin polarized degenerate fermions. Moreover, it is found that the pressure tensor enters the interaction term generalizing the p-wave interaction in the Euler equation. Hence, the PTEE allows to give a more accurate description of the interaction in Euler equation. Next, the interaction is calculated for the PTEE. The developed model is applied to the small amplitude bulk collective excitations in homogeneous and trapped fermions in order to suggest the methods of experimental measurement of the interaction constant of polarized fermions. It is demonstrated that the anisotropy in the momentum space revealing in the difference of the pressures in the anisotropy direction and the perpendicular directions leads to a method of detection of the interaction constant.
Abstract Repulsive Bose–Einstein condensates, where short-range interaction is included up to the third order by the interaction radius, demonstrate the existence of bright solitons in a narrow interval of parameters. These solitons are studied here for the boson–fermion mixture, where spin-1/2 fermions are considered in the regime of full-spin polarization. The influence of fermions on bosonic bright solitons via the boson–fermion interaction is considered up to the third order by the interaction radius. Fermions themselves are considered within the hydrodynamic model, which includes the kinetic pressure-evolution equation. The interactions between fermions are also considered. The first order by the interaction radius makes a zero contribution to the Euler equation and the kinetic pressure evolution equation for fermions, but the third order by the interaction radius provides nonzero contributions to both equations. The repulsive (attractive) boson–fermion interaction leads to bright (dark) fermionic solitons.
The system of hydrodynamic equations is generally limited to the continuity and Euler equations. However, taking higher moments of the distribution function into account improves the description of kinetic properties. We derive the pressure tensor evolution equation (PTEE) for spin-polarized degenerate fermions. We find that the pressure tensor enters the term describing the interaction that generalizes the
p -wave interaction in the Euler equation. Hence, calculating the interaction for the PTEE allows describing the interaction in the Euler equation more accurately. The proposed model is applied to small-amplitude bulk collective excitations in homogeneous fermions and trapped fermions, yielding a method for experimental measurements of the coupling constant of polarized fermions. It is demonstrated that the anisotropy in the momentum space, manifesting itself in the difference of pressures in the anisotropy direction and the perpendicular directions, leads to a method for determining the coupling constant.