The possibility of the hydrodynamic description of ultracold fermions via the microscopic derivation of the model is described. Differently truncated hydrodynamic models are derived and compared. All models are based on the microscopic many-particle Schrdinger equation. Minimal coupling models based on the continuity and Euler equations are considered. An extended hydrodynamic model including the independent dynamics of the momentum flux (the pressure evolution) is derived. The influence of the spin polarization is described. The short-range interaction is considered in the isotropic limit. The interaction is considered up to the third order by interaction radius. Therefore, the single-fluid model of spin-1/2 fermions and the two-fluid model of spin-1/2 fermions are under consideration in this paper. Spectra of bulk collective excitations are derived and compared in terms of different models.

描述了通过模型的微观推导对超冷费米子进行水动力描述的可能性。推导并比较了截短的流体动力学模型。所有模型均基于微观的多粒子薛定inger方程。考虑了基于连续性和欧拉方程的最小耦合模型。导出了包括动量通量的独立动力学（压力演化）的扩展流体力学模型。描述了自旋极化的影响。在各向同性极限内考虑了短程相互作用。根据相互作用半径，相互作用被认为达到三阶。因此，本文考虑了自旋1/2费米子的单流体模型和自旋1/2费米子的两流体模型。