On the interaction constant measurement of polarized fermions via sound wave spectra obtained from hydrodynamics with the pressure evolution equation

TL;DR

This paper develops a pressure tensor evolution equation for spin polarized degenerate fermions, enabling more accurate modeling of interactions and proposing experimental methods to measure the interaction constant via sound wave spectra.

Contribution

It introduces the pressure tensor evolution equation for polarized fermions, extending hydrodynamic models to include higher moments and anisotropic pressure effects.

Findings

Pressure tensor influences interaction terms in hydrodynamics.

Anisotropy in momentum space can be used to measure interaction constants.

The model applies to collective excitations in fermionic systems.

Abstract

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.