Grey solitons in the ultracold fermions at the full spin polarization

TL;DR

This paper models grey solitons in fully spin-polarized ultracold fermions using a quantum hydrodynamic approach, revealing conditions for their existence influenced by Fermi pressure and short-range interactions.

Contribution

It introduces a nonlinear Schrödinger equation-based model for grey solitons in fully spin-polarized fermions, accounting for Fermi pressure and short-range interactions.

Findings

Grey solitons exist below the Fermi velocity.

Fermi pressure causes localized density dips with nonzero minima.

Short-range interactions modify the pressure contribution.

Abstract

A minimal coupling quantum hydrodynamic model of spin-1/2 fermions at the full spin polarization corresponding to a nonlinear Schrodinger equation is considered. The nonlinearity is primarily caused by the Fermi pressure. It provides an effective repulsion between fermions. However, there is the additional contribution of the short-range interaction appearing in the third order by the interaction radius. It leads to the modification of the pressure contribution. Solitons are considered for the infinite medium with no restriction on the amplitude of the wave. The Fermi pressure leads to the soliton in form of the area of decreased concentration. However, the center of solution corresponding to the area of minimal concentration has nonzero value of concentration. Therefore, the grey soliton is found. Soliton exist if the speed of its propagation is below the Fermi velocity.