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Low Temperature Physics

Solitons in normal Fermi liquid

G. M. Peradze, Nodar L. Tsintsadze

Published Jan 1, 2019• 2 citations
Publisher

Abstract

To be based on the new quantum kinetic equation of Fermi particles, which recently was derived by N.L. Tsintsadze and L.N. Tsintsadze, a general quantum dispersion equation for almost ideal Fermi gas is derived and studied for some interesting cases. Here we consider only pair interactions between particles and we used energy expression derived by V.M. Galitski in the ordinary perturbation theory, which involves only the scattering amplitude. New effect that we have shown is that novel quantum term (Madelung term) in the kinetic equation leads to the formation of rarefaction solitary waves in neutral Fermi liquid. Furthermore, attraction and repulsion between particles have tendency to change rarefaction solitary wave speed and shape: Attraction between particles increases rarefaction soliton speed and amplitude, repulsion decreases soliton speed and amplitude.

DOI
10.1063/1.5082319

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To be based on the new quantum kinetic equation of Fermi particles, which recently was derived by N.L. Tsintsadze and L.N. Tsintsadze, a general quantum dispersion equation for almost ideal Fermi gas is derived and studied for some interesting cases. Here we consider only pair interactions between particles and we used energy expression derived by V.M. Galitski in the ordinary perturbation theory, which involves only the scattering amplitude. New effect that we have shown is that novel quantum term (Madelung term) in the kinetic equation leads to the formation of rarefaction solitary waves in neutral Fermi liquid. Furthermore, attraction and repulsion between particles have tendency to change rarefaction solitary wave speed and shape: Attraction between particles increases rarefaction soliton speed and amplitude, repulsion decreases soliton speed and amplitude.
A variety of solitary waves, such as solitons, vortex rings, solitonic vortices, and more complex entities, have recently been predicted to exist. They can move in superfluid ultracold gases along elongated traps. The theoretical description of this motion requires knowledge of the inertial soliton mass and the effective number of particles in it as functions of the soliton energy. While these functions can be calculated by a microscopic theory, it is also possible to express them directly in terms of observable quantities, such as the order parameter phase jump and the particle number depletion in the soliton. In this article, the corresponding equations are derived in a simple and physically clear way and applied to the recently predicted `magnetic soliton' in mixtures of Bose gases in various spin states.
A uniform ground-state three-dimensional Fermi gas with short-range repulsive pairwise interaction is under consideration. Its kinetic and interaction energies are calculated up to the second order of the expansion in the gas parameter. Similar to recent results for an interacting Bose gas, the quantities in question are found to depend on the pairwise interaction through two characteristic lengths: the former, aaa, is the sss-wave scattering length, and the latter, bbb, is related to aaa by $b=a\ensuremath{-}m(\ensuremath{\partial}a∕\ensuremath{\partial}m)$, where mmm stands for the fermion mass. To control the results, we proceed in two independent ways. The first involves the Hellmann-Feynman theorem applied to derive the kinetic and interaction energies from the total-energy expansion in the gas parameter first found by Huang and Yang. The second way operates with in-medium pair wave functions and allows one to calculate the quantities of interest ``from scratch.'' The results of the present investigation, taken together with those of the recent consideration of a dilute Bose gas, make it possible to conclude that the pairwise interaction in a quantum gas has an essential and nontrivial effect on the kinetic energy, which is not the case for a classical many-particle system.
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.