Diffusion wave modes and oscillating motions in superfluid $He^3-A$

TL;DR

This paper investigates diffusion wave modes in superfluid $He^3-A$, revealing how their dispersion depends on polarization, and analyzes the oscillating velocities and frictional forces in various boundary conditions.

Contribution

It introduces a detailed analysis of diffusion vibrational modes in superfluid $He^3-A$, including velocity oscillations and frictional forces under different geometries and boundary conditions.

Findings

Dispersion relation depends on wave polarization.

Superfluid component velocity oscillates alongside normal component.

Frictional forces have both parallel and perpendicular components.

Abstract

Diffusion vibrational modes are studied in superfluid $He^3-A$ in zero magnetic fields for different angles between the orbital axis and the wave vector. The dispersion relation for these modes is found to depend on the wave polarization. It is shown that in addition to the normal component velocity, the superfluid component velocity also oscillates in the diffusion modes of $He^3-A$. The frictional forces due to viscous waves in $He^3-A$, exerted in the plane surface which is in contact with a superfluid liquid layer of finite thickness and performs a simple harmonic oscillatory motion, are calculated. We also consider, volume of $He^3-A$ restricted by two parallel infinite surfaces, when the lower surface accomplishes simple harmonic oscillation and we calculate the frictional forces exerted on surfaces. It is found that the frictional force has not only parallel, but also a perpendicular component relative to the direction of oscillations.