Longitudinal and transverse forces on a vortex in superfluid $^4$He

TL;DR

This paper investigates the forces acting on a vortex in superfluid helium-4, focusing on the scattering interactions with phonon quasiparticles at low temperatures, and provides explicit formulas for dissipation coefficients.

Contribution

It introduces a Hamiltonian-based model for vortex dissipation and derives explicit expressions for vortex-quasiparticle interactions at temperatures below 0.4 K.

Findings

Explicit dissipation coefficients derived from reservoir correlation functions.

Analysis of scattering processes influencing vortex dissipation.

Discussion on the impact of vortex mass on dissipation mechanisms.

Abstract

We examine the transverse and longitudinal components of the drag force upon a straight vortex line due to the scattering of liquid $^4$He excitations. For this purpose, we consider a recently proposed Hamiltonian that describes the dissipative motion of a vortex, giving an explicit expression for the vortex-quasiparticle interaction. The involved dissipative coefficients are obtained in terms of the reservoir correlation function. Most of our explicit calculations are concerned to the range of temperatures below 0.4 K, at which the reservoir is composed by phonon quasiparticle excitations. We also discuss some important implications in the determination of possible scattering processes leading to dissipation, according to the values of vortex mass found in the literature.