Dissipative dynamics of vortex lines in superfluid $^{4}$He

TL;DR

This paper develops a Hamiltonian model to describe the dissipative dynamics of vortex lines in superfluid helium-4, linking microscopic interactions with macroscopic frictional behavior.

Contribution

It introduces a novel Hamiltonian framework and derives an irreversible motion equation for vortex density, connecting microscopic excitations to macroscopic vortex dynamics.

Findings

Derived an equation of motion incorporating drag force components.

Revealed the microscopic origin of mutual friction in superfluid helium.

Aligned theoretical model with phenomenological vortex friction theories.

Abstract

We propose a Hamiltonian model that describes the interaction between a vortex line in superfluid $^{4}$He and the gas of elementary excitations. An equation of irreversible motion for the density operator of the vortex, regarded as a macroscopic quantum particle with a finite mass, is derived in the frame of Generalized Master Equations. This enables us to cast the effect of the coupling as a drag force with one reactive and one dissipative component, in agreement with the assumption of the phenomenological theories of vortex mutual friction in the two fluid model.