Transverse force on a quantized vortex in a superfluid

TL;DR

This paper derives an exact expression for the nondissipative transverse force on a vortex in superfluids, showing it is the Magnus force proportional to superfluid density, unaffected by core states.

Contribution

It provides a rigorous derivation of the transverse force on vortices in superfluids, valid for both bosonic and fermionic systems with a complex scalar order parameter.

Findings

The transverse force is the Magnus force proportional to superfluid density.

Localized core states do not alter the transverse force.

The derivation applies to neutral boson and fermion superfluids.

Abstract

We have derived an exact expression for the total nondissipative transverse force acting on a quantized vortex moving in a uniform background. The derivation is valid for neutral boson or fermion superfluids, provided the order parameter is a complex scalar quantity. This force is determined by the one-particle density matrix far away from the vortex core, and is found to be the Magnus force proportional to the superfluid density. We conclude that contributions of the localized core states do not change this force.