Vortex mass in a superfluid at low frequencies

TL;DR

This paper investigates the inertial mass of vortices in superfluids at low frequencies, revealing its dependence on force fields and pinning potential, and deriving a simple formula within the Gross-Pitaevskii framework.

Contribution

It introduces a method to calculate vortex mass using a rotating pinning potential and analyzes the effects of force fields and potential range on the mass.

Findings

Vortex mass depends on the force field used for acceleration.

Mass diverges logarithmically as pinning potential radius approaches zero.

Non-zero compressibility leads to divergent vortex mass.

Abstract

An inertial mass of a vortex can be calculated by driving it round in a circle with a steadily revolving pinning potential. We show that in the low frequency limit this gives precisely the same formula that was used by Baym and Chandler, but find that the result is not unique and depends on the force field used to cause the acceleration. We apply this method to the Gross-Pitaevskii model, and derive a simple formula for the vortex mass. We study both the long range and short range properties of the solution. We agree with earlier results that the non-zero compressibility leads to a divergent mass. From the short-range behavior of the solution we find that the mass is sensitive to the form of the pinning potential, and diverges logarithmically when the radius of this potential tends to zero.