Iordanskii Force and the Gravitational Aharonov-Bohm effect for a Moving Vortex

TL;DR

This paper investigates phonon scattering by a moving vortex in a superfluid, linking the Iordanskii force to a gravitational Aharonov-Bohm effect, and emphasizes the importance of higher-order terms for consistency with fluid invariance.

Contribution

It demonstrates the necessity of including second-order velocity terms in sound-wave equations to correctly derive the Iordanskii force, supporting its interpretation as a gravitational Aharonov-Bohm effect.

Findings

Correct derivation of the Iordanskii force requires $O(v_s^2)$ terms.

The Iordanskii force is analogous to a gravitational Aharonov-Bohm effect.

Compatibility with galilean invariance is confirmed.

Abstract

I discuss the scattering of phonons by a vortex moving with respect to a superfluid condensate. This allows us to test the compatibility of the scattering-theory derivation of the Iordanskii force with the galilean invariance of the underlying fluid dynamics. In order to obtain the correct result we must retain $O(v_s^2)$ terms in the sound-wave equation, and this reinforces the interpretation, due to Volovik, of the Iordanskii force as an analogue of the gravitational Bohm-Aharonov effect.