Sound-induced vortex interactions in a zero-temperature two-dimensional superfluid

TL;DR

This paper derives an effective theory for vortex interactions in a 2D superfluid, showing sound-mediated effects do not cause vortex annihilation and thus support inverse energy cascades.

Contribution

It provides a systematic derivation of vortex dynamics without divergences, valid in dilute limits, and analyzes sound-induced effects on vortex-antivortex pairs.

Findings

No logarithmic divergences in equations of motion.

Sound interactions do not lead to vortex annihilation.

Support for inverse energy cascade in 2D superfluid turbulence.

Abstract

We present a systematic derivation of the effective action for interacting vortices in a non-relativistic two-dimensional superfluid described by the Gross-Pitaevskii equation by integrating out longitudinal fluctuations of the order parameter. There are no logarithmically divergent coefficients in the equations of motion. Our analysis is valid in a dilute limit of vortices where the intervortex spacing is large compared to the core size, and where number fluctuations of atoms in vortex cores are suppressed. We analyze sound-induced corrections to the dynamics of a vortex-antivortex pair and show that there is no instability to annihilation, suggesting that sound-mediated interactions are not strong enough to ruin an inverse energy cascade in two-dimensional zero-temperature superfluid turbulence.