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arXiv · 1408.5913

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

Andrew Lucas·Piotr Surówka
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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.

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Andrew Lucas, Piotr Surówka. 2014-11-21. Sound-induced vortex interactions in a zero-temperature two-dimensional superfluid. https://doi.org/10.1103/physreva.90.053617

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