Classical and quantum vortex leapfrogging in two-dimensional channels

TL;DR

This paper investigates vortex leapfrogging in narrow channels, revealing richer dynamics including new regimes, and compares classical and quantum behaviors using point vortex models and Gross-Pitaevskii simulations.

Contribution

It introduces new leapfrogging regimes in confined geometries and demonstrates their existence in quantum fluids through combined modeling approaches.

Findings

Identification of backward leapfrogging and periodic orbits in channels.

Confirmation of all classical regimes in quantum vortex dynamics.

Discussion of quantum effects like healing length and compressibility on vortex behavior.

Abstract

The leapfrogging of coaxial vortex rings is a famous effect which has been noticed since the times of Helmholtz. Recent advances in ultra-cold atomic gases show that the effect can now be studied in quantum fluids. The strong confinement which characterizes these systems motivates the study of leapfrogging of vortices within narrow channels. Using the two-dimensional point vortex model, we show that in the constrained geometry of a two-dimensional channel the dynamics is richer than in an unbounded domain: alongsize the known regimes of standard leapfrogging and the absence of it, we identify new regimes of backward leapfrogging and periodic orbits. Moreover, by solving the Gross-Pitaevskii equation for a Bose-Einstein condensate, we show that all four regimes exist for quantum vortices too. Finally, we discuss the differences between classical and quantum vortex leapfrogging which appear when the quantum healing length becomes significant compared to the vortex separation or the channel size, and when, due to high velocity, compressibility effects in the condensate becomes significant.