Magnus Force in Discrete and Continuous Two-Dimensional Superfluids

TL;DR

This paper investigates how the Magnus force acting on vortices in two-dimensional superfluids varies between discrete lattice and continuous systems, revealing a transition from full to vanishing force depending on lattice fineness.

Contribution

It demonstrates the transition of the Magnus force in superfluids from the continuous to the discrete regime through numerical simulations of the Gross-Pitaevskii equation.

Findings

Vortices follow superflow on fine lattices

Vortices move perpendicular to superflow on coarse lattices

Results align with experiments on Josephson junction arrays

Abstract

Motion of vortices in two-dimensional superfluids in the classical limit is studied by solving the Gross-Pitaevskii equation numerically on a uniform lattice. We find that, in the presence of a superflow directed along one of the main lattice periods, vortices move with the superflow on fine lattices but perpendicular to it on coarse ones. We interpret this result as a transition from the full Magnus force in the Galilean-invariant limit to vanishing effective Magnus force in a discrete system, in agreement with the existing experiments on vortex motion in Josephson junction arrays.