How superfluid vortex knots untie

TL;DR

This study uses simulations of superfluid vortex knots to reveal their efficient and predictable untying process, with insights into helicity preservation and topological pathways.

Contribution

It provides the first large-scale simulation analysis of vortex knot untying, uncovering predictable timescales and topological pathways in superfluid dynamics.

Findings

Knots untie efficiently within predictable times.

Centerline helicity is partially preserved during untying.

Topological pathways follow simple minimal 2D knot diagrams.

Abstract

Knotted and tangled structures frequently appear in physical fields, but so do mechanisms for untying them. To understand how this untying works, we simulate the behavior of 1,458 superfluid vortex knots of varying complexity and scale in the Gross-Pitaevskii equation. Without exception, we find that the knots untie efficiently and completely, and do so within a predictable time range. We also observe that the centerline helicity -- a measure of knotting and writhing -- is partially preserved even as the knots untie. Moreover, we find that the topological pathways of untying knots have simple descriptions in terms of minimal 2D knot diagrams, and tend to concentrate in states along specific maximally chiral pathways.