Quasi-stable configurations of torus vortex knots and links

TL;DR

This paper numerically investigates the quasi-stable states of torus vortex knots and links in superfluids, identifying parameter regions where these configurations remain stable over extended periods.

Contribution

It introduces a numerical simulation of vortex dynamics in superfluids for torus knots and links, revealing quasi-stability regions based on parameters.

Findings

Existence of quasi-stability regions in parameter space.

Vortex configurations can remain stable for hundreds of characteristic times.

Stability depends on parameters n, p, q, B_0, and Λ.

Abstract

The dynamics of torus vortex configurations $V_{n,p,q}$ in a superfluid liquid at zero temperature ($n$ is the number of quantum vortices, $p$ is the number of turns of each filament around the symmetry axis of the torus, and $q$ is the number of turns of the filament around its central circle; radii $R_0$ and $r_0$ of the torus at the initial instant are much larger than vortex core width $\xi$) has been simulated numerically based on a regularized Biot-Savart law. The lifetime of vortex systems till the instant of their substantial deformation has been calculated with a small step in parameter $B_0=r_0/R_0$ for various values of parameter $\Lambda=\log(R_0/\xi)$. It turns out that for certain values of $n$, $p$, and $q$, there exist quasi-stability regions in the plane of parameters $(B_0,\Lambda)$, in which the vortices remain almost invariable during dozens and even hundreds of characteristic times.