Long-Lived Quantum Vortex Knots

Abstract

The dynamics of the simplest torus quantum vortex knots in a superfluid at zero temperature has been simulated with a regularized Biot–Savart law (the torus radii R₀ and r₀ for the initial vortex configuration are much larger than the width of the vortex core ). The evolution times of knots until their significant deformation have been calculated with a small step in the parameter B₀ = r₀/R₀ for different values of the parameter Λ = log(R₀/ξ). It has been found that regions of quasi-stability appear at Λ ≳ 3 in the range B₀ ≲ 0.2, which correspond to long knot lifetimes and very large traveling distances up to several hundred R₀. This result is new and quite surprising because previously it was believed that the maximum lifetime of torus knots until reconnection does not exceed several typical periods. The opening of quasi-stable “windows” at increasing Λ is due to narrowing of main parametric resonances of the dynamic system in the parameter B₀.