Long-lived quantum vortex knots

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 $R_0$ and $r_0$ 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 $B_0=r_0/R_0$ for different values of the parameter $\Lambda=\log(R_0/\xi)$. It has been found that regions of quasi-stability appear at $\Lambda\gtrsim3$ in the range $B_0\lesssim0.2$, which correspond to long knot lifetimes and very large traveling distances up to several hundred $R_0$. 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 $\Lambda$ is due to narrowing of main parametric resonances of the dynamic system in the parameter $B_0$.