Long-lived quantum vortex knots

Dynamics of simplest quantum vortex knots of torus type in a superfluid at zero temperature has been simulated within a regularized Biot-Savart law (the torus radii $R_0$ and $r_0$ for initial vortex configuration were large in comparison with a vortex core width $\xi$). Computations of evolution times of knots until their significant deformation were carried out with a small step on parameter $B_0=r_0\mathrm{/}{R}_0$ for different values of parameter $\mathrm{\Lambda }=\log (R_0\mathrm{/}\xi )$. It has been found that at $\mathrm{\Lambda }\gtrsim 3$, bands of quasi-stability appear in a region of $B_0\lesssim 0.2$, which correspond to long knot lifetimes and to very large traveling distances — up to several hundreds of $R_0$. This result is new and quite unexpected, because previously it was believed that maximal lifetime of torus knots until reconnection does not exceed several typical periods. The opening of quasi-stable ‘windows’ at increasing $\mathrm{\Lambda }$ is due to narrowing main parametric resonances of the dynamical system on parameter $B_0$.