Long-lived quantum vortex knots

Abstract

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 $B_0=r_0/R_0$ for different values of parameter $\Lambda =\log (R_0/\xi )$. It has been found that at $\Lambda \gtrsim 3$, 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 $\Lambda$ is due to narrowing main parametric resonances of the dynamical system on parameter $B_0$.

(3+epsilon) pages, 7 figures, English translation of published Russian original

References in corpus (1)

• Nonlinear Schroedinger equation for a superfluid Bose gas from weak coupling to unitarity: Study of vortices

Cited by in corpus (6)

• Quasi-stable quantum vortex knots and links in anisotropic harmonically trapped Bose-Einstein condensates
• Three-dimensional numerical simulation of long-lived quantum vortex knots and links in a trapped Bose-Einstein condensate
• Three-dimensional stability of leapfrogging quantum vortex rings
• Nonlinearity and Topology
• Quasi-stable configurations of torus vortex knots and links
• Vortex knots on three-dimensional lattices of nonlinear oscillators coupled by space-varying links