长寿命量子涡旋结
Long-lived quantum vortex knots
摘要：
在正则化的毕奥-萨伐尔定律（初始涡旋构型的环面半径$R_0$和$r_0$大于涡核宽度$ξ$）下，模拟了零温下超流体中最简单的环面型量子涡结的动力学.对于参数$Λ=\log(R_0/ξ)$的不同值，在参数$B_0=r_0/R_0$上进行小步，计算节点直到其显著变形的演化时间。已经发现，在$Λ\gtrsim 3$，准稳定性带出现在$B_0\lesssim 0.2$的区域中，这对应于长的结寿命和非常大的行进距离--高达几百个$R_0$。这一结果是新的和相当出乎意料的，因为以前人们认为，最大寿命的环面结，直到重新连接不超过几个典型的时期。随着$Λ$的增加，准稳定“窗口”的打开是由于参数$B_0$上动力系统的主参数共振变窄。
英文摘要：
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 $ξ$). 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 $Λ=\log(R_0/ξ)$. It has been found that at $Λ\gtrsim 3$, 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 $Λ$ is due to narrowing main parametric resonances of the dynamical system on parameter $B_0$.
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