Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel.
Phys Rev Lett. 2013 Oct 4;111(14):145302. doi: 10.1103/PhysRevLett.111.145302. Epub 2013 Oct 2.
Experimental and simulational studies of the dynamics of vortex reconnections in quantum fluids showed that the distance d between the reconnecting vortices is close to a universal time dependence d=Dκ|t(0)-t| with α fluctuating around 1/2 and κ=h/m is the quantum of circulation. Dimensional analysis, based on the assumption that the quantum of circulation κ=h/m is the only relevant parameter in the problem, predicts α=1/2. The theoretical calculation of the dimensionless coefficient D in this formula remained an open problem. In this Letter we present an analytic calculation of D in terms of the given geometry of the reconnecting vortices. We start from the numerically observed generic geometry on the way to vortex reconnection and demonstrate that the dynamics is well described by a self-similar analytic solution which provides the wanted information.
实验和模拟研究表明，量子流中涡旋重联的动力学过程满足距离 d 与无量纲时间 t 的普适关系 d=Dκ|t(0)-t|，其中 α 在 1/2 附近波动，κ=h/m 是量子循环。基于量子循环 κ=h/m 是问题中唯一相关参数的假设，我们通过量纲分析得到 α=1/2。然而，该公式中无量纲系数 D 的理论计算仍是一个开放性问题。在这封信件中，我们根据重联涡旋的给定几何形状给出了 D 的解析计算。我们从数值观测到的重联过程中的通用几何形状开始，证明了动力学过程可以很好地由自相似解析解来描述，从而得到了所需的信息。
