Analytic solution of the dynamics of quantum vortex reconnection

TL;DR

This paper derives an analytical expression for the universal coefficient in the vortex reconnection distance formula in quantum fluids, based on the geometry of reconnecting vortices and self-similar solutions.

Contribution

It provides the first analytic calculation of the dimensionless coefficient D in the vortex reconnection distance law, linking geometry to dynamics.

Findings

Derived an explicit formula for D based on vortex geometry

Validated the self-similar solution as an accurate description of reconnection dynamics

Connected geometric features to universal reconnection behavior

Abstract

Experimental and simulational studies of the dynamics of vortex reconnections in quantum fluids showedthat the distance $d$ between the reconnecting vortices is close to a universal time dependence $d=D[\kappa|t_0-t|]^\alpha$ with $\alpha$ fluctuating around 1/2 and $\kappa=h/m$ is the quantum of circulation. Dimensional analysis, based on the assumption that the quantum of circulation $\kappa=h/m$ is the only relevant parameter in the problem, predicts $\alpha=1/2$. 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.