Vortex lifetime in the superfluid regime

Determine whether the vortex lifetime in the superfluid regime of the defocusing nonlinear Schrödinger equation in the D-shape billiard (for \(\beta > \beta_{sf}\)) is finite or infinite, and quantify its dependence on \(\beta\), the billiard geometry, and initial vortex conditions.

Background

The authors observe a sharp increase in vortex lifetime near $\beta \approx 45$ and conjecture a superfluid transition, but they do not establish whether the lifetime truly diverges.

They explicitly identify the vortex lifetime in the superfluid regime as an open question, linked to understanding the persistence of topological excitations under chaotic billiard dynamics.