Superfluid transition in vortex dynamics: critical nonlinearity and validation

Verify the proposed superfluid transition in the vortex dynamics of the defocusing nonlinear Schrödinger equation in the D-shape billiard, determine the critical nonlinearity parameter \(\beta_{sf}\), and characterize the associated critical superfluid velocity, vortex lifetime behavior, and quasiparticle radiation across the transition.

Background

Numerical results show an abrupt increase in vortex lifetime near β≈45\beta \approx 45, suggesting a transition from a regime where the vortex emits quasiparticles and decays to a superfluid-like regime where the vortex persists much longer.

Based on these observations, the authors formulate a conjecture about a superfluid transition, and explicitly note that its verification requires further paper.

References

Thus we make a superfluid transition conjecture: at $\beta < \beta_{sf} \approx 45$ the velocity of vortex center is higher than the critical superfluid velocity of light fluid and it starts to radiate quasi-particles breaking superfluidity, while for $\beta > \beta_{sf} \approx 45$ this velocity is below critical superfluid velocity and the vortex life-time is increased enormously or may become even infinite. The verification of this superfluid transition conjecture requires further studies which are beyond the scope of this work.

— Dynamical thermalization, Rayleigh-Jeans condensate, vortexes and wave collapse in quantum chaos fibers and fluid of light (2506.06534 - Ermann et al., 6 Jun 2025) in Section 8, Vortexes in defocusing fiber NSE