Abstract

By exploiting the hydrodynamic formulation of the Gross-Pitaevskii equation (GPE) for quantum fluids we present new results on the creation and evolution of defects forming knots and links [1]. Direct and inverse topological cascades are discussed, showing how a trefoil knot is created by the interaction and reconnection of initially unknotted, unlinked loops. The zero helicity condition is proven by writhe and twist exchange, and the analysis of kinetic and quantum energy contribution on phase surfaces shows that defect evolution is governed by minimal surface energy dynamics [1,2]. Moreover, considering a twist phase superposition on existing defects we prove that new phase defects can be produced as a manifestation of a Aharonov-Bohm type effect [3] by an instability criterium derived from a modified form of the GPE [4].

[1] Zuccher, S. & Ricca, R.L. (2022) Creation of quantum knots and links driven by minimal surfaces. J. Fluid Mech. 942, A8.

[2] Sumners, De W.L., Cruz-White, I.I. & Ricca, R.L. (2021) Zero helicity of Seifert framed defects. J. Phys. A: Math. Theor. 54, 295203.

[3] Foresti, M. & Ricca, R.L. (2019) Defect production by pure phase twist injection as Aharonov-Bohm effect. Phys. Rev. E 100 , 023107.

[4] Foresti, M. & Ricca, R.L.. (2022) Instability of a quantum vortex by twist perturbation. J. Fluid Mech. 949, A19 .