Quantum Topology Seminar
Renzzo Ricca
Department of Math and Applic, U. Milano-Bicocca, Italy
On Quantum Vortex Knots and Links
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 vortex defects forming knots and links. Direct and inverse topological cascades are discussed, showing how a trefoil knot is created by the interaction and reconnection of initially unknotted, unlinked loops [1]. By relying on the zero helicity condition [2] we show how writhe and twist exchange during evolution, and by analysing the associated phase surfaces we show that defect evolution is governed by minimal surface energy dynamics. Moreover, considering a twist phase superposition on existing defects we prove [3] that new phase defects can be produced as a manifestation of a Aharonov-Bohm type effect 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] Belloni, A. & Ricca, R.L.. (2023) On the zero helicity condition for quantum vortex defects. J. Fluid Mech., to appear.
[4] Foresti, M. & Ricca, R.L.. (2022) Instability of a quantum vortex by twist perturbation. J. Fluid Mech. 949, A19.
Thursday April 20, 2023 at 12:00 PM in Zoom