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Persistent current formation in double-ring geometries

Quenching an ultracold bosonic gas in a ring across the Bose-Einstein condensation phase transition is known, and has been experimentally observed, to lead to the spontaneous emergence of persistent currents. The present work examines how these phenomena generalize to a system of two experimentally accessible explicitly two-dimensional co-planar rings with a common interface, or to the related lemniscate geometry, and demonstrates an emerging independence of winding numbers across the rings, which can exhibit flow both in the same and in opposite directions. The observed persistence of such findings in the presence of dissipative coupled evolution due to the local character of the domain formation across the phase transition and topological protection of the randomly emerging winding numbers should be within current experimental reach.