Quantized Circulation Around a Vortex Loop — Superfluid Helium (2D)

This top-down companion to the rotating-superfluid-helium vortex lattice makes the defining property of a quantized vortex directly measurable. Every vortex line is still integrated with the real Hall–Vinen equation of motion — mutual Biot–Savart induction between every pair, an opposite-sign image vortex enforcing the container's no-flow-through-wall boundary condition, and mutual friction with the normal fluid that crystallizes the array into a triangular lattice — but the resulting velocity field is now rendered as a live heatmap and probed with a draggable measurement loop. The loop's circulation, computed frame by frame as a discretized line integral of the true velocity field, tracks the number of vortex cores it encloses exactly: Γ = n·κ, jumping by one full quantum the instant a core crosses the boundary. Adjust rotation rate and temperature to change the lattice, then drag the loop through it to watch quantization happen in real time.