Physics
Superfluid and quantum vortices
A stirred condensate sheds quantised vortices and they crystallise into a lattice.
What happens
A two dimensional Bose-Einstein condensate obeying the Gross-Pitaevskii equation. The trap is first relaxed to its ground state in imaginary time, then a gaussian stirrer orbits inside it the way a laser spoon does in the laboratory. A superfluid cannot rotate smoothly, so above a critical rate it sheds quantised vortices, and they arrange themselves into the Abrikosov lattice on their own. Nothing here is drawn by hand: a vortex is a hole in the density with a full turn of phase around it, and the counter measures that winding.
Equations used in the module
Equations iħ ∂ψ/∂t = (−ħ²∇²/2m + V + g|ψ|² − Ω L_z) ψ (Gross–Pitaevskii) circulation quantised: ∫ v·dl = n h / m vortices form a lattice at high Ω
