Semiclassical phase-space representation of quantum dynamics
The Wigner function W(x,p) is a quasi-probability distribution in phase space. It evolves via the Moyal bracket: ∂W/∂t = {H,W}_Moyal = (2/ℏ)H sin(ℏ∇⇝/2)W — the ℏ→0 limit gives classical Liouville flow. Negative regions (blue) signal quantum interference. The cat state shows dramatic negative fringes between two blobs.