Stadium Billiard — Quantum Scars

Quantum scars (Heller 1984): eigenstates of classically chaotic billiards show anomalously large probability density along short unstable periodic orbits. In the stadium (Bunimovich 1974), the classical dynamics is fully chaotic (positive Lyapunov exponent), yet quantum mechanics leaves these ghostly imprints. Integrable geometries instead show regular nodal patterns. Berry's conjecture: energy eigenfunctions in chaotic systems are locally Gaussian random waves.