Classical chaos vs quantum eigenstates concentrated on periodic orbits
Quantum scars (Heller 1984) are eigenstates of quantum chaotic billiards that concentrate anomalously along unstable periodic orbits, violating ergodicity expected from quantum chaos. In the Bunimovich stadium — a rectangle capped with semicircles — the classical dynamics is fully chaotic (positive Lyapunov exponent), yet quantum eigenstates sometimes "scar" along short periodic orbits.