The stadium boundary makes classical billiards fully chaotic (ergodic, mixing). Quantum eigenstates show scarring along classical periodic orbits. Level spacing obeys GOE (Wigner-Dyson) instead of Poisson.
Left: simulated wavefunction |ψₙ|² in the stadium. Right: level spacing distribution P(s) vs Wigner-Dyson (GOE) and Poisson predictions. Scarring along the "bouncing ball" orbit is visible in low modes.