Hard Sphere Glass — Mode Coupling Theory

Cage dynamics, MSD plateau, α/β relaxation near φ_c ≈ 0.516

φ = 0.45 — liquid phase
0.45
1.00
3
Mode Coupling Theory (Götze 1984): near φ_c, density fluctuations cage particles. MSD shows β-relaxation plateau (caged) then α-relaxation (cage escape). Above φ_c ≈ 0.516, MCT predicts structural arrest — the ideal glass transition. Watch the plateau grow as φ → φ_c.