MCT self-consistent equations for the density correlator F(q,t). Watch the two-step relaxation (β then α), the non-ergodicity parameter f_q, and the diverging relaxation time at the MCT glass transition T_c.
MCT (Bengtzelius-Götze-Sjölander 1984): ∂_t²F + Ω²F + Ω²∫₀ᵗ m(t-t')∂_{t'}F dt' = 0 where memory kernel m(t) ~ F(t)². Self-consistent → F_q(t→∞) = f_q > 0 in glass phase. Phase transition at ε=0 (T_c). β-relaxation: F ~ f_c + h·t^{-a} (critical decay); α-relaxation: F ~ exp(-(t/τ_α)^β) (stretched exponential). Scaling: τ_α ~ |ε|^{-γ}, γ=1/(2a)+1/(2b). MCT T_c lies above the actual glass transition T_g. RFOT theory extends this.