KPZ Interface Growth Universality Class

KPZ equation (Kardar, Parisi, Zhang 1986): ∂h/∂t = ν∇²h + (λ/2)(∇h)² + η(x,t). The nonlinear term λ(∇h)²/2 breaks up-down symmetry and drives the KPZ universality class. Universal exponents: growth β=1/3, roughness α=1/2, dynamic z=3/2. W(L,t) = ⟨(h−⟨h⟩)²⟩^½ ~ t^β early, ~ L^α late (Family-Vicsek scaling). EW (λ=0): β=1/4, α=1/2. Random deposition: β=1/2, no saturation.