KPZ Interface Roughening

The Kardar-Parisi-Zhang equation describes growing interfaces with lateral growth. The interface width W(t) ~ t^1/3 — universal KPZ exponent, distinct from diffusive β=1/4.

Nonlinearity λ 1.0

Diffusion ν 0.5

Noise σ 1.0

∂h/∂t = ν∇²h + (λ/2)(∇h)² + σ·η(x,t)
KPZ scaling: width W(t) = ⟨(h−⟨h⟩)²⟩^{1/2} ~ t^β, β=1/3 (KPZ), β=1/4 (EW: λ=0).
Gold line = t^{1/3} reference, blue dashed = t^{1/4} (Edwards-Wilkinson).