KPZ INTERFACE GROWTH
Kardar-Parisi-Zhang · Roughness β=1/3 · Family-Vicsek scaling
λ (nonlinear)
1.00
ν (diffusion)
0.50
Noise σ
1.00
Equation type
KPZ (λ≠0)
Edwards-Wilkinson (λ=0)
W(t) = —
β_eff = —
t = 0
∂h/∂t = ν∇²h + λ/2(∇h)² + η
KPZ (1986): universal roughening with
β=1/3
, α=1/2, z=3/2 in 1+1D.
Edwards-Wilkinson (λ=0): β=1/4.
Roughness W(t) = √⟨(h-h̄)²⟩ grows as t^β until saturation at L^α.
Top:
Interface profile h(x,t) over time
Bottom:
log W vs log t with β slope
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