Edwards-Wilkinson Interface Growth
Surface fluctuations, KPZ universality, and scaling exponents
Parameters
Model
Edwards-Wilkinson
KPZ (nonlinear)
Random Deposition
ν (surface tension)
1.0
λ (KPZ nonlin.)
0.5
Noise σ
1.0
Speed
3
EW exponents:
χ=1/2, z=2, β=1/4 (1D)
KPZ exponents:
χ=1/2, z=3/2, β=1/3 (1D)
W(t) =
—
⟨h⟩ =
—
W ~ t^β → L^χ (Family-Vicsek)
Interface Profile h(x,t)
Roughness W(t) = √⟨(h-⟨h⟩)²⟩ (log-log)