Interface width W(t)
—
Growth exponent β
—
Time t
0
Height max−min
—
KPZ equation (Kardar-Parisi-Zhang 1986):
∂h/∂t = ν∇²h + λ/2 (∇h)² + η
Growth exponents:
• KPZ: β=1/3, χ=1/2, z=3/2
• EW (λ=0): β=1/4
• Random: β=1/2
KPZ universality class describes: burning fronts, bacteria colonies, coffee rings, Tetris.
Fluctuations ∼ Tracy-Widom GUE distribution — a random matrix result!
∂h/∂t = ν∇²h + λ/2 (∇h)² + η
Growth exponents:
• KPZ: β=1/3, χ=1/2, z=3/2
• EW (λ=0): β=1/4
• Random: β=1/2
KPZ universality class describes: burning fronts, bacteria colonies, coffee rings, Tetris.
Fluctuations ∼ Tracy-Widom GUE distribution — a random matrix result!