Noise and fluctuations of rough surfaces

Correlated non-Gaussian noise of the quenched disorder on rough surfaces is analyzed on the basis of stochastic differential and integral equations. The irregular fluctuations reflect the microstructure of rough surfaces and the stochastic process is treated as Brownian motion. The microstructure refers to the standard deviation sigma, correlation length xi, and roughness exponent alpha that defines the scaling properties of the surface. We have derived the noise correlation function [eta(0)eta(r)] similar to (r/xi)(2 alpha-2) for 1/2 < alpha < 1 on a self-affine rough surface. This provides a physical justification of noise with long-range correlation, and the anomalous behavior of alpha > 1/2 observed experimentally.