1/fnoise for driven interfaces

Velocity-fluctuation spectra are proposed as a probe of the dynamic scaling of moving interfaces. Using the theory of Kardar, Parisi, and Zhang [Phys. Rev. Lett. 56, 889 (1986)] it is shown that the spectrum of the spatially averaged displacement velocity diverges as 1/f at low frequencies, where {α}=1/3 ({α}{}0.7) for a one- (two-) dimensional interface. This implies superdiffusive motion of the average interface position, which is verified numerically. The fluctuation spectrum of the stationary interface width diverges as 1/f^2+α Simulations of interfaces driven by non-Gaussian noise are also presented.