  Investigating the relationship between structure and dynamical processes is a
central goal in condensed matter physics. Perhaps the most noted relationship
between the two is the phenomenon of de Gennes narrowing, in which relaxation
times in liquids are proportional to the scattering structure factor. Here a
similar relationship is discovered during the self-organized ion beam
nanopatterning of silicon using coherent x-ray scattering. However, in contrast
to the exponential relaxation of fluctuations in classic de Gennes narrowing,
the dynamic surface exhibits a wide range of behaviors as a function of length
scale, with a compressed exponential relaxation at lengths corresponding to the
dominant structural motif - self-organized nanoscale ripples. These behaviors
are reproduced in simulations of a nonlinear model describing the surface
evolution. We suggest that the compressed exponential behavior observed here is
due to the morphological persistence of the self-organized surface ripple
patterns which form and evolve during ion beam nanopatterning.
