We measure the dispersion relation of capillary waves on a liquid surface by heterodyne x-ray photon correlation spectroscopy near the transition from propagating to overdamped dynamic behavior. A strong deviation of the propagation frequency from the small-damping result omega(p) proportional, variant k(3/2) is observed long before the actual transition where ( partial differential omega(p)/ partial differential k)<0 and omega(p) tends to zero. This behavior is successfully described by expressions derived within linear response theory.
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Madsen et al. (2004) studied this question.
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