Phason Dynamics of Incommensurate Crystals

It is shown that phase modulations (phasons) of the order parameters of incommensurate lattices are always diffusive at sufficiently large wavelengths $\lambda$. In general there is a crossover from diffusive behavior for $\lambda \gg \Lambda$ to propagating behavior for $\lambda \ll \Lambda$ where $\Lambda$ is a mean free path due to nonlinear interactions. The present results explain why light- and neutron-scattering experiments probe different dynamical behavior of phasons.