Theory of the Crossover in the Low-Frequency Dynamics of an Incommensurate System,Hg3−δAsF6

The dynamic structure factor of a three-dimensional crystal, with an interpenetrating set of atomic chains which form one-dimensional fluids, is studied. At high frequencies there are two longitudinal acoustic modes arising from the separate motion of the lattice and fluid. At low frequencies there is one combined propagating longitudinal acoustic mode and a diffusive excitation due to particle motion. The crossover between these regions is predicted to occur at a frequency ∼ MHz in ${\mathrm{Hg}}_{3-\delta }\mathrm{As}{\mathrm{F}}_6$.