Theory of coupled phason and sound-wave normal modes in the incommensurate phase of quartz

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Abstract
A phenomenological theory for coupled phasons and sound waves in the presence of viscous damping of the relative phase motion is developed for the incommensurate phase of quartz. For weak damping, five propagating normal modes occur, whereas for strong damping we find propagating nearly pure sound waves, fast relaxing nearly pure relative phase motion, and diffusive coupled sound-wave and relative phase motion. Technical points of interest are the introduction of a relative phase-displacement field, and the discussion of the rotational invariance of the free energy.