Phason self-actions in quasicrystals

On the basis of first invariance principles, we discuss reasons for claiming, within continuum mechanics of quasicrystals, the existence of a phason self-action with both conservative and dissipative components. We foresee also the possible presence of deformation-induced rotational phason inertia. In non-linear setting we derive consequences of S O ( 3 ) invariance requirements on state functions and show also that in linearized elastic regime the conservative part of the self-action assures a non-linear spatial decay of the phason field in the absence of inertia effects. Closed form solutions obtained in a simple one-dimensional setting can guide possible experiments.