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 SO(3)SO(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.

► Possible presence of a conservative self-action in quasicrystals is proven.
► Possible rotational phason inertia is foreseen.
► Local and gradient phason friction are discussed.
► Closed form solutions in a simple case can be used in designing experiments.