Theory of Phasons in Aperiodic Crystals

The possibility of embedding a quasi-periodic structure into a higher-dimensional superspace gives rise to an interpretation of certain dynamical excitations as motions in the additional space. These excitations then are called phason excitations. There is always infinite degeneracy of the ground state of an aperiodic quasi-periodic system, but this degeneracy leads only to zero frequency modes if the atomic surfaces are smooth. If this is not the case, there is a phason gap. When the atomic surfaces are continuous, the linear phason excitations with low frequency may get an arbitrary amplitude. The excitations are almost frictionless when the velocity is below a threshold value. Above that value there is dissipation (i.e. energy transfer to phonons) even for smooth atomic surfaces.