Amended tunneling model to explain the anisotropy of the glassy properties of crystals and quasicrystals*

The low temperature acoustic and thermal properties of amorphous, glassy materials are remarkably similar and they can be explained to a large extent by assuming that the material contains a large number of dynamic defects. These dynamic defects are tunneling systems and are modeled by an ensemble of two-level systems (TLS). Crystals with defects--with a large enough amount of disorder--exhibit also glass-like properties, but these properties are not so universal and, even more, they are not isotropic. In Phys. Rev. B {\bf 75}, 064202 (2007) we proposed an amended model for the description of the interaction of two-level systems with arbitrary strain fields. Here we show how this model explains the anisotropy of the glass-like properties of disordered crystals and quasicrystals.