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.