Inversion symmetric two-level systems and the low-temperature universality in disordered solids

The low-temperature universal properties in disordered and amorphous solids are considered. We introduce a model that includes two types of two-level systems (TLSs), which, based on their local symmetry, interact weakly or strongly with the phonon field. This accounts well for the experimental results and addresses some long-standing questions: the nature of the TLSs, the smallness and universality of the phonon attenuation, and the energy scale of 3 K below which universality is observed. Our model describes disordered lattices; we also discuss its application to amorphous solids.