New paradigm for glassy-like anomalies in solids from fundamental symmetries

Glasses and disordered materials are known to display anomalous features in the density of states, in the specific heat and in thermal transport. Nevertheless, in recent years, the question whether these properties are really anomalous (and peculiar of disordered systems) or rather more universal than previously thought, has emerged. New experimental and theoretical observations have questioned the origin of the boson peak (BP) and the linear in T specific heat exclusively from disorder and two-level systems (TLS). The same properties have been indeed observed in ordered or minimally disordered compounds and in incommensurate structures for which the standard explanations are not applicable. Using the formal analogy between phason modes (e.g., in quasicrystals and incommensurate lattices) and diffusions, and between amplitude modes and optical phonons, we suggest the existence of a more universal physics behind these properties. In particular, we strengthen the idea that linear in T specific heat is linked to low energy diffusive modes resulting from fundamental symmetries, and that a BP excess can be induced in crystals either by gapped optical-like modes and/or by anharmonic diffusive (Akhiezer) damping.