A hydrodynamic description of the vibrational modes of ordered and disordered systems.

In ordinary crystals, Debye theory represents a very successful framework to characterize the dynamics of the vibrational excitations – the phonons, and to predict macroscopic quantities such as specific heat. Disordered systems and in general systems with dissipation provide a challenge to this description, which is manifested in several anomalous properties, e.g. the Boson Peak (BP) excess in the VDOS and the linear in temperature specific heat. Given the universality of these anomalies and their recent observation also in ordered single crystals with no disorder, a more general derivation (not necessarily relying on the presence of disorder) is needed. In this talk we provide such description using a hydrodynamic- effective field theory approach. We prove that a universal BP emerges naturally from the competition between propagation-elasticity and dissipation/diffusive damping. We also show a dependence of the BP in function of the material density which is in perfect agreement with the experimental data. Additionally, we show that the existence of hydrodynamic quasi-localized diffusive mode – the diffusons – can explain the linear in T specific heat in glasses and be therefore an alternative to the well-known TTLS theory.