Amorphous solids as fuzzy crystals: A Debye-like theory of low-temperature specific heat.

The formulation of a fundamental theoretical description of disordered solids is a standing challenge in condensed matter physics. So far, the structure and dynamics of glasses is described in the literature on the basis of phenomenological models. We develop a theoretical framework for amorphous materials, relying on the basic principle that the disorder in a glass is similar to the disorder in a classical fluid, while the latter is mathematically encoded by noncommutative coordinates in the Lagrange formulation of fluid mechanics. Under this principle, we construct a model of the amorphous solids as fuzzy crystals and we establish an analytical theory of vibrations for glasses, that naturally contains the boson peak as a manifestation of an extended van Hove singularity.