On the Euclidean random matrix model of vibrations in glass

Despite their important role in industrial applications and everyday life, and decades of research, disordered solids still lack a full theoretical understanding. In this perspective, we propose that the Euclidean random matrix model can serve as a paradigm for a low-temperature glass. It combines disorder, viz. random particle positions, with the harmonic approximation of the potential energy valid for any stable solid as temperature vanishes. It brings random-matrix concepts to bear on a fundamental understanding of the vibrational anomalies of glasses. We discuss recent studies that demonstrated non-affine displacements renormalizing the Born elastic constants, damping of sound waves via correlated scattering processes from the intrinsic disorder, excess low-frequency modes linked to the widely-observed boson peak, and elastic instabilities. Disordered solids are ubiquitous yet still lack a complete theoretical description. This perspective proposes the Euclidean random matrix model, combining disorder via random positions with harmonic interactions, as a minimal framework for vibrational anomalies in glasses.