Physics Practical Magic

A new mathematical tool can finally sort the chaotic vibrations of glass into organized maps.

April 23, 2026

Original Paper

The vibrational spectrum of vitreous silica: rigorous decomposition via recursive orthogonal splitting analysis

arXiv · 2604.17933

The Takeaway

Atoms in a crystal vibrate in predictable patterns, but the atoms in glass are a jumbled mess. This structural randomness has made it nearly impossible for scientists to categorize how glass vibrates and transfers heat. A new framework called ROSA uses recursive math to decompose this chaos into distinct types of motion. It provides the first clear map for the internal energy of amorphous materials. This tool will allow engineers to design glass and polymers with specific thermal or acoustic properties. It turns the study of random materials into a precise science.

From the abstract

Our understanding of vibrations in solids currently rests on concepts and techniques designed for crystals and explicitly relying on periodicity, hence inapplicable to amorphous materials. As a consequence, no established framework enables a systematic decomposition of the vibrational spectrum of amorphous solids into contributions associated with well-defined types of atomic motions. This methodological gap obscures the interpretation of various experimental probes of linear response, based on