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The low-temperature properties of glasses present important differences withrespect to crystalline matter. In particular, models such as the Debye model ofsolids, which assume the existence of an underlying regular lattice, predictthat the specific heat of solids varies with the cube of temperature at lowtemperatures. Since the 1970s' at least, it is a well established experimentalfact that the specific heat of glasses is instead just linear in $T$ at $T \sim1K$, and presents a pronounced peak when normalized by $T^{3}$, known as theboson peak. Here we present a new approach which suggests that the vibrationaland thermal properties of amorphous solids are affected by the random matrixpart of the vibrational spectrum. The model is also able to reproduce, for thefirst time, the experimentally observed inverse proportionality between theboson peak in the specific heat and the shear modulus.

Vibrational density of states and specific heat in glasses from random matrix theory