The Debye approximation for the acoustic modes in crystals is based on the assumption that the medium is an elastic continuum. It holds true for wavelengths much larger than the typical interatomic distance and gradually breaks down on approaching the microscopic scale. In glasses, the structural disorder undermines this approximation in a quite subtle way, still not completely clarified. Using molecular dynamics simulations of a model monoatomic glass of unprecedent size, we will show that the breakdown of the Debye approximation appears in glasses quite abruptly. It shows up as a significant reduction of the sound velocity with respect to the macroscopic value, on the mesoscopic length-scale of the order of ten interatomic spacings. We will also show that this features allows us to rationalize the ubiquitous excess over the Debye level found in the specific heat of glasses at low temperatures.

G. Monaco and S. Mossa, preprint arXiv:0901.4736v1 (2009)