Vibrations of amorphous, nanometric structures: When does continuum theory apply?

We investigate the low-frequency end of the vibrational spectrum in small (nanometric) disordered systems. Using numerical simulation and exact diagonalization for simple two-dimensional models, we show that continuum elasticity, applied to these systems, actually breaks down below a length scale of typically 30 to 50 molecular sizes. This length scale is likely related to the one which is generally invoked to explain the peculiar vibrational properties of glassy systems.