Vibrational spectra of amorphous clusters: Universal aspects

We have performed extensive numerical computations on the vibrational spectra of isolated amorphous clusters of medium to large size and containing one or two types of atoms. The interaction potential is also varied to study possible universality. For all the potentials and cluster sizes we find that the cumulative density of states can be described very accurately by the same functional form over a large central region of the spectrum. This functional form contains only one scale of frequency. We also find that the statistical fluctuations of the spectra are described by the Gaussian orthogonal ensemble of random matrices. For the largest clusters this is tested to a very high degree of precision in the central region and to a somewhat lower degree for most of the rest of the spectrum. We put forward a conjecture regarding the domain of the space of local minima of the potential energy function where universality with respect to the density of states function may be expected.