All the information  relating to the vibrational dynamics of a solid is encoded within the dynamical matrix, D, of second derivatives of the interatomic potential [1]. For a  disordered system, such as a glass,  D is a random matrix, but subject to certain sum-rule correlations (unlike the case for electrons), so that it does not belong to the Gaussian Orthogonal Ensemble of random  matrices [2] (the number of correlations is comparable with the number of random elements). The dynamical matrix  consists of blocks of matrix  elements arranged both on and off the diagonal.  Thus, D for a disordered system can be characterised by four distributions: the distribution of diagonal matrix elements in diagonal blocks (diagonal-diagonal), off-diagonal-diagonal, diagonal-off-diagonal and off-diagonal-off-diagonal.  The aim of this project  is to understand the  behaviour of these distributions for different  model systems showing very different tendencies of glass formation:
(i) fragile systems (a model glass with predominantly icosahedral order [3] will be studied) and

(ii) strong-forming systems (vitreous silica [4] will be studied).

The comparative evolution of the matrix-element distributions with temperature  in these models will be studied. The temperature region around the glass transition is of particular interest with a view to understanding how the transition between solid glass and liquid melt takes place [5]. In addition, an attempt will be made to understand the shapes of the distribution functions, e.g. by comparing with those for positionally disordered crystalline analogues (e.g. cristobalite).