The second-order phase transition between extended and localized states is well-studied in the case of electrons [1]. However, only very recently the similar problem has been addressed and treated by multifractal analysis for atomic vibrations in disordered structures [2]. The aim of the project is to adapt the other known (for electrons) numerical techniques to the case of  atomic vibrations in disordered materials. There are two independent aspects of the project, either:
(i) Implementation of the transfer-matrix formalism to study (numerically) the localization-delocalization (LD) transition for vibrational excitations. This includes a check of the validity of one-parameter scaling theory for atomic vibrations [4],
or
(ii) Calculation of the level statistics (of eigenvalues of the dynamical matrix) in different ranges of the spectrum for atomic vibrations in disordered structures. This implies a search for the LD threshold using the universality properties of the level statistics at the threshold [1].