  Despite the presence of topological disorder, phonons seem to exist also in
glasses at very high frequencies (THz) and they remarkably persist into the
supercooled liquid. A universal feature of such a systems is the Boson peak, an
excess of states over the standard Debye contribution at the vibrational
density of states. Exploiting the euclidean random matrix theory of vibrations
in amorphous systems we show that this peak is the signature of a phase
transition in the space of the stationary points of the energy, from a
minima-dominated phase (with phonons) at low energy to a saddle-point dominated
phase (without phonons). The theoretical predictions are checked by means of
numeric simulations.
