Ciliberti, S.Grigera, T.S.Martín Mayor, VíctorParisi, G.Verrocchio, P.2023-06-202023-06-202004-060094-243x10.1063/1.1764225https://hdl.handle.net/20.500.14352/52190© 2004 American Institute of Physics. International Symposium on Slow Dynamics in Complex Systems (3rd. 2004. Sendai, Japan). V.M.-M. is a Ramón y Cajal research fellow (MCyT, Spain). P.V. was supported through the European Community's Human Potential Programme under contract HPRN-CT-2002-00307, DYGLAGEMEM.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.engjournal articlehttp://aip.scitation.org/doi/abs/10.1063/1.1764225http://aip.scitation.orghttps://arxiv.org/abs/cond-mat/0312073v1open access53Instantaneous normal-modesDensity-of-statesDynamical structure factorRandom-matrix theorySupercooled liquidsVibrational excitationsDisordered-systemsVitreous silicaRelaxation processesMolucular-dynamics.Física-Modelos matemáticos