title: Phonon interpretation of the 'boson peak' in supercooled liquids.
abstract: Glasses are amorphous solids, in the sense that they display elastic behaviour. In crystalline solids, elasticity is associated with phonons, which are quantized vibrational excitations. Phonon-like excitations also exist in glasses at very high (terahertz; 10(12) Hz) frequencies; surprisingly, these persist in the supercooled liquids. A universal feature of such amorphous systems is the boson peak: the vibrational density of states has an excess compared to the Debye squared-frequency law. Here we investigate the origin of this feature by studying the spectra of inherent structures (local minima of the potential energy) in a realistic glass model. We claim that the 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 boson peak moves to lower frequencies on approaching the phonon-saddle transition, and its height diverges at the critical point. Our numerical results agree with the predictions of euclidean random matrix theory on the existence of a sharp phase transition between an amorphous elastic phase and a phonon-free one.
authors.affiliation: Dipartimento di Fisica, Sezione INFN, SMC and INFM unità di Roma 1, Università di Roma La Sapienza, Piazzale Aldo Moro 2, I-00185 Roma, Italy.
authors.forename: T S
authors.initials: TS
authors.lastname: Grigera
authors.forename: V
authors.initials: V
authors.lastname: Martín-Mayor
authors.forename: G
authors.initials: G
authors.lastname: Parisi
authors.forename: P
authors.initials: P
authors.lastname: Verrocchio