Brillouin and boson peaks in glasses from vector Euclidean random matrix theory

Abstract

A simple model of harmonic vibrations in topologically disordered systems, such as glasses and supercooled liquids, is studied analytically by extending Euclidean Random Matrix Theory to include vector vibrations. Rather generally, it is found that i) the dynamic structure factor shows sound-like Brillouin peaks whose longitudinal/transverse character can only be distinguished for small transferred momentum, p, ii) the model presents a mechanical instability transition at small densities, for which scaling laws are analytically predicted and confirmed numerically, iii) the Brillouin peaks persist deep into the unstable phase, the phase transition being noticeable mostly in their linewidth, iv) the Brillouin linewidth scales like p 2 in the stable phase, and like p in the unstable one. The analytical results are checked numerically for a simple potential. The main features of glassy vibrations previously deduced from scalar ERMT are not substantially altered by these new results.

Glasslike Structure of Globular Proteins and the Boson Peak

“…our effective density, decreases. From the lower panels of Fig 2 one can clearly appreciate that the scaling followed by ω BP and h BP is very well interpolated by the analytical functional forms predicted by the ERM theory in the mean-field approximation [16], i.e.…”

“…Recently, a quantitative description of the BP phenomenology has been given whithin the formalism of the Euclidean Random Matrix (ERM) theory [16], whose predictions have been confirmed by numerical simulations on realistic glass-forming systems, emphasizing its universal character [17].…”

“…In this context, several possible explanations have been proposed, from the two-level system scenario [10] to localized modes arising from a strong scattering of the phonons by the disorder [11], from "glassy" van Hove singularities [12] to a mechanical instability [13]. Recently, the possibility that a BP may be a general feature of weakly connected systems has also been investigated [14,15].In a different analytical framework [16], the excess of low-energy modes with respect to the Debye behaviour is viewed as a symptomatic effect of the topological phase transition which is conjectured to happen in glasses at low temperatures [13]. Recently, a quantitative description of the BP phenomenology has been given whithin the formalism of the Euclidean Random Matrix (ERM) theory [16], whose predictions have been confirmed by numerical simulations on realistic glass-forming systems, emphasizing its universal character [17].…”

“…In a different analytical framework [16], the excess of low-energy modes with respect to the Debye behaviour is viewed as a symptomatic effect of the topological phase transition which is conjectured to happen in glasses at low temperatures [13]. Recently, a quantitative description of the BP phenomenology has been given whithin the formalism of the Euclidean Random Matrix (ERM) theory [16], whose predictions have been confirmed by numerical simulations on realistic glass-forming systems, emphasizing its universal character [17].…”

Elastic anomalies at terahertz frequencies and excess density of vibrational states in silica glass

“…In the one-phonon approximation the inelastic contribution to the dynamic structure factor can be written in terms of the longitudinal part G L (Q,z) of the resolvent operator of the dynamical matrix in the wave vector representation: 38,39 …”