arXiv subjects

P. Verrocchio

Publications and source records attributed to P. Verrocchio.

29 records · Page 2Linked to original sources

arXiv2003

Brillouin and Boson peaks in Glasses from vector Euclidean Random Matrix Theory

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 square 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.

cond-mat.dis-nn↗

arXiv2003

Phonons in supercooled liquids: a possible explanation for the Boson Peak

Glasses are amorphous solids, in the sense that they display elastic behaviour. In crystals, elasticity is associated with phonons, quantized sound-wave excitations. Phonon-like excitations exist also in glasses at very high frequencies (THz), and they remarkably persist into the supercooled liquid. A universal feature of these amorphous systems is the Boson peak: the vibrational density of states $g(ω)$ has an excess over the Debye (squared frequency) law, seen as a peak in $g(ω)/ω^2$. We claim 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). Here, by studying the spectra of inherent structures (local minima of the potential energy), we show that this is the case in a realistic glass model: the Boson peak moves to lower frequencies on approaching the phonon-saddle transition and its height diverges at the critical point. The numerical results agree with Euclidean Random Matrix Theory predictions on the existence of a sharp phase transition between an amorphous elastic phase and a phonon-free one.

cond-mat↗

arXiv2002

The liquid-glass transition of silica

We studied the liquid-glass transition of $SiO_2$ by means of replica theory, utilizing an effective pair potential which was proved to reproduce a few experimental features of silica. We found a finite critical temperature $T_0$, where the system undergoes a phase transition related to replica symmetry breaking, in a region where experiments do not show any transition. The possible sources of this discrepancy are discussed.

cond-mat↗

arXiv2001

Vibrations in glasses and Euclidean Random Matrix theory

We study numerically and analytically a simple off-lattice model of scalar harmonic vibrations by means of Euclidean random matrix theory. Since the spectrum of this model shares the most puzzling spectral features with the high-frequency domain of glasses (non-Rayleigh broadening of the Brillouin peak, boson peak and secondary peak), the Euclidean random matrix theory provide a single and fairly simple theoretical framework to their explanation.

cond-mat↗

arXiv2001

Boson peak in an harmonic scalar model

We study, analytically and numerically, an off-lattice model of scalar harmonic vibrations for structural glasses. The model has a Boson-Peak which we argue can be considered as a prototype for materials with a Boson Peak frequency that decreases with lowering temperature. The density evolution of the Boson Peak in silica is qualitatively reproduced. The dispersion relation is linear at the Boson Peak frequency, in agreement with experiments. In our model the Boson Peak is a precursor of a nearby mechanical instability. The Boson Peak is built up by the hybridization of the sound waves with extended, but non propagating (in the sense of a flat dispersion relation), modes.

cond-mat↗

arXiv2001

Vibrational spectrum of topologically disordered systems

The topological nature of the disorder of glasses and supercooled liquids strongly affects their high-frequency dynamics. In order to understand its main features, we analytically studied a simple topologically disordered model, where the particles oscillate around randomly distributed centers, interacting through a generic pair potential. We present results of a resummation of the perturbative expansion in the inverse particle density for the dynamic structure factor and density of states. This gives accurate results for the range of densities found in real systems.

cond-mat.dis-nn↗

arXiv2001

Vibrational spectra in glasses

The findings of X-ray and neutron scattering experiments on amorphous systems are interpreted within the framework of the theory of Euclidean random matrices. This allows to take into account the topological nature of the disorder, a key ingredient which strongly affects the vibrational spectra of those systems. We present a resummation scheme for a perturbative expansion in the inverse particle density, allowing an accurate analytical computation of the dynamical structure factor within the range of densities encountered in real systems.

cond-mat.dis-nn↗

arXiv2001

The dynamical structure factor in topologically disordered systems

A computation of the dynamical structure factor of topologically disordered systems, where the disorder can be described in terms of euclidean random matrices, is presented. Among others, structural glasses and supercooled liquids belong to that class of systems. The computation describes their relevant spectral features in the region of the high frequency sound. The analytical results are tested with numerical simulations and are found to be in very good agreement with them. Our results may explain the findings of inelastic X-ray scattering experiments in various glassy systems.

cond-mat.dis-nn↗

arXiv1999

The dynamical structure factor in disordered systems

We study the spectral width as a function of the external momentum for the dynamical structure factor of a disordered harmonic solid, considered as a toy model for supercooled liquids and glasses. Both in the context of single-link coherent potential approximation and of a single-defect approximation, two different regimes are clearly identified: if the density of states at zero energy is zero, the Rayleigh $p^4$ law is recovered for small momentum. On the contrary, if the disorder induces a non vanishing density of states at zero energy, a linear behaviour is obtained. The dynamical structure factor is numerically calculated in lattices as large as $96^3$, and satisfactorily agrees with the analytical computations.

cond-mat↗

arXiv1999

Lennard-Jones binary mixture: a thermodynamical approach to glass transition

We study the liquid-glass transition of the Lennard-Jones binary mixture introduced by Kob and Andersen from a thermodynamic point of view. By means of the replica approach, translating the problem in the study of a molecular liquid, we study the phase transition due to the entropy crisis and we find that the Kauzmann's temperature $\tk$ is $\sim 0.32$. At the end we compare analytical predictions with numerical results.

cond-mat.dis-nn↗

arXiv1996

Inflation for Bianchi IX model

The influence of Inflation on initial (i.e. at Planck's epoch) large anisotropy of the Universe is studied, considering a more general metric than the isotropic one: the locally rotationally symmetric (L.R.S.) Bianchi IX metric. We find, then, a large set of initial conditions of intrinsic curvature and shear allowing an inflationary epoch that make the anisotropy negligible. These are not trivial because of the non-linearity of the Einstein's equations.

gr-qc↗