Raman scattering from fractals: Simulation on large structures by the method of moments

Mean-field model for the density of states of jammed soft spheres

We propose a class of mean-field models for the isostatic transition of systems of soft spheres, in which the contact network is modeled as a random graph and each contact is associated to d degrees of freedom. We study such models in the hypostatic, isostatic, and hyperstatic regimes. The density of states is evaluated by both the cavity method and exact diagonalization of the dynamical matrix. We show that the model correctly reproduces the main features of the density of states of real packings and, moreover, it predicts the presence of localized modes near the lower band edge. Finally, the behavior of the density of states D(ω)∼ω^{α} for ω→0 in the hyperstatic regime is studied. We find that the model predicts a nontrivial dependence of α on the details of the coordination distribution.

Raman scattering and the low-frequency vibrational spectrum of glasses

We present a theory of low-frequency Raman scattering in glasses, based on the concept that light couples to the elastic strains via spatially fluctuating elasto-optic (Pockels) constants. We show that the Raman intensity is not proportional to the vibrational density of states (as was widely believed), but to a convolution of Pockels constant correlation functions with the dynamic strain susceptibilities of the glass. Using the dynamic susceptibilities of a system with fluctuating elastic constants we are able for the first time to describe the Raman intensity and the anomalous vibration spectrum of a glass on the same footing. Good agreement between the theory and experiment for the Raman spectrum, the density of states, and the specific heat is demonstrated at the example of glassy As(2)S(3).

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. In the contexts of both the single-link coherent potential approximation and a single-defect approximation, two different regimes are clearly identified: if the density of states at zero energy is zero, the usual p(4) law is recovered for small momentum. On the contrary, if the disorder induces a nonvanishing density of states at zero energy, a linear behavior is obtained. The dynamical structure factor is numerically calculated in lattices as large as 96(3) and satisfactorily agrees with the analytical computations.

Relaxation processes in harmonic glasses?

A relaxation process, with the associated phenomenology of sound attenuation and sound velocity dispersion, is found in a simulated harmonic Lennard-Jones glass. We propose to identify this process with the so-called microscopic (or, instantaneous) relaxation process observed in real glasses and supercooled liquids. A model based on the memory function approach accounts for the observation and allows one to relate to each other (1) the characteristic time and strength of this process, (2) the low frequency limit of the dynamic structure factor of the glass, and (3) the high frequency sound attenuation coefficient, with its observed quadratic dependence on the momentum transfer.

Frustration and sound attenuation in structural glasses

Three classes of harmonic disorder systems (Lennard-Jones-like glasses, percolators above threshold, and spring disordered lattices) have been numerically investigated in order to clarify the effect of different types of disorder on the mechanism of high frequency sound attenuation. We introduce the concept of frustration in structural glasses as a measure of the internal stress, and find a strong correlation between the degree of frustration and the exponent alpha that characterizes the momentum dependence of the sound attenuation gamma(Q) approximately Qalpha. In particular, alpha decreases from approximately d+1 in low-frustration systems (where d is the spectral dimension) to approximately 2 for high-frustration systems such as the realistic glasses examined.