Using a stable random matrix approach, we consider the diffusion of vibrations in $3d$ harmonic lattices with strong force-constant disorder. Above some frequency ${\omega }_{\mathrm{IR}}$, corresponding to the Ioffe-Regel crossover, the notion of phonons becomes ill defined. They cannot propagate through the system and transfer energy. Nevertheless, most of the vibrations in this range are not localized. We show that they are similar to diffusons introduced by Allen et al. [P. B. Allen, J. L. Feldman, J. Fabian, and F. Wooten, Phil. Mag. B 79, 1715 (1999)] to describe heat transport in glasses. The crossover frequency ${\omega }_{\mathrm{IR}}$ is close to the position of the boson peak. By changing the strength of disorder we can vary ${\omega }_{\mathrm{IR}}$ from zero value (when the rigidity is zero and there are no phonons in the lattice) up to a typical frequency in the system. Above ${\omega }_{\mathrm{IR}}$, the energy in the lattice is transferred by means of diffusion of vibrational excitations. We calculated the diffusivity of the modes $D\left(\omega \right)$ using both the direct numerical solution of the Newton equations and the formula of Edwards and Thouless. It is nearly a constant above ${\omega }_{\mathrm{IR}}$ and goes to zero at the localization threshold. We show that apart from the diffusion of energy, a diffusion of particle displacements in the lattice takes place as well. Above ${\omega }_{\mathrm{IR}}$, a displacement structure factor $S(\mathbf{q},\omega )$ coincides well with a structure factor of random walk on the lattice. As a result, the vibrational line width is $\Gamma \left(q\right)=D_u{q}^2$, where $D_u$ is a diffusion coefficient of particle displacements. These findings may be important for the interpretation of experimental data on inelastic x-ray scattering and mechanisms of heat transfer in glasses. We also show that the scaling with model parameters in our model maps directly onto the scaling observed in the jamming transition model.

The vibrational properties of model amorphous materials are studied by combining complete analysis of the vibration modes, dynamical structure factor, and energy diffusivity with exact diagonalization of the dynamical matrix and the kernel polynomial method, which allows a study of very large system sizes. Different materials are studied that differ only by the bending rigidity of the interactions in a Stillinger-Weber modelization used to describe amorphous silicon. The local bending rigidity can thus be used as a control parameter, to tune the sound velocity together with local bonds directionality. It is shown that for all the systems studied, the upper limit of the Boson peak corresponds to the Ioffe-Regel criterion for transverse waves, as well as to a minimum of the diffusivity. The Boson peak is followed by a diffusivity's increase supported by longitudinal phonons. The Ioffe-Regel criterion for transverse waves corresponds to a common characteristic mean-free path of 5–7 Å (which is slightly bigger for longitudinal phonons), while the fine structure of the vibrational density of states is shown to be sensitive to the local bending rigidity.

By numerical simulations and analytical studies, we show that the phenomenon of microwave-induced resistance oscillations can be understood as a classical memory effect caused by recollisions of electrons with scattering centers after a cyclotron period. We develop a Drude-like approach to magnetotransport in the presence of a microwave field, taking into account memory effects, and find an excellent agreement between numerical and analytical results, as well as a qualitative agreement with experiment.

In amorphous solids, a non-negligible part of thermal conductivity results from phonon scattering on the structural disorder. The conversion of acoustic energy into thermal energy is often measured by the dynamical dtructure factor (DSF) thanks to inelastic neutron or x-ray scattering. The DSF is used to quantify the dispersion relation of phonons, together with their damping. However, the connection of the dynamical structure factor with dynamical attenuation of wave packets in glasses is still a matter of debate. We focus here on the analysis of wave-packet propagation in numerical models of amorphous silicon. We show that the damped harmonic oscillator model fits of the dynamical structure factors give a good estimate of the wave packets mean free path, only below the Ioffe-Regel frequency. Above the Ioffe-Regel frequency and below the mobility edge, a pure diffusive regime without a definite mean free path is observed. The high-frequency mobility edge is characteristic of a transition to localized vibrations. Below the Ioffe-Regel frequency, a mixed regime is evidenced at intermediate frequencies, with a coexistence of propagative and diffusive wave fronts. The transition between these different regimes is analyzed in detail and reveals a complex dynamics for energy transport, thus raising the question of the correct modeling of thermal transport in amorphous materials.

The paper presents a comprehensive analysis of the elastic properties of polystyrene-based nanocomposites filled with different types of inclusions: small spherical particles (SiO₂ and Al₂O₃), alumosilicates (montmorillonite, halloysite natural tubules and mica), and carbon nanofillers (carbon black and multi-walled carbon nanotubes). Block samples of composites with different filler concentrations were fabricated by melt technology, and their linear and non-linear elastic properties were studied. The introduction of more rigid particles led to a more profound increase in the elastic modulus of a composite, with the highest rise of about 80% obtained with carbon fillers. Non-linear elastic moduli of composites were shown to be more sensitive to addition of filler particles to the polymer matrix than linear ones. A non-linearity modulus β_s comprising the combination of linear and non-linear elastic moduli of a material demonstrated considerable changes correlating with those of the Young’s modulus. The changes in non-linear elasticity of fabricated composites were compared with parameters of bulk non-linear strain waves propagating in them. Variations of wave velocity and decay decrement correlated with the observed enhancement of materials’ non-linearity.

The random matrix theory has been used for analyzing vibrational spectra of amorphous solids. The random dynamical matrix M = AA T with nonnegative eigenvalues ɛ = ω2has been investigated. The...