Euclidean random matrix theory: low-frequency non-analyticities and Rayleigh scattering

By calculating all terms of the high-density expansion of the euclidean random matrix theory (up to second-order in the inverse density) for the vibrational spectrum of a topologically disordered system we show that the low-frequency behavior of the self energy is given by $\Sigma(k,z)\propto k^2z^{d/2}$ and not $\Sigma(k,z)\propto k^2z^{(d-2)/2}$, as claimed previously. This implies the presence of Rayleigh scattering and long-time tails of the velocity autocorrelation function of the analogous diffusion problem of the form $Z(t)\propto t^{(d+2)/2}$.Comment: 27 page

Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"

We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the single-bond coherent potential approximation. The results for the density of states $g(\omega)$ are in excellent agreement with each other. As the degree of disorder is increased the system becomes unstable due to the presence of negative force constants. If the system is near the borderline of stability a low-frequency peak appears in the reduced density of states $g(\omega)/\omega^2$ as a precursor of the instability. We argue that this peak is the analogon of the "boson peak", observed in structural glasses. By means of the level distance statistics we show that the peak is not associated with localized states

Physical Origin of the Boson Peak Deduced from a Two-Order-Parameter Model of Liquid

We propose that the boson peak originates from the (quasi-) localized vibrational modes associated with long-lived locally favored structures, which are intrinsic to a liquid state and are randomly distributed in a sea of normal-liquid structures. This tells us that the number density of locally favored structures is an important physical factor determining the intensity of the boson peak. In our two-order-parameter model of the liquid-glass transition, the locally favored structures act as impurities disturbing crystallization and thus lead to vitrification. This naturally explains the dependence of the intensity of the boson peak on temperature, pressure, and fragility, and also the close correlation between the boson peak and the first sharp diffraction peak (or prepeak).Comment: 5 pages, 1 figure, An error in the reference (Ref. 7) was correcte

Continuum limit of amorphous elastic bodies: A finite-size study of low frequency harmonic vibrations

The approach of the elastic continuum limit in small amorphous bodies formed by weakly polydisperse Lennard-Jones beads is investigated in a systematic finite-size study. We show that classical continuum elasticity breaks down when the wavelength of the sollicitation is smaller than a characteristic length of approximately 30 molecular sizes. Due to this surprisingly large effect ensembles containing up to N=40,000 particles have been required in two dimensions to yield a convincing match with the classical continuum predictions for the eigenfrequency spectrum of disk-shaped aggregates and periodic bulk systems. The existence of an effective length scale \xi is confirmed by the analysis of the (non-gaussian) noisy part of the low frequency vibrational eigenmodes. Moreover, we relate it to the {\em non-affine} part of the displacement fields under imposed elongation and shear. Similar correlations (vortices) are indeed observed on distances up to \xi~30 particle sizes.Comment: 28 pages, 13 figures, 3 table

Nature of vibrational eigenmodes in topologically disordered solids

We use a local projectional analysis method to investigate the effect of topological disorder on the vibrational dynamics in a model glass simulated by molecular dynamics. Evidence is presented that the vibrational eigenmodes in the glass are generically related to the corresponding eigenmodes of its crystalline counterpart via disorder-induced level-repelling and hybridization effects. It is argued that the effect of topological disorder in the glass on the dynamical matrix can be simulated by introducing positional disorder in a crystalline counterpart.Comment: 7 pages, 6 figures, PRB, to be publishe

Localized and Delocalized Charge Transport in Single-Wall Carbon-Nanotube Mats

We measured the complex dielectric constant in mats of single-wall carbon-nanotubes between 2.7 K and 300 K up to 0.5 THz. The data are well understood in a Drude approach with a negligible temperature dependence of the plasma frequency (omega_p) and scattering time (tau) with an additional contribution of localized charges. The dielectric properties resemble those of the best ''metallic'' polypyrroles and polyanilines. The absence of metallic islands makes the mats a relevant piece in the puzzle of the interpretation of tau and omega_p in these polymers.Comment: 4 pages including 4 figure

Hopping Transport in the Presence of Site Energy Disorder: Temperature and Concentration Scaling of Conductivity Spectra

Recent measurements on ion conducting glasses have revealed that conductivity spectra for various temperatures and ionic concentrations can be superimposed onto a common master curve by an appropriate rescaling of the conductivity and frequency. In order to understand the origin of the observed scaling behavior, we investigate by Monte Carlo simulations the diffusion of particles in a lattice with site energy disorder for a wide range of both temperatures and concentrations. While the model can account for the changes in ionic activation energies upon changing the concentration, it in general yields conductivity spectra that exhibit no scaling behavior. However, for typical concentrations and sufficiently low temperatures, a fairly good data collapse is obtained analogous to that found in experiment.Comment: 6 pages, 4 figure

Density of states in random lattices with translational invariance

We propose a random matrix approach to describe vibrational excitations in disordered systems. The dynamical matrix M is taken in the form M=AA^T where A is some real (not generally symmetric) random matrix. It guaranties that M is a positive definite matrix which is necessary for mechanical stability of the system. We built matrix A on a simple cubic lattice with translational invariance and interaction between nearest neighbors. We found that for certain type of disorder phonons cannot propagate through the lattice and the density of states g(w) is a constant at small w. The reason is a breakdown of affine assumptions and inapplicability of the elasticity theory. Young modulus goes to zero in the thermodynamic limit. It strongly reminds of the properties of a granular matter at the jamming transition point. Most of the vibrations are delocalized and similar to diffusons introduced by Allen, Feldman et al., Phil. Mag. B v.79, 1715 (1999).Comment: 4 pages, 5 figure

Elastic constant dishomogeneity and Q2Q^2 dependence of the broadening of the dynamical structure factor in disordered systems

We propose an explanation for the quadratic dependence on the momentum $Q$, of the broadening of the acoustic excitation peak recently found in the study of the dynamic structure factor of many real and simulated glasses. We ascribe the observed $Q^2$ law to the spatial fluctuations of the local wavelength of the collective vibrational modes, in turn produced by the dishomegeneity of the inter-particle elastic constants. This explanation is analitically shown to hold for 1-dimensional disordered chains and satisfatorily numerically tested in both 1 and 3 dimensions.Comment: 4 pages, RevTeX, 5 postscript figure