Related papers: Sparse random matrices and vibrational spectra of …
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…
We present a random matrix approach to study general vibrational properties of stable amorphous solids with translational invariance using the correlated Wishart ensemble. Within this approach, both analytical and numerical methods can be…
The density of vibrational states $g(\omega)$ of an amorphous system is studied by using the random-matrix theory. Taking into account the most important correlations between elements of the random matrix of the system, equations for the…
We present an O(N) algorithm to study the vibrational properties of amorphous silicon within the framework of tight-binding approach. The dynamical matrix elements have been evaluated numerically in the harmonic approximation exploiting the…
We propose a new method to characterize the spatial distribution of particles' vibrations in solids with much lower computational costs compared to the usual normal mode analysis. We excite the specific vibrational mode in a two dimensional…
We develop a theoretical approach to compute the conditioned spectral density of $N \times N$ non-invariant random matrices in the limit $N \rightarrow \infty$. This large deviation observable, defined as the eigenvalue distribution…
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…
We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…
The low-temperature properties of glasses present important differences with respect to crystalline matter. In particular, models such as the Debye model of solids, which assume the existence of an underlying regular lattice, predict that…
We study the spectrum of a system of coupled disordered harmonic oscillators in the thermodynamic limit. This Euclidean random matrix ensemble has been suggested as model for the low-temperature vibrational properties of glass. Exact…
Matrix Models are the most effective way to describe strongly interacting systems with many degrees of freedom. They have proven successful in describing very different settings, from nuclei spectra to conduction in mesoscopic systems, from…
We present a novel approach for parameter-free modeling of the structural, dynamical and electronic properties of non-crystalline materials based on ab-initio Molecular Dynamics, improved signal processing technique and computer…
The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…
Amorphous solids are dynamically inhomogeneous due to in lack of translational symmetry and hence exhibit vibrational properties different from crystalline solids with anomalous low frequency vibrational density of states (VDOS) and related…
We perform Discrete Element Method (DEM) simulations of granular particles (polystyrene spheres) vibrated inside a cubic container. The study investigates the evolution of the packing fraction with and without rotational friction at…
We study amorphous solids with strong elastic disorder and find an un-jamming instability that exists, inter alia, in an harmonic model built using Euclidean random matrices (ERM). Employing the Zwanzig-Mori projection operator formalism…
An algebraic model taking into account the influence of the molecular rotation on the wave functions of vibrational-rotational states of the diatomic molecule using the formalism of the ladder operators and an expansion in a small parameter…
We consider diffusion of vibrations in 3d harmonic lattices with strong force-constant disorder. Above some frequency w_IR, corresponding to the Ioffe-Regel crossover, notion of phonons becomes ill defined. They cannot propagate through the…
We study energy minimized configurations of amorphous solids with a simple shear degree of freedom. We show that the low-frequency regime of the vibrational density of states of structural glass formers is crucially sensitive to the…
It is demonstrated on a realistic model of amorphous alloy Si$_{0.9}$Ge$_{0.1}$ with 1000 atoms, that short-range spectral fluctuations of propagons and diffusons are universal and in agreement with random matrix theory. The universality…