Related papers: Sparse random matrices and vibrational spectra of …
We investigate the noise sensitivity of the top eigenvector of a sparse random symmetric matrix. Let $v$ be the top eigenvector of an $N\times N$ sparse random symmetric matrix with an average of $d$ non-zero centered entries per row. We…
The motion of molecules on solid surfaces is of interest for technological applications such as catalysis and lubrication, but it is also a theoretical challenge at a more fundamental level. The concept of activation barriers is very…
Amorphous solids exhibit an excess of low-frequency vibrational modes beyond the Debye prediction, contributing to their anomalous mechanical and thermal properties. Although a $\omega^4$ power-law scaling is often proposed for the…
We comprehensively study mechanical and vibrational properties of dimer packings in three-dimensional space with particular attention on critical scaling behaviors near the jamming transition. First, we confirm the dependence of the packing…
Random banded matrices with linearly increasing diagonal elements are recently considered as an attractive model for complex nuclei and atoms. Apart from early papers by Wigner \cite{Wig} there were no analytical studies on the subject. In…
We propose a general one-dimensional {\em continuous} formulation to analyze the vibrational modes of antenna-like nanomechanical resonators consisting of two symmetric arrays of cantilevers affixed to a central nano-beam. The cantilever…
Dispersive waves in two-dimensional blocky materials with periodic microstructure made up of equal rigid units having polygonal centro-symmetric shape with mass and gyroscopic inertia, connected each other through homogeneous linear…
In the jamming transition of monodisperse packings, spatial heterogeneity is irrelevant as the transition is described by mean-field theories. Here, we show that this situation drastically changes if the particle-size dispersity is large…
We consider the joint distribution of real and imaginary parts of eigenvalues of random matrices with independent entries with mean zero and unit variance. We prove the convergence of this distribution to the uniform distribution on the…
Several general results are derived for diffuse waves in anisotropic solids, including concise expressions for the modal density per unit volume and for the participation factor matrix G. The latter is a second order tensor which describes…
Matrices are said to behave as free non-commuting random variables if the action which governs their dynamics constrains only their eigenvalues, i.e. depends on traces of powers of individual matrices. The authors use recently developed…
Recent research has made significant progress in understanding the non-phonon vibrational states present in amorphous materials. It has been established that their vibrational density of states follows non-Debye scaling laws. Here, we show…
We consider random non-normal matrices constructed by removing one row and column from samples from Dyson's circular ensembles or samples from the classical compact groups. We develop sparse matrix models whose spectral measures match these…
Resonance modes are intrinsic characteristics of objects when excited at those frequencies. Probing the resonance signatures can reveal useful information about material composition, geometry, presence of defects, and other characteristics…
We consider a collection of weakly interacting diffusion processes moving in a two-scale locally periodic environment. We study the large deviations principle of the empirical distribution of the particles' positions in the combined limit…
An invariant ensemble of $N\times N$ random matrices can be characterised by a joint distribution for eigenvalues $P(\lambda_1,\cdots,\lambda_N)$. The study of the distribution of linear statistics, i.e. of quantities of the form…
The quasiprobability distribution of the discrete Wigner function provides a complete description of a quantum state and is, therefore, a useful alternative to the usual density matrix description. Moreover, the experimental quantum state…
Many systems, including polymers and molecular liquids, when adequately cooled and/or compressed, solidify into a disordered solid, i.e., a glass. The~transition is not abrupt, featuring progressive decrease of the microscopic mobility and…
Statistical properties of coherent radiation propagating in a quasi - 1D random media is studied in the framework of random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission…
The equations of motion in a macroscopically inhomogeneous porous medium saturated by a fluid are derived. As a first verification of the validity of these equations, a two-layer rigid frame porous system considered as one single porous…