Related papers: Sparse random matrix configurations for two or thr…
We numerically study the structure of the interactions occurring in three-dimensional systems of hard spheres at jamming, focusing on the large-scale behavior. Given the fundamental role they play in the configuration of jammed packings, we…
We study ensembles of sparse random block matrices generated from the adjacency matrix of a Erd\"os-Renyi random graph with $N$ vertices of average degree $Z$, inserting a real symmetric $d \times d$ random block at each non-vanishing…
Much evidence has been collected to date which shows that repulsive electron-electron interaction can lead to the formation of particle pairs in a one-dimensional random energy landscape. The localization length \lambda_2 of these pair…
The spectral properties of a disordered system with few interacting three-dimensional spinless fermions are investigated. We show the existence of a critical spacings distribution which is invariant upon increase of the system size, but…
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…
A transfer matrix approach is used to study the electronic transport in graphene superlattices with long-range correlated barrier spacements. By considering the low-energy electronic excitations as massless Dirac fermions, we compute by…
The input to the configuration-interaction shell model includes many dozens or hundreds of independent two-body matrix elements. Previous studies have shown that when fitting to experimental low-lying spectra, the greatest sensitivity is to…
A systematic method to account for electron correlation in periodic systems which can predict quantitatively correct band structures of non-conducting solids from first principles is presented. Using localized Hartree-Fock orbitals (both…
We review recently introduced numerical methods for the unbiased detection of the order parameter and/or dominant correlations, in many-body interacting systems, by using reduced density matrices. Most of the paper is devoted to the…
We extend probability estimates on the smallest singular value of random matrices with independent entries to a class of sparse random matrices. We show that one can relax a previously used condition of uniform boundedness of the variances…
A cross matrix $X$ can have nonzero elements located only on the main diagonal and the anti-diagonal, so that the sparsity pattern has the shape of a cross. It is shown that $X$ can be factorized into products of matrices that are at most…
The task of analytically diagonalizing a tridiagonal matrix can be considerably simplified when a part of the matrix is uniform. Such quasi-uniform matrices occur in several physical contexts, both classical and quantum, where…
This paper concerns the large deviations of a system of interacting particles on a random graph. There is no stochasticity, and the only sources of disorder are the random graph connections, and the initial condition. The average number of…
In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding…
We analyse the stability of large, linear dynamical systems of variables that interact through a fully connected random matrix and have inhomogeneous growth rates. We show that in the absence of correlations between the coupling strengths,…
We consider a model of an electric circuit, where differential algebraic equations for a circuit part are coupled to partial differential equations for an electromagnetic field part. An uncertainty quantification is performed by changing…
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…
Short-range corrections to long-range selected configuration interaction calculations are derived from perturbation theory considerations and applied to harmonium (with two to six electrons for some low-lying states). No fitting to…
We present a non-perturbative expression for the scattering matrix of $N$ particles interacting inside a quantum dot. Characterizing the dot by its resonances, we find a compact form for the scattering matrix in a real-time representation.…
Motivated by the recent finding of superconductivity in layered CoO_2 compounds, we investigate superconducting and magnetic instabilities of interacting electrons on the two-dimensional triangular lattice. Using a one-loop renormalization…