Related papers: Statistical Properties of Random Banded Matrices w…
Using the supersymmetry method we analytically calculate the local density of states, the localiztion length, the generalized inverse participation ratios, and the distribution function of eigenvector components for the superposition of a…
We show that the diagonal elements of the second-order reduced density matrix (RDM2) can be chosen as basic variables for describing the superconducting state, instead of the off-diagonal elements of the RDM2 that are usually adopted as…
We study statistical properties of a class of band random matrices which naturally appears in systems of interacting particles. The local spectral density is shown to follow the Breit-Wigner distribution in both localized and delocalized…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
Using numerical exact diagonalization, we study matrix elements of a local spin operator in the eigenbasis of two different nonintegrable quantum spin chains. Our emphasis is on the question to what extent local operators can be represented…
We consider the Gaussian ensembles of random matrices and describe the normal modes of the eigenvalue spectrum, i.e., the correlated fluctuations of eigenvalues about their most probable values. The associated normal mode spectrum is…
In this paper we demonstrate numerically that random networks whose adjacency matrices ${\bf A}$ are represented by a diluted version of the Power--Law Banded Random Matrix (PBRM) model have multifractal eigenfunctions. The PBRM model…
Our goal is to study statistical properies of "dielectric resonances" which are poles of conductance of a large random $LC$ network. Such poles are a particular example of eigenvalues $\lambda_n$ of matrix pencils ${\bf H}-\lambda {\bf W}$,…
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 wave propagation in random medium plays a critical role in optics and quantum physics. Multiple scattering of coherent wave in a random medium determines the transport procedure. Brownian motions of the scatterers perturb each…
In this paper we consider random block matrices, which generalize the general beta ensembles, which were recently investigated by Dumitriu and Edelmann (2002, 2005). We demonstrate that the eigenvalues of these random matrices can be…
We investigate the statistical properties of the complexness parameter which characterizes uniquely complexness (biorthogonality) of resonance eigenstates of open chaotic systems. Specifying to the regime of isolated resonances, we apply…
The diagonalization of Hermitian supermatrices is studied. Such a change of coordinates is inevitable to find certain structures in random matrix theory. However it still poses serious problems since up to now the calculation of all…
We develop a supersymmetric field theoretical description of the Gaussian ensemble of the almost diagonal Hermitian Random Matrices. The matrices have independent random entries H_{ij} with parametrically small off-diagonal elements…
We analytically calculate the local density of states for Cauchy random band matrices with strongly fluctuating diagonal elements. The Breit-Wigner form for ordinary band matrices is replaced by a Levy distribution of index $\mu=1/2$ and…
We consider a class of random banded Hessenberg matrices with independent entries having identical distributions along diagonals. The distributions may be different for entries belonging to different diagonals. For a sequence of $n\times n$…
We study random normal matrix models whose eigenvalues tend to be distributed within a narrow "band" around the unit circle of width proportional to $\frac1n$, where $n$ is the size of matrices. For general radially symmetric potentials…
We consider a general class of random matrices whose entries are centred random variables, independent up to a symmetry constraint. We establish precise high-probability bounds on the averages of arbitrary monomials in the resolvent matrix…
We consider ensembles of real symmetric band matrices with entries drawn from an infinite sequence of exchangeable random variables, as far as the symmetry of the matrices permits. In general the entries of the upper triangular parts of…