相关论文: Correlation Functions in Disordered Systems
A recursive method is derived to calculate all eigenvalue correlation functions of a random hermitian matrix in the large size limit, and after smoothing of the short scale oscillations. The property that the two-point function is…
We consider the correlation functions of eigenvalues of a unidimensional chain of large random hermitian matrices. An asymptotic expression of the orthogonal polynomials allows to find new results for the correlations of eigenvalues of…
The complicated interactions in presence of disorder lead to a correlated randomization of states. The Hamiltonian as a result behaves like a multi-parametric random matrix with correlated elements. We show that the eigenvalue correlations…
The behavior of correlation functions is studied in a class of matrix models characterized by a measure $\exp(-S)$ containing a potential term and an external source term: $S=N\tr(V(M)-MA)$. In the large $N$ limit, the short-distance…
It has been observed that the statistical distribution of the eigenvalues of random matrices possesses universal properties, independent of the probability law of the stochastic matrix. In this article we find the correlation functions of…
This paper establishes the universality of parametric correlations of eigenfunctions in chaotic and weakly disordered systems. We demonstrate this universality in the framework of the gaussian random matrix process and obtain predictions…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
The universal connected correlations proposed recently between eigenvalues of unitary random matrices is examined numerically. We perform an ensemble average by the Monte Carlo sampling. Although density of eigenvalues and a bare…
We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay…
We derive the connected correlation functions for eigenvalues of large Hermitian random matrices with independently distributed elements using both a diagrammatic and a renormalization group (RG) inspired approach. With the diagrammatic…
We study the behavior of two-time correlation functions at late times for finite system sizes considering observables whose (one-point) average value does not depend on energy. In the long time limit, we show that such correlation functions…
We consider the (smoothed) average correlation between the density of energy levels of a disordered system, in which the Hamiltonian is equal to the sum of a deterministic H0 and of a random potential $\varphi$. Remarkably, this correlation…
We explore the influence of external perturbations on the energy levels of a Hamiltonian drawn at random from the Gaussian unitary distribution of Hermitian matrices. By deriving the joint distribution function of eigenvalues, we obtain the…
We study the response of the transmission eigenvalue spectrum of disordered metallic conductors to an arbitrary external perturbation. For systems without time-reversal symmetry we find an exact non-perturbative solution for the two-point…
Correlations of eigenfunctions, $\langle|\psi_k(r_1)|^2|\psi_l(r_2)|^2\rangle$, in a disordered system are investigated. We derive general formulae expressing these correlation functions in terms of the supermatrix sigma-model. In…
It was shown roughly thirty years ago that the density correlations of eigenvalues of large random matrices display a universal form, independent of most of the details of the distribution of the random matrix itself. We show that when the…
We adopt the concept of the correlation matrix to study correlations among sequences of time-extended events occuring repeatedly at consecutive time-intervals. As an application we analyse the magnetoencephalography recordings obtained from…
The goal of this article is to study how much the eigenvalues of large Hermitian random matrices deviate from certain deterministic locations -- or in other words, to investigate optimal rigidity estimates for the eigenvalues. We do this in…
Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…
A remarkable property of Hermitian ensembles is their universal behavior, that is, once properly rescaled the eigenvalue statistics does not depend on particularities of the ensemble. Recently, normal matrix ensembles have attracted…