Related papers: Random-matrix theory and complex atomic spectra
We apply random matrix theory to complex networks. We show that nearest neighbor spacing distribution of the eigenvalues of the adjacency matrices of various model networks, namely scale-free, small-world and random networks follow…
Correlation functions involving products and ratios of half-integer powers of characteristic polynomials of random matrices from the Gaussian Orthogonal Ensemble (GOE) frequently arise in applications of Random Matrix Theory (RMT) to…
The distribution function of the local density of states is computed exactly for the Wigner-Dyson ensemble of random Hamiltonians. In the absence of time-reversal symmetry, precise agreement is obtained with the "supersymmetry" theory by…
Over the past decades, a great body of theoretical and mathematical work has been devoted to random-matrix descriptions of open quantum systems. In these notes, based on lectures delivered at the Les Houches Summer School "Stochastic…
We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref.[1]. The relevant ensembles of Hamiltonians are those…
We survey recent mathematical results about the spectrum of random band matrices. We start by exposing the Erd{\H o}s-Schlein-Yau dynamic approach, its application to Wigner matrices, and extension to other mean-field models. We then…
We review the ideas of how random matrix theory has to be properly applied to quantum physics; particularly we focus on how the spectrum has to be properly prepared and the random matrix correctly identified before the random matrix and the…
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…
We develop an ab initio analytic theory of random lasing in an ensemble of atoms that both scatter and amplify light. The theory applies all the way from low to high density of atoms. The properties of the random laser are controlled by an…
We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…
A new universality class distinct from the standard Wigner-Dyson ones is identified. This class is realized by putting a metallic quantum dot in contact with a superconductor, while applying a magnetic field so as to make the pairing field…
The random matrix ensembles are applied to the quantum statistical systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
In the last few years several new Random Matrix Models have been proposed and studied. They have found application in various different contexts, ranging from the physics of mesoscopic systems to the chiral transition in lattice gauge…
We use ab initio electronic-structure methods to investigate random-matrix theory (RMT) universality in molecular electronic structure. Using single-reference electronic structure methods, including Hartree-Fock, configuration-interaction…
The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
We present a Gaussian ensemble of random cyclic matrices on the real field and study their spectral fluctuations. These cyclic matrices are shown to be pseudo-symmetric with respect to generalized parity. We calculate the joint probability…
We develop a scattering-matrix formalism to numerically study the resonant scattering of light on generic assemblies of atoms. Protocols to eliminate the artifacts of the method and extract physical information from the numerical data are…
The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the `spectral estimator') for the new class of `generalized elliptical distributions' is presented. It…
We study the fluctuation properties of transition intensities applying a recently proposed generalization of the random matrix theory, which is based on Beck and Cohen's superstatistics. We obtain an analytic expression for the distribution…
In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of…