Related papers: Spectral statistics of a pseudo-integrable map: th…
Cumulant mapping employs a statistical reconstruction of the whole by sampling its parts. The theory developed in this work formalises and extends ad hoc methods of `multi-fold' or `multi-dimensional' covariance mapping. Explicit formulae…
The spectral statistics of non-Hermitian random matrices are of importance as a diagnostic tool for chaotic behavior in open quantum systems. Here, we investigate the statistical properties of singular values in non-Hermitian random…
We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level…
We obtain sequences of inclusion sets for the spectrum, essential spectrum, and pseudospectrum of banded, in general non-normal, matrices of finite or infinite size. Each inclusion set is the union of the pseudospectra of certain…
The generalized pseudospectral method is employed for the accurate calculation of eigenvalues, densities and expectation values for the spiked harmonic oscillators. This allows \emph{nonuniform} and \emph{optimal} spatial discretization of…
We introduce a notion of local level spacings and study their statistics within a random-matrix-theory approach. In the limit of infinite-dimensional random matrices, we determine universal sequences of mean local spacings and of their…
In a series of two papers we investigate the universal spectral statistics of chaotic quantum systems in the ten known symmetry classes of quantum mechanics. In this first paper we focus on the construction of appropriate ensembles of star…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…
This paper studies the spectrum of a multi-dimensional split-step quantum walk with a defect that cannot be analysed in the previous papers. To this end, we have developed a new technique which allow us to use a spectral mapping theorem for…
We study the effects of an arbitrary external perturbation in the statistical properties of the S-matrix of quantum chaotic scattering systems in the limit of isolated resonances. We derive, using supersymmetry, an exact non-perturbative…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…
We examine the utility of the quadratic pseudospectrum in photonics and condensed matter. Specifically, the quadratic pseudospectrum represents a method for approaching systems with incompatible observables, as it both minimizes the…
While the notion of quantum chaos is tied to random matrix spectral correlations, also eigenstate properties in chaotic systems are often assumed to be described by random matrix theory. Analytic insights into eigenstate correlations can be…
Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…
We compare the statistical fluctuation properties of the baryon and meson experimental mass spectra with those obtained from theoretical models (quark models and lattice QCD). We find that for the experimental spectra the statistical…
The quantum baker's map is the quantization of a simple classically chaotic system, and has many generic features that have been studied over the last few years. While there exists a semiclassical theory of this map, a more rigorous study…
We quantize graphs (networks) which consist of a finite number of bonds and vertices. We show that the spectral statistics of fully connected graphs is well reproduced by random matrix theory. We also define a classical phase space for the…
Stochastic matrices and positive maps in matrix algebras proved to be very important tools for analysing classical and quantum systems. In particular they represent a natural set of transformations for classical and quantum states,…