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A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). For single particle systems with fully chaotic classical…
Random banded matrices with linearly increasing diagonal elements are recently considered as an attractive model for complex nuclei and atoms. Apart from early papers by Wigner \cite{Wig} there were no analytical studies on the subject. In…
Previous results indicate that while chaos can lead to substantial entropy production, thereby maximizing dynamical entanglement, this still falls short of maximality. Random Matrix Theory (RMT) modeling of composite quantum systems,…
In this paper the relationship between the problem of constructing the ground state energy for the quantum quartic oscillator and the problem of computing mean eigenvalue of large positively definite random hermitean matrices is…
These lecture notes provide a comprehensive, self-contained introduction to the analysis of Wishart matrix moments. This study may act as an introduction to some particular aspects of random matrix theory, or as a self-contained exposition…
Random matrix theory is a powerful way to describe universal correlations of eigenvalues of complex systems. It also may serve as a schematic model for disorder in quantum systems. In this review, we discuss both types of applications of…
It is generally accepted that statistics of energy levels in closed chaotic quantum systems is adequately described by the theory of Random Hermitian Matrices. Much less is known about properties of "resonances" - generic features of open…
In the last decade, spectral linear statistics on large dimensional random matrices have attracted significant attention. Within the physics community, a privileged role has been played by invariant matrix ensembles for which a two…
The starting point of this paper is that a spectral method is essentially a combination of an orthonormal basis of the underlying Hilbert space with Galerkin conditions. The choice of an orthonormal basis depends on a number of desirable…
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless systems, with say $m$ particles in $N$ single particle states…
This work introduces a method for determining the energy spectrum of lattice quantum chromodynamics (LQCD) by applying the Lanczos algorithm to the transfer matrix and using a bootstrap generalization of the Cullum-Willoughby method to…
We employ the random matrix theory (RMT) framework to revisit the distribution of resonance widths in quantum chaotic systems weakly coupled to the continuum via a finite number M of open channels. In contrast to the standard first-order…
We present a brief overview of random matrix theory (RMT) with the objectives of highlighting the computational results and applications in financial markets as complex systems. An oft-encountered problem in computational finance is the…
This review article provides an overview of random matrix theory (RMT) with a focus on its growing impact on the formulation and inference of statistical models and methodologies. Emphasizing applications within high-dimensional statistics,…
The high complexity of many-body quantum dynamics means that essentially all approaches either exploit special structure or are approximate in nature. One such approach--the memory function formalism--involves a carefully chosen split into…
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…
This is an elementary review, aimed at non-specialists, of results that have been obtained for the limiting distribution of eigenvalues and for the operator norms of real symmetric random matrices via the method of moments. This method goes…
Three-dimensional icosahedral random tilings with rhombohedral cells are studied in the semi-entropic model. We introduce a global energy measure defined by the variance of the quasilattice points in the orthogonal space. The internal…
The ratio of two consecutive level spacings has emerged as a very useful metric in investigating universal features exhibited by complex spectra. It does not require the knowledge of density of states and is therefore quite convenient to…
The Wegner orbital model is a class of random operators introduced by Wegner to model the motion of a quantum particle with many internal degrees of freedom (orbitals) in a disordered medium. We consider the case when the matrix potential…