Related papers: Random Matrices with Correlated Elements: A Model …
We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric…
Using a non-Hermitian Hamiltonian approach to open systems, we study the interplay of disorder and superradiance in a one- and three-dimensional Anderson model. Analyzing the complex eigenvalues of the non-Hermitian Hamiltonian, a…
Correlation matrices are widely used to analyze the interdependence of variables in various real-world scenarios. Often, a perturbation in a few variables leads to mild differences in many correlation coefficients associated with these…
We systematically study the effect of disorder and interactions on a quasi-one dimensional diamond chain possessing flat bands. Disorder localizes all the single particle eigenstates, while at low disorder strengths we obtain weak flat-band…
In the last decade there has been increasing interest in the fields of random matrices, interacting particle systems, stochastic growth models, and the connections between these areas. For instance, several objects appearing in the limit of…
It has become increasingly clear that a full understanding of the physics of electrons in disordered systems requires an approach in which both disorder and interactions are taken into account. Work on small numbers of electrons has…
Many-body localized systems in which interactions and disorder come together defy the expectations of quantum statistical mechanics: In contrast to ergodic systems, they do not thermalize when undergoing nonequilibrium dynamics. What is…
An interacting lattice model describing the subspace spanned by a set of strongly-correlated bands is rigorously coupled to density functional theory to enable ab initio calculations of geometric and topological material properties. The…
Quantum chaos is linked to Brownian diffusion of the underlying quantum energy level-spacing sequences. The level-spacings viewed as functions of their order execute random walks which imply uncorrelated random increments of the…
Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered…
We argue that in a large class of disordered quantum many-body systems, the late time dynamics of time-dependent correlation functions is captured by random matrix theory, specifically the energy eigenvalue statistics of the corresponding…
This paper summarizes some work I've been doing on eigenvalue correlators of Random Matrix Models which show some interesting behaviour. First we consider matrix models with gaps in there spectrum or density of eigenvalues. The…
We discuss the discrete spectrum of the Hamiltonian describing a two-dimensional quantum particle interacting with an infinite family of point interactions. We suppose that the latter are arranged into a star-shaped graph with N arms and a…
We obtain general, exact formulas for the overlaps between the eigenvectors of large correlated random matrices, with additive or multiplicative noise. These results have potential applications in many different contexts, from quantum…
The theory of correlated electron systems is formulated in a form which allows to use as a reference point an ab initio band structure theory (AIBST). The theory is constructed in two steps. As a first step the total Hamiltonian is…
Circular Brownian motion models of random matrices were introduced by Dyson and describe the parametric eigenparameter correlations of unitary random matrices. For symmetric unitary, self-dual quaternion unitary and an analogue 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…
The spectral statistics and entanglement within the eigenstates of generic spin chain Hamiltonians are analysed. A class of random matrix ensembles is defined which include the most general nearest-neighbour qubit chain Hamiltonians. For…
We present a modified Brownian motion model for random matrices where the eigenvalues (or levels) of a random matrix evolve in "time" in such a way that they never cross each other's path. Also, owing to the exact integrability of the level…
An explicit expression is derived for the statistical description of small quantum systems, which are relatively-weakly and directly coupled to only small parts of their environments. The derived expression has a canonical form, but is…