Related papers: Correlated random band matrices: localization-delo…
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…
Given an $N$-dimensional sample of size $T$ and form a sample correlation matrix $\mathbf{C}$. Suppose that $N$ and $T$ tend to infinity with $T/N $ converging to a fixed finite constant $Q>0$. If the population is a factor model, then the…
We consider a one-dimensional quantum many-body system and investigate how the interplay between interaction and on-site disorder affects spatial localization and quantum correlations. The hopping amplitude is kept constant. To measure…
We draw an explicit connection between the statistical properties of an entangled two-mode continuous variable (CV) resource and the amount of entanglement that can be dynamically transferred to a pair of non-interacting two-level systems.…
Continuous One-dimensional models supporting extended states are studied. These delocalized statesoccur at well defined values of the energy and are consequences of simple statistical correlation rules. We explicitly study alloys of…
Here we introduce the non-Hermitian diluted banded random matrix (nHdBRM) ensemble as the set of $N\times N$ real non-symmetric matrices whose entries are independent Gaussian random variables with zero mean and variance one if $|i-j|<b$…
We consider the block band matrices, i.e. the Hermitian matrices $H_N$, $N=|\Lambda|W$ with elements $H_{jk,\alpha\beta}$, where $j,k \in\Lambda=[1,m]^d\cap \mathbb{Z}^d$ (they parameterize the lattice sites) and $\alpha, \beta= 1,\ldots,…
Localization effects and quantum decoherence driven by the mass-eigenstate wave packet propagation are shown to support a statistical correlation between quantum entanglement and damped oscillations in the scenario of three-flavor quantum…
Banded random matrices were introduced as a more realistic alternative to full random matrices for describing the spectral statistics of heavy nuclei. Initially considered by Wigner, they have since become a paradigmatic model for…
Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the matrix eigenvalues, which corresponds to shifting some of the…
As a hallmark of pure quantum effect, quantum entanglement has provided unconventional routes to condensed matter systems. Here, from the perspective of quantum entanglement, we disclose exotic quantum physics in non-Hermitian…
We study the spectra and eigenvectors of the adjacency matrices of scale-free networks when bi-directional interaction is allowed, so that the adjacency matrix is real and symmetric. The spectral density shows an exponential decay around…
Two-dimensional lattice models subjected to an external effective magnetic field can form nontrivial band topologies characterized by nonzero integer band Chern numbers. In this Letter, we investigate such a lattice model originating from…
Using Random Matrix Theory one can derive exact relations between the eigenvalue spectrum of the covariance matrix and the eigenvalue spectrum of its estimator (experimentally measured correlation matrix). These relations will be used to…
Much effort has been spent on characterizing the spectrum of the non-backtracking matrix of certain classes of graphs, with special emphasis on the leading eigenvalue or the second eigenvector. Much less attention has been paid to the…
In this work, propagation of acoustic waves in a one-dimensional binary chain with different types of correlations in elasticity distribution is studied. We applied entropic analysis to investigate and quantify the…
It is shown that local temporal correlations in addition to non-local spatial correlations are important to understand the size and the doping dependence of the d-wave superconducting order parameter of high-temperature superconductors. To…
We present a novel block reduction method for the study of a general class of random band matrices (RBM) defined on the $d$-dimensional lattice $\mathbb{Z}_{L}^d:=\{1,2,\ldots,L\}^{d}$ for $d\in \{1,2\}$, with band width $W$ and an almost…
We study statistical properties of a class of band random matrices which naturally appears in systems of interacting particles. The local spectral density is shown to follow the Breit-Wigner distribution in both localized and delocalized…
We study non-local measures of spectral correlations and their utility in characterizing and distinguishing between the distinct eigenstate phases of quantum chaotic and many-body localized systems. We focus on two related quantities, the…