Related papers: Random Matrices with Correlated Elements: A Model …
Numerical study of the parametric motion of energy levels in a model system built on Random Matrix Theory is presented. The correlation function of levels' slopes (the so called velocity correlation function) is determined numerically and…
We seek the possibility of a disorder driven transition in a tight-binding lattice with a flat band using complexity parameter approach. Our results indicate the existence of a localized to extended states transition with increasing…
We derive the general form of a master equation describing the interaction of an arbitrary multipartite quantum system, consisting of a set of subsystems, with an environment, consisting of a large number of sub-envirobments. Each subsystem…
We consider a system of $N$ Brownian particles, with or without inertia, interacting in the mean-field regime via a weak, smooth, long-range potential, and starting initially from an arbitrary exchangeable $N$-particle distribution. In this…
A time-delayed response of individual living organisms to information exchanged within flocks or swarms leads to the emergence of complex collective behaviors. A recent experimental setup by (Khadka et al 2018 Nat. Commun. 9 3864),…
We introduce a simple model for addressing the controversy in the study of financial systems, sometimes taken as brownian-like processes and other as critical systems with fluctuations of arbitrary magnitude. The model considers a…
We consider a generalized model of repeated quantum interactions, where a system $\mathcal{H}$ is interacting in a random way with a sequence of independent quantum systems $\mathcal{K}_n, n \geq 1$. Two types of randomness are studied in…
The mutual information, I, of the three-state neural network can be obtained exactly for the mean-field architecture, as a function of three macroscopic parameters: the overlap, the neural activity and the {\em activity-overlap}, i.e. the…
We extend random matrix theory to consider randomly interacting spin systems with spatial locality. We develop several methods by which arbitrary correlators may be systematically evaluated in a limit where the local Hilbert space dimension…
We propose a characterization of quantum many-body chaos: given a collection of simple operators, the set of all possible pair-correlations between these operators can be organized into a matrix with random-matrix-like spectrum. This…
Financial markets are a typical example of complex systems where interactions between constituents lead to many remarkable features. Here, we show that a pairwise maximum entropy model (or auto-logistic model) is able to describe switches…
Motivated by the importance ascribed to correlations in random matrices used to model phenomena in various scientific disciplines, we report how algebraic correlations between matrix elements affect the eigenvalue statistics and spectral…
The entanglement of eigenstates in two coupled, classically chaotic kicked tops is studied in dependence of their interaction strength. The transition from the non-interacting and unentangled system towards full random matrix behavior is…
A Fourier analysis of parametric level dynamics for random matrices periodically depending on a phase is developed. We demonstrate both theoretically and numerically that under very general conditions the correlation $C(\varphi )$ of level…
A nearest-neighbor tight-binding model on a tree structure is investigated. The full energy spectrum of the normalized Hamiltonian can be expressed in terms of successively increasing number of contributions at any finite step of…
Economic and ecological models can be extremely complex, with a large number of agents/species each featuring multiple interacting dynamical quantities. In an attempt to understand the generic stability properties of such systems, we define…
The entanglement spectrum, i.e., the full distribution of Schmidt eigenvalues of the reduced density matrix, contains more information than the conventional entanglement entropy and has been studied recently in several many-particle…
When electron correlations are important it is often necessary to use numerical methods to solve the Hamiltonian for a finite system (cluster) "exactly". Unfortunately, such methods are restricted to small systems. We propose to combine the…
Higher order interactions are increasingly recognised as a fundamental aspect of complex systems ranging from the brain to social contact networks. Hypergraph as well as simplicial complexes capture the higher-order interactions of complex…
We study the behavior of two-time correlation functions at late times for finite system sizes considering observables whose (one-point) average value does not depend on energy. In the long time limit, we show that such correlation functions…