Related papers: Dynamical Detection of Level Repulsion in the One-…
We derive an expression for the nearest-neighbor spacing distribution $P(s)$ of the energy levels of quantum systems with intermediate dynamics between regularity and chaos and missing levels due to random experimental errors. The…
A quasi-one-dimensional quantum dot containing two interacting electrons is analyzed in search of signatures of chaos. The two-electron energy spectrum is obtained by diagonalization of the Hamiltonian including the exact Coulomb…
We investigate the transition to quantum chaos, induced by static imperfections, for an operating quantum computer that simulates efficiently a dynamical quantum system, the sawtooth map. For the different dynamical regimes of the map, we…
We investigate the dynamics of a quantum particle in disordered tight-binding models in one and two dimensions which are exceptions to the common wisdom on Anderson localization, in the sense that the localization length diverges at some…
Anomalies represent deviations from the intended system operation and can lead to decreased efficiency as well as partial or complete system failure. As the causes of anomalies are often unknown due to complex system dynamics, efficient…
Epstein's model for a civil disorder is an agent-based model that simulates a social protest process where the central authority uses the police force to dissuade it. The interactions of police officers and citizens produce dynamics that do…
We assume that the energy spectrum of a chaotic system undergoing symmetry breaking transitions can be represented as a superposition of independent level sequences, one increasing on the expense of the others. The relation between the…
Many natural systems undergo critical transitions, i.e. sudden shifts from one dynamical regime to another. In the climate system, the atmospheric boundary layer can experience sudden transitions between fully turbulent states and…
The emergence of quantum chaos for interacting Fermi systems is investigated by numerical calculation of the level spacing distribution $P(s)$ as function of interaction strength $U$ and the excitation energy $\epsilon$ above the Fermi…
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…
We develop a real-time anomaly detection algorithm for directed activity on large, sparse networks. We model the propensity for future activity using a dynamic logistic model with interaction terms for sender- and receiver-specific latent…
The paradigm of the two-level atom is revisited and its perturbative analysis is discussed in view of the principle of duality in perturbation theory. The models we consider are a two-level atom and an ensemble of two-level atoms both…
We propose a novel and efficient method, that we shall call TopRank in the following paper, for detecting change-points in high-dimensional data. This issue is of growing concern to the network security community since network anomalies…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…
In this review the problem of statistical description of isolated quantum systems of interacting particles is discussed. Main attention is paid to a recently developed approach which is based on chaotic properties of compound states in the…
Statistics of many particle energy levels of a finite two-dimensional system of interacting electrons is numerically studied. It is shown that the statistics of these levels undergoes a Poisson to Wigner crossover as the strength of the…
We introduce a two-dimensional generalisation of the quasiperiodic Aubry-Andr\'e model. Even though this model exhibits the same duality relation as the one-dimensional version, its localisation properties are found to be substantially more…
Tables are an abundant form of data with use cases across all scientific fields. Real-world datasets often contain anomalous samples that can negatively affect downstream analysis. In this work, we only assume access to contaminated data…
Characterizing topological phases for strongly interacting fermions in the mixed-state regime remains a major challenge. Here we introduce a general and numerically efficient framework to diagnose mixed-state topological phases in strongly…
The authors study the spectral theory of self-adjoint operators that are subject to certain types of perturbations. An iterative introduction of infinitely many randomly coupled rank-one perturbations is one of our settings. Spectral…