Related papers: Dynamical Detection of Level Repulsion in the One-…
This note presents a unified analysis of the identification of dynamical systems with low-rank constraints under high-dimensional scaling. This identification problem for dynamic systems are challenging due to the intrinsic dependency of…
New method is developed for calculation of single-particle occupation numbers in finite Fermi systems of interacting particles. It is more accurate than the canonical distribution method and gives the Fermi-Dirac distribution in the limit…
Level fluctuations in quantum system have been used to characterize quantum chaos using random matrix models. Recently time series methods were used to relate level fluctuations to the classical dynamics in the regular and chaotic limit. In…
We investigate quantum dynamical systems defined on a finite dimensional Hilbert space and subjected to an interaction with an environment. The rate of decoherence of initially pure states, measured by the increase of their von Neumann…
This paper addresses the issue of detecting hierarchical changes in latent variable models (HCDL) from data streams. There are three different levels of changes for latent variable models: 1) the first level is the change in data…
The low energy dynamics of mesoscopic systems strongly depends on the presence of internal equilibration. For this reason, a better interpretation of ultracold atom experiments requires a more accurate understanding of how quantum chaos…
Disorder and localization have dramatic influence on the topological properties of a quantum system. While strong disorder can close the band gap thus depriving topological materials of topological features, disorder may also induce…
Most anomaly detection systems try to model normal behavior and assume anomalies deviate from it in diverse manners. However, there may be patterns in the anomalies as well. Ideally, an anomaly detection system can exploit patterns in both…
We propose a plasma model for spectral statistics displaying level repulsion without long-range spectral rigidity, i.e. statistics intermediate between random matrix and Poisson statistics similar to the ones found numerically at the…
The dynamical status of isolated quantum systems, partly due to the linearity of the Schrodinger equation is unclear: Conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation --…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…
Traditionally, computation of Lyapunov exponents has been the marque method for identifying chaos in a time series. Recently, new methods have emerged for systems with both known and unknown models to produce a definitive 0--1 diagnostic.…
Complex spectra of dissipative quantum systems may exhibit degeneracies known as exceptional points (EPs). At these points the systems' dynamics may undergo drastic changes. Phenomena associated with EPs and their applications have been…
We discuss a deterministic model of detector coupled to a two-level system (a qubit). The detector is a quasi-classical object whose dynamics is described by the kicked rotator Hamiltonian. We show that in the regime of quantum chaos the…
The $\Delta_3(L)$ statistic is studied as a tool to detect missing levels in the neutron resonance data where 2 sequences are present. These systems are problematic because there is no level repulsion, and the resonances can be too close to…
Many real-life dynamical systems change abruptly followed by almost stationary periods. In this paper, we consider streams of data with such abrupt behavior and investigate the problem of tracking their statistical properties in an online…
We address the phenomenon of statistical orthogonality catastrophe in insulating disordered systems. More in detail, we analyse the response of a system of non-interacting fermions to a local perturbation induced by an impurity. By…
We explore the connections between dissipative quantum phase transitions and non-Hermitian random matrix theory. For this, we work in the framework of the dissipative Dicke model which is archetypal of symmetry-breaking phase transitions in…
We briefly review recent progress in techniques for modeling and analyzing hyperspectral images and movies, in particular for detecting plumes of both known and unknown chemicals. For detecting chemicals of known spectrum, we extend the…
The dynamics of a passive scalar plume in a turbulent boundary layer is experimentally investigated via vertical turbulent transport time-series. Data are acquired in a rough-wall turbulent boundary layer that develops in a recirculating…