Related papers: Dynamical Detection of Level Repulsion in the One-…
We introduce aspects of quantum chaos by analyzing the eigenvalues and the eigenstates of quantum many-body systems. The properties of quantum systems whose classical counterparts are chaotic differ from those whose classical counterparts…
The out-of-time-ordered correlator has been proposed as an indicator of chaos in quantum systems due to its simple interpretation in the semiclassical limit. In particular, its rate of possible exponential growth at $\hbar \to 0$ is closely…
We introduce randomness into a class of integrable models and study the spectral form factor as a diagnostic to distinguish between randomness and chaos. Spectral form factors exhibit a characteristic dip-ramp-plateau behavior in the $N>2$…
Based on the non-autonomous quantum master equation, we investigate the dissipative and decoherence properties of the two-level atom system interacting with the environment of thermal quantum radiation fields. For this system, by a novel…
Anomaly detection is the process of finding data points that deviate from a baseline. In a real-life setting, anomalies are usually unknown or extremely rare. Moreover, the detection must be accomplished in a timely manner or the risk of…
We present an experimental study of missing level statistics of three-dimensional chaotic microwave cavities. The investigation is reinforced by the power spectrum of level fluctuations analysis which also takes into account the missing…
A two dimensional model for quantum percolation with variable tunneling range is studied. For this purpose the Lifshitz model is considered where the disorder enters the Hamiltonian via the nondiagonal elements. We employ a numerical method…
We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior,…
We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. The corresponding…
The thermal fluctuations that exist at very low temperature in disordered systems are often attributed to the existence of some two-level excitations. In this paper, we revisit this question via the explicit studies of the following 1D…
We present experimental and theoretical results for the fluctuation properties in the incomplete spectra of quantum systems with symplectic symmetry and a chaotic dynamics in the classical limit. To obtain theoretical predictions, we extend…
We propose a new method to define anomaly scores and apply this to particle physics collider events. Anomalies can be either rare, meaning that these events are a minority in the normal dataset, or different, meaning they have values that…
The spectral fluctuations of quantum (or wave) systems with a chaotic classical (or ray) limit are mostly universal and faithful to random-matrix theory. Taking up ideas of Pechukas and Yukawa we show that equilibrium statistical mechanics…
We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties…
In this work we analyze the spectral level statistics of the one-dimensional ionic Hubbard model, the Hubbard model with an alternating on-site potential. In particular, we focus on the statistics of the gap ratios between consecutive…
Motivated by the role that spectral properties play for the dynamical evolution of a quantum many-body system, we investigate the level spacing statistic of the extended Bose-Hubbard model. In particular, we focus on the distribution of the…
Change point detection in high dimensional data has found considerable interest in recent years. Most of the literature either designs methodology for a retrospective analysis, where the whole sample is already available when the…
We consider a non-interacting many-fermion system populating levels of a unitary random matrix ensemble (equivalent to the q=2 complex Sachdev-Ye-Kitaev model) - a generic model of single-particle quantum chaos. We study the corresponding…
We introduce a complex-plane generalization of the consecutive level-spacing distribution, used to distinguish regular from chaotic quantum spectra. Our approach features the distribution of complex-valued ratios between nearest- and…
We present the results of a wavelet-based approach to the study of the chaotic dynamics of a one dimensional model that shows a direct transition to spatiotemporal chaos. We find that the dynamics of this model in the spatiotemporally…