Related papers: Missing-level statistics in classically chaotic qu…
We address the quantum-classical correspondence for chaotic systems with a crossover between symmetry classes. We consider the energy level statistics of a classically chaotic system in a weak magnetic field. The generating function of…
In the present work we study the two-point correlation function $R(\epsilon)$ of the quantum mechanical spectrum of a classically chaotic system. Recently this quantity has been computed for chaotic and for disordered systems using periodic…
The statistics of the resonance widths and the behavior of the survival probability is studied in a particular model of quantum chaotic scattering (a particle in a periodic potential subject to static and time-periodic forces) introduced…
Bayesian inference is applied to the level fluctuations of two coupled microwave billiards in order to extract the coupling strength. The coupled resonators provide a model of a chaotic quantum system containing two coupled symmetry classes…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear…
We study the effect of gradual symmetry breaking in a non-integrable system on the level fluctuation statistics. We consider the case when the symmetry is represented by a quantum number that takes one of two possible values, so that the…
While limitations on quantum computation by Markovian environmental noise are well-understood in generality, their behavior for different quantum circuits and noise realizations can be less universal. Here we consider a canonical quantum…
The quantum ratchet effect in fully chaotic systems is approached by studying, for the first time, \emph{statistical} properties of the ratchet current over well-defined sets of initial states. Natural initial states in a semiclassical…
We perform a comprehensive analysis of the spectral statistics of the molecular resonances in $^{166}$Er and $^{168}$Er observed in recent ultracold collision experiments [Frisch et al., Nature {\bf 507}, 475 (2014)] with the aim of…
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…
Previous results indicate that while chaos can lead to substantial entropy production, thereby maximizing dynamical entanglement, this still falls short of maximality. Random Matrix Theory (RMT) modeling of composite quantum systems,…
A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace…
We present a semiclassical approach to eigenfunction statistics in chaotic and weakly disordered quantum systems which goes beyond Random Matrix Theory, supersymmetry techniques, and existing semiclassical methods. The approach is based on…
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…
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…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
For systems whose classical dynamics is chaotic, it is generally believed that the local statistical properties of the quantum energy levels are well described by Random Matrix Theory. We present here two counterexamples - the hydrogen atom…
We report a systematic investigation of universal quantum chaotic signatures in the transverse field Ising model on an Erd\H{o}s-R\'enyi network. This is achieved by studying local spectral measures such as the level spacing and the level…
Through simple analytical calculations and numerical simulations, we demonstrate the generic existence of a self-organized macroscopic state in any large multivariate system possessing non-vanishing average correlations between a finite…
We present an analysis of the quantum adiabatic algorithm for solving hard instances of 3-SAT (an NP-complete problem) in terms of Random Matrix Theory (RMT). We determine the global regularity of the spectral fluctuations of the…