Related papers: A unified time scale for quantum chaotic regimes
We propose a method to study dynamical response of a quantum system by evolving it with an imaginary-time dependent Hamiltonian. The leading non-adiabatic response of the system driven to a quantum-critical point is universal and…
An algorithm to characterize collective motion is presented, with the introduction of ``collective Lyapunov exponent'', as the orbital instability at a macroscopic level. By applying the algorithm to a globally coupled map, existence of…
Quantitative estimates are derived, on the whole space, for the relative entropy between the joint law of random interacting particles and the tensorized law at the limiting systeme. The developed method combines the relative entropy method…
Quantum coherences are paramount resources for applications, such as quantum-enhanced light-harvesting or quantum computing, which are fragile against environmental noise. We here derive generalized quantum master equations using…
We use a recent result to show that the rate of loss of coherence of a quantum system increases with increasing system phase space structure and that a chaotic quantal system in the semiclassical limit decoheres exponentially with rate $2…
In this article the statistical properties of symmetrical random matrices whose elements are drawn from a q-parameterized non-extensive statistics power-law distribution are investigated. In the limit as q->1 the well known Gaussian…
We uncover the dynamics at the chaos threshold $\mu_{\infty}$ of the logistic map and find it consists of trajectories made of intertwined power laws that reproduce the entire period-doubling cascade that occurs for $\mu <\mu_{\infty}$. We…
An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…
We introduce a new characteristics of chaoticity of classical and quantum dynamical systems by defining the notion of the dissipation time which enables us to test how the system responds to the noise and in particular to measure the speed…
We present a semiclassical calculation of the generalized form factor which characterizes the fluctuations of matrix elements of the quantum operators in the eigenbasis of the Hamiltonian of a chaotic system. Our approach is based on some…
Classical counterparts of a great variety of quantum systems, from atomic physics to quantum wells and quantum dots, to optical, microwave, and acoustic resonators exhibit partially chaotic dynamics. Since it is often impossible to measure…
Nowadays there is no universally accepted definition of quantum chaos. In this paper we review and critically discuss different approaches to the subject, such as Quantum Chaology and the Random Matrix Theory. Then we analyze the problem of…
Randomness generation through quantum-chaotic evolution underpins foundational questions in statistical mechanics and applications across quantum information science, including benchmarking, tomography, metrology, and demonstrations of…
A detailed numerical study reveals that the asymptotic values of the standard deviation-to-mean ratio of the out-of-time-ordered correlator can be successfully used as a measure of the quantum chaoticity of the system. We employ a…
We consider the effect of multiple stochastic parameters on the time-average quantities of chaotic systems. We employ the recently proposed \cite{Kantarakias_Papadakis_2023} sensitivity-enhanced generalized polynomial chaos expansion,…
We review application of level dynamics to spectra of quantally chaotic systems. We show that statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss…
We establish a general scaling law for the entanglement of a large class of ground states and dynamically evolving states of quantum spin chains: we show that the geometric entropy of a distinguished block saturates, and hence follows an…
This paper presents a synthesis approach aiming to guarantee a minimum upper-bound for the time taken to reach a target set of non-zero measure that encompasses the origin, while taking into account uncertainties and input and state…
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 --…
This work provides a nonasymptotic error analysis of quantum Krylov algorithms based on real-time evolutions, subject to generic errors in the outputs of the quantum circuits. We prove upper and lower bounds on the resulting ground state…