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We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
We investigate the existence of a fundamental computation-information gap for the problem of clustering a mixture of isotropic Gaussian in the high-dimensional regime, where the ambient dimension $p$ is larger than the number $n$ of points.…
The harmonic oscillator is an essential tool, widely used in all branches of Physics in order to understand more realistic systems, from classical to quantum and relativistic regimes. We know that the harmonic oscillator is integrable in…
We focus on a linear chain of $N$ first-neighbor-coupled logistic maps at their edge of chaos in the presence of a common noise. This model, characterised by the coupling strength $\epsilon$ and the noise width $\sigma_{max}$, was recently…
When implemented in the digital domain with time, space and value discretized in the binary form, many good dynamical properties of chaotic systems in continuous domain may be degraded or even diminish. To measure the dynamic complexity of…
This study investigates the dynamics of quantum information and computational resources using a tractable model of coupled harmonic oscillators. We precisely characterize the interplay between mutual information, synchronization, and…
Chaotic dynamics is widely used to design pseudo-random number generators and for other applications such as secure communications and encryption. This paper aims to study the dynamics of discrete-time chaotic maps in the digital (i.e.,…
We develop a theoretical framework for defining and identifying flows of information in computational systems. Here, a computational system is assumed to be a directed graph, with "clocked" nodes that send transmissions to each other along…
Digital implementations of chaotic systems often suffer from inherent degradation, limiting their long-term performance and statistical quality. To address this challenge, we propose a novel four-stage synchronized piecewise linear chaotic…
We study the chaos of travelling waves (TW) in unidirectional chains of bistable maps. Previous numerical results suggested that this property is selective, {\sl viz.}\ given the parameters, there is at most a single (non-trivial) velocity…
Quantum chaos is presented as a paradigm of information processing by dynamical systems at the bottom of the range of phase-space scales. Starting with a brief review of classical chaos as entropy flow from micro- to macro-scales, I argue…
A fractal method to detect, locate and quantify chaos in multi-dimensional-conservative-closed systems, based on the creation of artificial exits, is presented. The method is invariant under space-time changes of coordinates and can be used…
Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying…
Information theory and the framework of information dynamics have been used to provide tools to characterise complex systems. In particular, we are interested in quantifying information storage, information modification and information…
We systematically investigate the entanglement and information dynamics of quasiperiodic systems across their extended, critical, and localized phases, aiming to identify dynamical signatures that can reveal the multifractal spatial…
The understanding of non-linear effects in circular storage rings and colliders based on superconducting magnets is a key issue for the luminosity the beam lifetime optimisation. A detailed analysis of the multidimensional phase space…
Our understanding of complex systems rests on our ability to characterise how they perform distributed computation and integrate information. Advances in information theory have introduced several quantities to describe complex information…
Symbolic dynamics, which partitions an infinite number of finite-length trajectories into a finite number of trajectory sets, describes the dynamics of a system in a simplified and coarse-grained way with a limited number of symbols. The…
In this study, we explore the information capacity of open quantum systems, focusing on the effective channels formed by the subsystem of random quantum circuits and quantum Hamiltonian evolution. By analyzing the subsystem information…
Understanding quantum chaos is of profound theoretical interest and carries significant implications for various applications, from condensed matter physics to quantum error correction. Recently, out-of-time ordered correlators (OTOCs) have…