Related papers: Exploring Transition from Stability to Chaos throu…
Our research highlights the effectiveness of utilizing matrices akin to Wishart matrices, derived from magnetization time series data under specific dynamics, to elucidate phase transitions and critical phenomena in the Q-state Potts model.…
We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…
The striking fractal geometry of strange attractors underscores the generative nature of chaos: like probability distributions, chaotic systems can be repeatedly measured to produce arbitrarily-detailed information about the underlying…
Dynamical fluctuations or rare events associated with atypical trajectories in chaotic maps due to specific initial conditions can crucially determine their fate, as the may lead to stability islands or regions in phase space otherwise…
Slow-fast dynamics and resonant phenomena can be found in a wide range of physical systems, including problems of celestial mechanics, fluid mechanics, and charged particle dynamics. Important resonant effects that control transport in the…
We train an artificial neural network which distinguishes chaotic and regular dynamics of the two-dimensional Chirikov standard map. We use finite length trajectories and compare the performance with traditional numerical methods which need…
We investigate chaos in mixed-phase-space Hamiltonian systems using time series of the finite- time Lyapunov exponents. The methodology we propose uses the number of Lyapunov exponents close to zero to define regimes of ordered…
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…
In this paper we continue to develop our approach to the chaoticity properties of the quantum Hamiltonian systems. Our earlier suggested chaoticity criterion characterizes the initial symmetry breaking and the destruction of the…
We predict that continuously monitored quantum dynamics can be chaotic. The optimal paths between past and future boundary conditions can diverge exponentially in time when there is time-dependent evolution and continuous weak monitoring.…
Chaos control techniques have been applied to a wide variety of experimental systems, including magneto-elastic ribbons, lasers, chemical reactions, arrhythmic cardiac tissue, and spontaneously bursting neuronal networks. An underlying…
Chaotic systems, presenting complex and non-reproducible dynamics, may be found in nature from the interaction between planets to the evolution of the weather, but can also be tailored using current technologies for advanced signal…
We uncover and characterize different chaotic transport scenarios on perfect periodic surfaces by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect. After identifying…
We consider the classical and quantum properties of the "Chirikov typical map", proposed by Boris Chirikov in 1969. This map is obtained from the well known Chirikov standard map by introducing a finite number $T$ of random phase shift…
Matrix concentration inequalities and their recently discovered sharp counterparts provide powerful tools to bound the spectrum of random matrices whose entries are linear functions of independent random variables. However, in many…
Distributions of eigenmodes are widely concerned in both bounded and open systems. In the realm of chaos, counting resonances can characterize the underlying dynamics (regular vs. chaotic), and is often instrumental to identify…
Conventional spectral probes of quantum chaos require eigenvalues, and sometimes, eigenvectors of the quantum Hamiltonian. This involves computationally expensive diagonalization procedures. We test whether an unsupervised neural network…
Extracting reliable indicators of chaos from a single experimental time series is a challenging task, in particular, for systems with many degrees of freedom. The techniques available for this purpose often require unachievably long time…
The earlier times of evolution of a magnetic system contain more information than we can imagine. Capturing correlation matrices G of different time evolutions of a simple testbed spin system, as the Ising model, we analyzed the density of…
This article is an introductory review of random matrix theory (RMT) and its applications, with special focus on quantum chaos. Random matrices were first used by Wigner to understand the spectra of complex nuclei from a statistical…