Related papers: A Bound on Chaos from Stability
We investigate the dynamics of classical and quantum N-component phi^4 oscillators in the presence of an external field. In the large N limit the effective dynamics is described by two-degree-of-freedom classical Hamiltonian systems. In the…
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 --…
Quantum chaos cannot develop faster than $\lambda \leq 2 \pi/(\hbar \beta)$ for systems in thermal equilibrium [Maldacena, Shenker & Stanford, JHEP (2016)]. This `MSS bound' on the Lyapunov exponent $\lambda$ is set by the width of the…
The presence of chaos in classical Hamiltonian systems is witnessed by its maximal Lyapunov exponent, that quantifies the instability of motion through the exponential growth of indicators such as the trace of the stability matrix or the…
We study properties of chaos in generic one-dimensional nonlinear Hamiltonian lattices comprised of weakly coupled nonlinear oscillators, by numerical simulations of continuous-time systems and symplectic maps. For small coupling, the…
We consider transitions to chaos in random dynamical systems induced by an increase of noise amplitude. We show how the emergence of chaos (indicated by a positive Lyapunov exponent) in a logistic map with bounded additive noise can be…
We study the motion of a spinning test particle in Schwarzschild spacetime, analyzing the Poincar\'e map and the Lyapunov exponent. We find chaotic behavior for a particle with spin higher than some critical value (e.g. $S_{cr} \sim 0.64…
Classically chaotic systems relax to coarse grained states of equilibrium. Here we numerically study the quantization of such bounded relaxing systems, in particular the quasi-periodic fluctuations associated with the correlation between…
Classical quasi-integrable systems are known to have Lyapunov times much shorter than their ergodicity time -- the most clear example being the Solar System -- but the situation for their quantum counterparts is less well understood. As a…
This paper is mainly devoted to applying the invariant, fast, Lyapunov indicator to clarify some doubt regarding the apparently conflicting results of chaos in spinning compact binaries at the second-order post-Newtonian approximation of…
We study the quantum-classical correspondence for systems with interacting spin-particles that are strongly chaotic in the classical limit. This is done in the presence of constants of motion associated with the fixed angular momenta of…
This paper deals with the problem of analytically computing the largest Lyapunov exponent for many degrees of freedom Hamiltonian systems. This aim is succesfully reached within a theoretical framework that makes use of a geometrization of…
In order to study the chaotic behavior of a system with non-local interactions, we will consider weakly coupled non-commutative field theories. We compute the Lyapunov exponent of this exponential growth in the large Moyal-scale limit to…
We investigate why the Lyapunov exponents $\lambda$ of out-of-time-ordered correlators (OTOCs) satisfy a universal bound $\lambda < 2 \pi k_B T/{\hbar}$ by probing imaginary-time path-integral space using ring-polymer molecular dynamics…
This paper summarises a numerical investigation of the statistical properties of orbits evolved in `frozen,' time-independent N-body realisations of smooth, time-independent density distributions, allowing for 10^(2.5)<N<10^(5.5). Two…
We consider a mechanism for area preserving Hamiltonian systems which leads to the enhanced probability, $P(\lambda, t)$, to find small values of the finite time Lyapunov exponent, $\lambda$. In our investigation of chaotic dynamical…
In this article, using the principles of Random Matrix Theory (RMT), we give a measure of quantum chaos by quantifying Spectral From Factor (SFF) appearing from the computation of two-point Out of Time Order Correlation function (OTOC)…
We study the notion of quantum Kac's chaos which was implicitly introduced by Spohn and explicitly formulated by Gottlieb. We prove the analogue of a result of Sznitman which gives the equivalence of Kac's chaos to 2-chaoticity and to…
Transient chaos is an ubiquitous phenomenon characterizing the dynamics of phase space trajectories evolving towards a steady state attractor in physical systems as diverse as fluids, chemical reactions and condensed matter systems. Here we…
We explore the transition from order to chaos for the Bohmian trajectories of a simple quantum system corresponding to the superposition of three stationary states in a 2D harmonic well with incommensurable frequencies. We study in…