Related papers: Speed limits on classical chaos
We prove that two well-known measures of information are interrelated in interesting and useful ways when applied to nonequilibrium circumstances. A nontrivial form of the lower bound for the Fisher information measure is derived in…
It is shown that the vacuum state of weakly interacting quantum field theories can be described, in the Heisenberg picture, as a linear combination of randomly distributed incoherent paths that obey classical equations of motion with…
A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. A Coulomb friction force applies linear and angular forces…
The search for universal laws that help establish a relationship between dynamics and computation is driven by recent expansionist initiatives in biologically inspired computing. A general setting to understand both such dynamics and…
Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final…
According to the standard model of cosmology, the arrangement of matter in the cosmos on scales much larger than galaxies is entirely specified by the initial conditions laid down during inflation. But zooming in by dozens of orders of…
An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential…
The quantum and classical dynamics of particles kicked by a gaussian attractive potential are studied. Classically, it is an open mixed system (the motion in some parts of the phase space is chaotic, and in some parts it is regular). The…
In Physics, we have laws that determine the time evolution of a given physical system, depending on its parameters and its initial conditions. When we have multi-stable systems, many attractors coexist so that their basins of attraction…
We study how spatiotemporal chaos in dynamical systems can be controlled by stochastically returning them to their initial conditions. Focusing on discrete nonlinear maps, we analyze how key measures of chaos -- the Lyapunov exponent and…
Non-deterministic chaos is a new dynamical paradigm where a non-deterministic system is influenced by random perturbations to produce the appearance of complexity. The non-determinism is envisioned to occur only at a single point in phase…
We study the limitations for defining spatial and temporal intervals when the only available reference frame is a single composite quantum system, whose internal degrees of freedom serve as a temporal reference, a clock, and whose center of…
We study the minimum time related to the quantum speed limit that characterizes the evolution of an open quantum system with the help of a simple model in the short and long time limits. We compare in particular the situation corresponding…
We investigate the sensitivity of quantum systems that are chaotic in a classical limit, to small perturbations of their equations of motion. This sensitivity, originally studied in the context of defining quantum chaos, is relevant to…
Complex physical systems are unavoidably subjected to external environments not accounted for in the set of differential equations that models them. The resulting perturbations are standardly represented by noise terms. We derive conditions…
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…
From a kinematical point of view, the geometrical information of hamiltonian chaos is given by the (un)stable directions, while the dynamical information is given by the Lyapunov exponents. The finite time Lyapunov exponents are of…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
We discuss our recent study of local quantum mechanical uncertainty relations in quantum many body systems. These lead to fundamental bounds for quantities such as the speed, acceleration, relaxation times, spatial gradients and the…
A rich variety of non-equilibrium dynamical phenomena and processes unambiguously calls for the development of general numerical techniques to probe and estimate a complex interplay between spatial and temporal degrees of freedom in…