Propagation of rays in 2D and 3D waveguides: a stability analysis with Lyapunov and Reversibility fast indicators

Microscopic and Macroscopic Rayleigh-Benard Flows : Continuum and Particle Simulations, Turbulence, Fluctuations, Time Reversibility, and Lyapunov Instability

We discuss the irreversibility, nonlocality, and fluctuations, as well as the Lyapunov and hydrodynamic instabilities characterizing atomistic, smooth-particle, and finite-difference solutions of the two-dimensional Rayleigh-Bénard problem. To speed up the numerical analysis we control the time-dependence of the Rayleigh number so as to include many distinct flow morphologies in a single simulation. The relatively simple nature of these computational algorithms and the richness of the results they can yield make such studies and their interpretation particularly well suited to graduate-level r…

Lyapunov 与可逆性误差不变量指标

Lyapunov and Reversibility error invariant indicators

本文提出推广 Lyapunov Error 与 Reversibility Error 为对初始条件不变的高阶指标集合，利用协方差矩阵迹与行列式刻画轨道扰动演化，并在哈密顿系统中验证其准确性与可靠性。

Loschmidt echo in quantum maps: the elusive nature of the Lyapunov regime

The Loschmidt echo is a measure of the stability and reversibility of quantum evolution under perturbations of the Hamiltonian. One of the expected and most relevant characteristics of this quantity for chaotic systems is an exponential decay with a perturbation independent decay rate given by the classical Lyapunov exponent. However, a non-uniform decay -- instead of the Lyapunov regime -- has been reported in several systems. In this work we find an analytical semiclassical expression for the averaged fidelity amplitude that can be related directly to the anomalous -- unexpected-- behaviour …