2015/12/14 by Ignacio García-Mata, Ignacio Garcia-Mata, Augusto J. Roncaglia +1
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Chaotic #Classical mechanics #Dynamical billiards #Hilbert space #Lyapunov exponent #Lyapunov function #Mathematics #Nonlinear system #Perturbation (astronomy) #Physics #Quantum #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum many-body systems #Quantum mechanics #Statistical physics #Universality (dynamical systems) #nlin.CD #quant-ph
paper · pdf · doi:10.1098/rsta.2015.0157
published as Phil. Trans. R. Soc. A 374: 20150157 (2016) · 8 pages, 6 figures. Accepted in Phil. Trans. R. Soc. A
arxiv created 2015/12/14 · arxiv updated 2016/04/18 · openalex publication_date 2016/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Loschmidt echo--also known as fidelity--is a very useful tool to study irreversibility in quantum mechanics due to perturbations or imperfections. Many different regimes, as a function of time and strength of the perturbation, have been identified. For chaotic systems, there is a range of perturbation strengths where the decay of the Loschmidt echo is perturbation independent, and given by the classical Lyapunov exponent. But observation of the Lyapunov decay depends strongly on the type of initial state upon which an average is carried out. This dependence can be removed by averaging the fidelity over the Haar measure, and the Lyapunov regime is recovered, as has been shown for quantum maps. In this work, we introduce an analogous quantity for systems with infinite dimensional Hilbert space, in particular the quantum stadium billiard, and we show clearly the universality of the Lyapunov regime.