title: Lyapunov decay in quantum irreversibility.
abstract: 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.
authors.affiliation: Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), CONICET-UNMdP, Mar del Plata, Argentina Consejo Nacional de Investigaciones Científicas y Tecnológicas (CONICET), Buenos Aires, Argentina nacho.garcia.mata@gmail.com.
authors.forename: Ignacio
authors.identifier: http://orcid.org/0000-0002-6965-2977
authors.initials: I
authors.lastname: García-Mata
authors.affiliation: Departamento de Física 'J. J. Giambiagi' and IFIBA, FCEyN, Universidad de Buenos Aires, Buenos Aires 1428, Argentina.
authors.forename: Augusto J
authors.initials: AJ
authors.lastname: Roncaglia
authors.affiliation: Departamento de Física 'J. J. Giambiagi' and IFIBA, FCEyN, Universidad de Buenos Aires, Buenos Aires 1428, Argentina.
authors.forename: Diego A
authors.initials: DA
authors.lastname: Wisniacki
keywords: foundations of quantum mechanics; irreversibility; quantum chaos