title: Sensitivity to perturbations in a quantum chaotic billiard.
abstract: The Loschmidt echo (LE) measures the ability of a system to return to the initial state after a forward quantum evolution followed by a backward perturbed one. It has been conjectured that the echo of a classically chaotic system decays exponentially, with a decay rate given by the minimum between the width Gamma of the local density of states and the Lyapunov exponent. As the perturbation strength is increased one obtains a crossover between both regimes. These predictions are based on situations where the Fermi golden rule (FGR) is valid. By considering a paradigmatic fully chaotic system, the Bunimovich stadium billiard, with a perturbation in a regime for which the FGR manifestly does not work, we find a crossover from Gamma to Lyapunov decay. We find that, challenging the analytic interpretation, these conjectures are valid even beyond the expected range.
authors.affiliation: Departamento de Física, Comisión Nacional de Energía Atómica, Avenida Libertador 8250, 1429 Buenos Aires, Argentina.
authors.forename: Diego A
authors.initials: DA
authors.lastname: Wisniacki
authors.forename: Eduardo G
authors.initials: EG
authors.lastname: Vergini
authors.forename: Horacio M
authors.initials: HM
authors.lastname: Pastawski
authors.forename: Fernando M
authors.initials: FM
authors.lastname: Cucchietti