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Sensitivity to perturbations in a quantum chaotic billiard

Diego A. Wisniacki·Eduardo Vergini·Horacio M. Pastawski·Fernando M. Cucchietti
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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 $Γ$ of the local density of states and the Lyapunov exponent. As the perturbation strength is increased one obtains a cross-over 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 cross over from $Γ$ to Lyapunov decay. We find that, challenging the analytic interpretation, these conjetures are valid even beyond the expected range.

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Diego A. Wisniacki, Eduardo Vergini, Horacio M. Pastawski, Fernando M. Cucchietti. 2002-04-04. Sensitivity to perturbations in a quantum chaotic billiard. https://doi.org/10.1103/physreve.65.055206

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