Sensitivity to perturbations in a quantum chaotic billiard

Details Sensitivity to perturbations in a quantum chaotic billiard Sensitivity to perturbations in a quantum chaotic billiard

2001-11-22

arxiv.org/abs/nlin/0111051v2

Phys. Review E 65, 055206(R) 2002

Nonlinear Sciences

Chaotic Dynamics

Significantly revised version. To appear in Physical Review E Rapid Communications

Scientific paper

10.1103/PhysRevE.65.055206

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 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 $\Gamma$ to Lyapunov decay. We find that, challenging the analytic interpretation, these conjetures are valid even beyond the expected range.

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