Algebraic fidelity decay for local perturbations

Abstract

From a reflection measurement in a rectangular microwave billiard with randomly distributed scatterers the scattering and the ordinary fidelity was studied. The position of one of the scatterers is the perturbation parameter. Such perturbations can be considered as {\em local} since wave functions are influenced only locally, in contrast to, e. g., the situation where the fidelity decay is caused by the shift of one billiard wall. Using the random-plane-wave conjecture, an analytic expression for the fidelity decay due to the shift of one scatterer has been obtained, yielding an algebraic $1/t$ decay for long times. A perfect agreement between experiment and theory has been found, including a predicted scaling behavior concerning the dependence of the fidelity decay on the shift distance. The only free parameter has been determined independently from the variance of the level velocities.

4 pages, 5 figures

References in corpus (3)

• Dynamics of Loschmidt echoes and fidelity decay
• Anomalous power law of quantum reversibility for classically regular dynamics
• Universality of Parametric Spectral Correlations: Local versus Extended Perturbing Potentials

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• Lyapunov decay in quantum irreversibility
• Scattering approach to fidelity decay in closed systems and parametric level correlations