Algebraic fidelity decay for local perturbations

Details Algebraic fidelity decay for local perturbations Algebraic fidelity decay for local perturbations

2007-11-27

arxiv.org/abs/0711.4258v2

PRL 100, 124101 (2008)

Physics

Quantum Physics

4 pages, 5 figures

Scientific paper

10.1103/PhysRevLett.100.124101

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.

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