Scattering approach to fidelity decay in closed systems and parametric level correlations

TL;DR

This paper extends the scattering approach to predict fidelity decay in closed systems under various perturbations, deriving new analytical expressions and validating them with microwave experiment data.

Contribution

It introduces a generalized analytical framework for fidelity decay and parametric level correlations applicable to arbitrary Hermitian perturbations in closed systems.

Findings

Re-derived known results for global perturbations.

Derived exact expression for moving S-wave scatterer perturbation.

Validated theoretical predictions with microwave experiment data.

Abstract

This paper is based on recent work which provided an exact analytical description of scattering fidelity experiments with a microwave cavity under the variation of an antenna coupling [K\"ober et al., Phys. Rev. E 82, 036207 (2010)]. It is shown that this description can also be used to predict the decay of the fidelity amplitude for arbitrary Hermitian perturbations of a closed system. Two applications are presented: First, the known result for global perturbations is re-derived, and second, the exact analytical expression for the perturbation due to a moving S-wave scatterer is worked out. The latter is compared to measured data from microwave experiments, which have been reported some time ago. Finally, we generalize an important relation between fidelity decay and parametric level correlations to arbitrary perturbations.