orrelation function with a complex effective transmission coefficient \[Eq. (\[eq:Teff\])\], thus expressing coupling fidelity in terms of a modified VWZ integral. This theory holds for an arbitrary number of channels and describes the experimental coupling fidelity results well. It would be interesting to investigate, whether it is possible to relate coupling fidelity obtained via the VWZ ansatz to an approximation using the random plane wave conjecture, as used to explain the local fidelity [@hoeh08a].

We have found two additional important result. First, a smooth variation of the coupling, e.g. by varying the coupling to an attached wave guide will not easily yield the information about the effect of coupling to the continuum on the scattering fidelity. Each geometric variation will give rise to both a change of coupling and internal scattering properties, thus screening the purely external effect, as is also discussed in Appendix \[app:Exp\].

Second, we have included closed channels within the description of VWZ. The speed of the fidelity decay for the open-end and hard-wall reflection oscillates with frequency due to the corresponding variation of the phase with frequency. An important relation (\[eq:s15\]) between the coupling constants of the antenna terminations has been established, enabling us to connect the results found for the closed channel ($\lambda_{\rm oe}$, $\lambda_{\rm hw}$) to those for the open channel ($\lambda_{50\Omega}$). In all cases the fidelity decay for at least one of the reflecting antennas is faster than for the open channel, showing the strong influence of the imaginary part on the coupling constant $\lambda$.

One of us (D.V.S.) is grateful to I. Smolyarenko for useful discussions of the results. We would like to acknowledge the generous hospitality of CIC (Cuernavaca, Mexico) during our stay there at the program RMT-MEX09, where this work has been partly completed. The experiments have been founded by the Deutsche Forschungsgemeinschaft via the research group 760 “Scatt