Probing Localization in Scattering Systems via Fidelity

Using scattering measurements from a microwave cavity filled with randomly distributed scatterers, we evaluate the scattering fidelity. We show that depending on the degree of localization inside the sample, the fidelity decay deviates from ``traditional'' Gaussian law, applied in the case of diffusive/chaotic cavities when small perturbations are involved. We instead show that for small displacements of one of the walls of the cavity, the fidelity decays in a novel way that reflects the degree of localization (or randomness) inside the cavity. The outcome of the experimental measurements are explained on the basis of a parametric Banded Random Matrix modeling which incoorporates localization phenomena. The theoretical results are in good agreement with those of the experiment.