Fidelity in Quasi-1D Systems as a Probe for Anderson Localization

We analyze the echo dynamics in quasi-one-dimensional random media to investigate how the transition from localization to delocalization is encoded in its temporal decay properties. Our analysis extends from the standard perturbative regime corresponding to small perturbations (with respect to the mean level spacing) in the echo dynamics, out to the Wigner decay regime. On the theoretical side, our results rely on a banded random matrix modeling, and show in the localized regime under small perturbations a novel decay of the fidelity (Loschmidt echo), differing from the typical Gaussian decay seen within both diffusive and chaotic systems. For larger perturbation strengths, typical Wigner exponential decays are observed. Scattering echo measurements are performed experimentally within a quasi-1D microwave cavity randomly populated with point-like scatterers. Agreements are observed between experiments, numerics, and theoretical predictions.