Probing Complex Dynamics via Loschmidt Echoes

This dissertation investigates echo dynamics (Loschmidt Echo) due to small perturbations, in the framework of disordered media where Anderson localization is the dominant mechanism dictating the transport. Various temporal decay laws of the Loschmidt Echo (LE) were identified and shown to accurately probe the diffusive, localized, or even critical nature of the transport. Our theory, based on Random Matrix Theory modeling, agrees perfectly with scattering echo experiments (that we have recently proposed and performed) on a quasi-one-dimensional microwave cavity filled with randomly distributed scatterers.