Lack of thermalization for integrability-breaking impurities

We investigate the effects of localized integrability-breaking perturbations on the large times dynamics of thermodynamic quantum and classical systems. In particular, we suddenly activate an impurity which breaks the integrability of an otherwise homogeneous system. We focus on the large times dynamics and on the thermalization properties of the impurity, which is shown to have mere perturbative effects even at infinite times, thus preventing thermalization. This is in clear contrast with homogeneous integrability-breaking terms, which display the prethermalization paradigm and are expected to eventually cause thermalization, no matter the weakness of the integrability-breaking term. Analytic quantitative results are obtained in the case where the bulk Hamiltonian is free and the impurity interacting.