Some such phenomena resisting the tendency to thermalize include (see, e.g., a quantum scar):
* Conventional quantum scars, which refer to eigenstates with enhanced probability density along unstable periodic orbits much higher than one would intuitively predict from classical mechanics.
* Perturbation-induced quantum scarring: despite the similarity in appearance to conventional scarring, these scars have a novel underlying mechanism stemming from the combined effect of nearly-degenerate states and spatially localized perturbations, and they can be employed to propagate quantum wave packets in a disordered quantum dot with high fidelity.
* Many-body quantum scars.
*Many-body localisation (MBL), quantum many-body systems retaining memory of their initial condition in local observables for arbitrary amounts of time.
Other systems that resist thermalisation and are better understood are quantum integrable systems and systems with dynamical symmetries.