Quantum thermalization and the route to ergodicity

We consider a minimal Bose-Hubbard model for quantum thermalization of coupled chaotic subsystems. The route toward ergodicity is explored as a function of the coupling strength. The results are contrasted with the predictions of standard random matrix theory and the eigenstates thermalization hypothesis. We highlight a coupling regime of disparity between the spectral statistics that indicates chaos and ergodicity measures that indicate lack of eigenstate thermalization. The analysis involves a revision of the energy-shell concept, in a way that is consistent but independent of the semiclassical perspective.