Quantum thermalization and the route to ergodicity

Abstract: We consider a minimal model for quantum thermalization of coupled chaotic subsystems. The route towards ergodicity is explored as a function of the coupling strength. The results are contrasted with the predictions of standard Random Matrix Theory (RMT) and the Eigenstates Thermalization Hypothesis (ETH). We highlight a coupling regime of disparity between the spectral statistics that indicates chaos, and ergodicity measures that indicate lack of ETH thermalization. The analysis involves a revision of the energy shell concept, in a way that is consistent but independent of the semiclassical perspective.