Abstract
We investigate thermalization and the quantum-classical correspondence in the collective Bose-Hubbard model, focusing on the four-site case. Our analysis of the classical phase-space structure and its excited-state quantum phase transitions leads us to three dynamical regimes: symmetry-breaking low-energy states, an intermediate region where quantum and classical equilibrium states markedly disagree, and a high-energy regime with restored correspondence. The observed classical intermittency above the first excited-state quantum phase transition contrasts with quantum dynamics, which remains trapped in symmetry-breaking sectors despite the existence of a classically connected phase. This mismatch originates from the population of imbalance-carrying eigenstates and persists even for relatively large number of particles. Our results reveal unexpectedly slow convergence to the classical limit, signaling robust finite-size effects in collective many-body dynamics.