  Generic low-dimensional Hamiltonian systems feature a structured, mixed
classical phase-space. The traditional Percival classification of quantum
spectra into regular states supported by quasi-integrable regions and irregular
states supported by quasi-chaotic regions turns out to be insufficient to
capture the richness of the Hilbert space. Berry's conjecture and the
eigenstate thermalization hypothesis are not applicable and quantum effects
such as tunneling, scarring, and localization, do not obey the standard
paradigms. We demonstrate these statements for a prototype Bose-Hubbard model.
We highlight the hybridization of chaotic and regular regions from opposing
perspectives of ergodicity and localization.
