Characterization of hybrid quantum eigenstates in systems with mixed classical phase space

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 quasichaotic 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.