  We consider the Bose-Hubbard model describing attractive bosonic particles
hopping across the sites of a translation-invariant lattice, and compare the
relevant ground-state properties with those of the corresponding
symmetry-breaking semiclassical nonlinear theory. The introduction of a
suitable measure allows us to highlight many correspondences between the
nonlinear theory and the inherently linear quantum theory, characterized by the
well-known self-trapping phenomenon. In particular we demonstrate that the
localization properties and bifurcation pattern of the semiclassical
ground-state can be clearly recognized at the quantum level. Our analysis
highlights a finite-number effect.
