  We consider a family of chaotic Bose-Hubbard Hamiltonians (BHH) parameterized
by the coupling strength $k$ between neighboring sites. As $k$ increases the
eigenstates undergo changes, reflected in the structure of the Local Density of
States. We analyze these changes, both numerically and analytically, using
perturbative and semiclassical methods. Although our focus is on the quantum
trimer, the presented methodology is applicable for the analysis of longer
lattices as well.
