Complexity in parametric Bose-Hubbard Hamiltonians and structural   analysis of eigenstates
  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. 
Moritz Hiller, Tsampikos Kottos, and T. Geisel