Triangular Bose-Hubbard trimer as a minimal model for a superfluid circuit

The triangular Bose-Hubbard trimer is topologically the minimal model for a BEC superfluid circuit. As a dynamical system of two coupled freedoms it has mixed phase space with chaotic dynamics. We employ a semiclassical perspective to study triangular trimer physics beyond the conventional picture of the superfluid-to-insulator transition. From the analysis of the Peierls-Nabarro energy landscape, we deduce the various regimes in the (Ω,u) parameter space, where u is the interaction and Ω is the superfluid rotation-velocity. We thus characterize the superfluid stability and chaoticity of the many-body eigenstates throughout the Hilbert space.