Bifurcations in resonance widths of an open Bose-Hubbard dimer

We investigate the structure of resonance widths of a Bose-Hubbard dimer with intersite hopping amplitude k, which is coupled to a continuum at one of the sites with strength gamma. Using an effective non-Hermitian Hamiltonian formalism, we show that by varying the on-site interaction term chi the resonances undergo consequent bifurcations. For Lambda=k/gamma >= 0.5, the bifurcation points follow a scaling law (chi) over tilde (m)equivalent to chi N-m/k=f(Lambda)(m-0.5/Lambda), where N is the number of bosons. For the function f(Lambda) two different Lambda dependences are found around the minimum and maximum bifurcation points.