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 γ. Using an effective non-Hermitian Hamiltonian formalism, we show that by varying the on-site interaction term χ the resonances undergo consequent bifurcations. For Λ=k∕γ0.5, the bifurcation points follow a scaling law ̃ \~χₘ≡χₘN∕k=f_Λ(m-0.5∕Λ), where N is the number of bosons. For the function f_Λ two different Λ dependences are found around the minimum and maximum bifurcation points.