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 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 $\mathrm{\Lambda }=k\mathrm{/}\gamma \ge 0.5$, the bifurcation points follow a scaling law ${\tilde \chi}n \equiv \chi_n N/k = f{\Lambda}(n-0.5/\Lambda)$,where$N$ is the number of bosons. For the function $f_{\mathrm{\Lambda }}$ two different $\mathrm{\Lambda }$ dependences are found around the minimum and the maximum bifurcation point.