Bifurcations in Resonance Widths of an Open Bose-Hubbard Dimer

Abstract

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 $\Lambda =k/\gamma \ge 0.5$, 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 $f_{\Lambda }$ two different $\Lambda$ dependences are found around the minimum and the maximum bifurcation point.

4 pages, 3 figures

References in corpus (1)

• Is the concept of the non-Hermitian effective Hamiltonian relevant in the case of potential scattering?

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