Two-exciton bound state quantum self-trapping in an extended star graph

An attractive Bose-Hubbard model is applied for describing quantum self-trapping in an extended star graph. In the strong coupling limit and when two excitons are created on the core of the star, the dynamics is dominated by pair states whose properties are governed by the branch number N. When N = 2, the star reduces to a linear chain so that the energy does not self-localize. Conversely, when N ≥ 3, restructuring of the eigenstates arises and a low-energy state occurs describing a pair localized on the core of the star. Preferentially excited, this localized state gives rise to quantum self-trapping of the energy, a process that intensifies as N increases.