Quantum self-trapping on a star graph.

The attractive Bose-Hubbard model is applied for describing the two-exciton dynamics in a nonlinear quantum star graph. When the excitons are created on the core of the star, it is shown that the interplay between the complex architecture of the network and the nonlinearity favors the occurrence of a real quantum self-trapping. Quite weak in the small nonlinearity limit, this self-localization is enhanced as the nonlinearity increases. This feature originates in the restructuring of the two-exciton eigenstates whose localized nature intensifies with the nonlinearity. Nevertheless, the quantum self-trapping is never complete since it is impossible to localize the entire exciton density, even in the strong nonlinearity limit.